Region | Standard | Description | Level | |
---|---|---|---|---|

Alabama | K.CC.1 | Students will: Count to 100 by ones and by tens. | Kindergarten | |

Alabama | K.CC.2 | Students will: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten | |

Alabama | K.CC.3 | Students will: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten | |

Alabama | K.CC.4 | Students will: Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten | |

Alabama | K.CC.5 | Students will: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten | |

Alabama | K.CC.6 | Students will: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten | |

Alabama | K.CC.7 | Students will: Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten | |

Alabama | K.G.17 | Students will: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten | |

Alabama | K.G.18 | Students will: Correctly name shapes regardless of their orientations or overall size. | Kindergarten | |

Alabama | K.G.19 | Students will: Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten | |

Alabama | K.G.20 | Students will: Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices or “corners”), and other attributes (e.g., having sides of equal length). | Kindergarten | |

Alabama | K.G.21 | Students will: Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. | Kindergarten | |

Alabama | K.G.22 | Students will: Compose simple shapes to form larger shapes. | Kindergarten | |

Alabama | K.MD.14 | Students will: Describe measurable attributes of objects such as length or weight. Describe several measurable attributes of a single object. | Kindergarten | |

Alabama | K.MD.15 | Students will: Directly compare two objects, with a measurable attribute in common, to see which object has “more of” or “less of” the attribute, and describe the difference. | Kindergarten | |

Alabama | K.MD.16 | Students will: Classify objects into given categories; count the number of objects in each category, and sort the categories by count. | Kindergarten | |

Alabama | K.NBT.13 | Students will: Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten | |

Alabama | K.OA.8 | Students will: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten | |

Alabama | K.OA.9 | Students will: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten | |

Alabama | K.OA.10 | Students will: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten | |

Alabama | K.OA.11 | Students will: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten | |

Alabama | K.OA.12 | Students will: Fluently add and subtract within 5. | Kindergarten | |

Alabama | 1.G.19 | Students will: Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 | |

Alabama | 1.G.20 | Students will: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 | |

Alabama | 1.G.21 | Students will: Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 | |

Alabama | 1.MD.15 | Students will: Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 | |

Alabama | 1.MD.16 | Students will: Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 | |

Alabama | 1.MD.17 | Students will: Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 | |

Alabama | 1.MD.18 | Students will: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 | |

Alabama | 1.NBT.9 | Students will: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 | |

Alabama | 1.NBT.10 | Students will: Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 | |

Alabama | 1.NBT.11 | Students will: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 | |

Alabama | 1.NBT.12 | Students will: Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 | |

Alabama | 1.NBT.13 | Students will: Given a two-digit number, mentally find 10 more or 10 less than the number without having to count; explain the reasoning used. | Grade 1 | |

Alabama | 1.NBT.14 | Students will: Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. | Grade 1 | |

Alabama | 1.OA.1 | Students will: Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 | |

Alabama | 1.OA.2 | Students will: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 | |

Alabama | 1.OA.3 | Students will: Apply properties of operations as strategies to add and subtract. | Grade 1 | |

Alabama | 1.OA.4 | Students will: Understand subtraction as an unknown-addend problem. | Grade 1 | |

Alabama | 1.OA.5 | Students will: Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 | |

Alabama | 1.OA.6 | Students will: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 − 4 = 13 − 3 − 1 = 10 − 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 − 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 | |

Alabama | 1.OA.7 | Students will: Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 | |

Alabama | 1.OA.8 | Students will: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 | |

Alabama | 2.G.24 | Students will: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 | |

Alabama | 2.G.25 | Students will: Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them. | Grade 2 | |

Alabama | 2.G.26 | Students will: Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 | |

Alabama | 2.MD.14 | Students will: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 | |

Alabama | 2.MD.15 | Students will: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 | |

Alabama | 2.MD.16 | Students will: Estimate lengths using units of inches, feet, centimeters, and meters. | Grade 2 | |

Alabama | 2.MD.17 | Students will: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 | |

Alabama | 2.MD.18 | Students will: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 | |

Alabama | 2.MD.19 | Students will: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram. | Grade 2 | |

Alabama | 2.MD.20 | Students will: Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 | |

Alabama | 2.MD.21 | Students will: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 | |

Alabama | 2.MD.22 | Students will: Generate measurement data by measuring lengths of several objects to the nearest whole unit or by making repeated measurements of the same object. Show the measurements by making a line plot where the horizontal scale is marked off in whole-number units. | Grade 2 | |

Alabama | 2.MD.23 | Students will: Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 | |

Alabama | 2.NBT.5 | Students will: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 | |

Alabama | 2.NBT.6 | Students will: Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 | |

Alabama | 2.NBT.7 | Students will: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 | |

Alabama | 2.NBT.8 | Students will: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons. | Grade 2 | |

Alabama | 2.NBT.9 | Students will: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 | |

Alabama | 2.NBT.10 | Students will: Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 | |

Alabama | 2.NBT.11 | Students will: Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 | |

Alabama | 2.NBT.12 | Students will: Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 | |

Alabama | 2.NBT.13 | Students will: Explain why addition and subtraction strategies work, using place value and the properties of operations. | Grade 2 | |

Alabama | 2.OA.1 | Students will: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 | |

Alabama | 2.OA.2 | Students will: Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 | |

Alabama | 2.OA.3 | Students will: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 | |

Alabama | 2.OA.4 | Students will: Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 | |

Alabama | 3.G.24 | Students will: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 | |

Alabama | 3.G.25 | Students will: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 | |

Alabama | 3.MD.16 | Students will: Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 | |

Alabama | 3.MD.17 | Students will: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 | |

Alabama | 3.MD.18 | Students will: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 | |

Alabama | 3.MD.19 | Students will: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units–whole numbers, halves, or quarters. | Grade 3 | |

Alabama | 3.MD.20 | Students will: Recognize area as an attribute of plane figures, and understand concepts of area measurement. | Grade 3 | |

Alabama | 3.MD.21 | Students will: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 | |

Alabama | 3.MD.22 | Students will: Relate area to the operations of multiplication and addition. | Grade 3 | |

Alabama | 3.MD.23 | Students will: Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 | |

Alabama | 3.NBT.10 | Students will: Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 | |

Alabama | 3.NBT.11 | Students will: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 | |

Alabama | 3.NBT.12 | Students will: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 | |

Alabama | 3.NF.13 | Students will: Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts and size 1/𝘣. | Grade 3 | |

Alabama | 3.NF.14 | Students will: Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 | |

Alabama | 3.NF.15 | Students will: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 | |

Alabama | 3.OA.1 | Students will: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 | |

Alabama | 3.OA.2 | Students will: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 | |

Alabama | 3.OA.3 | Students will: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 | |

Alabama | 3.OA.4 | Students will: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 | |

Alabama | 3.OA.5 | Students will: Apply properties of operations as strategies to multiply and divide. | Grade 3 | |

Alabama | 3.OA.6 | Students will: Understand division as an unknown-factor problem. | Grade 3 | |

Alabama | 3.OA.7 | Students will: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 | |

Alabama | 3.OA.8 | Students will: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 | |

Alabama | 3.OA.9 | Students will: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 | |

Alabama | 4.G.26 | Students will: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 | |

Alabama | 4.G.27 | Students will: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 | |

Alabama | 4.G.28 | Students will: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 | |

Alabama | 4.MD.19 | Students will: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 | |

Alabama | 4.MD.20 | Students will: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 | |

Alabama | 4.MD.21 | Students will: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. | Grade 4 | |

Alabama | 4.MD.22 | Students will: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 | |

Alabama | 4.MD.23 | Students will: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 | |

Alabama | 4.MD.24 | Students will: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 | |

Alabama | 4.MD.25 | Students will: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 | |

Alabama | 4.NBT.6 | Students will: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 | |

Alabama | 4.NBT.7 | Students will: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 | |

Alabama | 4.NBT.8 | Students will: Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 | |

Alabama | 4.NBT.9 | Students will: Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 | |

Alabama | 4.NBT.10 | Students will: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Alabama | 4.NBT.11 | Students will: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Alabama | 4.NF.12 | Students will: Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 | |

Alabama | 4.NF.13 | Students will: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 | |

Alabama | 4.NF.14 | Students will: Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 | |

Alabama | 4.NF.15 | Students will: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 | |

Alabama | 4.NF.16 | Students will: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 | |

Alabama | 4.NF.17 | Students will: Use decimal notation for fractions with denominators 10 or 100. | Grade 4 | |

Alabama | 4.NF.18 | Students will: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 | |

Alabama | 4.OA.1 | Students will: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 | |

Alabama | 4.OA.2 | Students will: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 | |

Alabama | 4.OA.3 | Students will: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 | |

Alabama | 4.OA.4 | Students will: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 | |

Alabama | 4.OA.5 | Students will: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 | |

Alabama | 5.G.23 | Students will: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 | |

Alabama | 5.G.24 | Students will: Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 | |

Alabama | 5.G.25 | Students will: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 | |

Alabama | 5.G.26 | Students will: Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 | |

Alabama | 5.MD.18 | Students will: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, real-world problems. | Grade 5 | |

Alabama | 5.MD.19 | Students will: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 | |

Alabama | 5.MD.20 | Students will: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. | Grade 5 | |

Alabama | 5.MD.21 | Students will: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 | |

Alabama | 5.MD.22 | Students will: Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 | |

Alabama | 5.NBT.4 | Students will: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 | |

Alabama | 5.NBT.5 | Students will: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 | |

Alabama | 5.NBT.6 | Students will: Read, write, and compare decimals to thousandths. | Grade 5 | |

Alabama | 5.NBT.7 | Students will: Use place value understanding to round decimals to any place. | Grade 5 | |

Alabama | 5.NBT.8 | Students will: Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 | |

Alabama | 5.NBT.9 | Students will: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 | |

Alabama | 5.NBT.10 | Students will: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. | Grade 5 | |

Alabama | 5.NF.11 | Students will: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 | |

Alabama | 5.NF.12 | Students will: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. | Grade 5 | |

Alabama | 5.NF.13 | Students will: Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 | |

Alabama | 5.NF.14 | Students will: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 | |

Alabama | 5.NF.15 | Students will: Interpret multiplication as scaling (resizing). | Grade 5 | |

Alabama | 5.NF.16 | Students will: Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 | |

Alabama | 5.NF.17 | Students will: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 | |

Alabama | 5.OA.1 | Students will: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 | |

Alabama | 5.OA.2 | Students will: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 | |

Alabama | 5.OA.3 | Students will: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 | |

Alabama | 6.EE.12 | Students will: Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 | |

Alabama | 6.EE.13 | Students will: Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 | |

Alabama | 6.EE.14 | Students will: Apply the properties of operations to generate equivalent expressions. | Grade 6 | |

Alabama | 6.EE.15 | Students will: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 | |

Alabama | 6.EE.16 | Students will: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 | |

Alabama | 6.EE.17 | Students will: Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. | Grade 6 | |

Alabama | 6.EE.18 | Students will: Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲, and 𝘹 are all nonnegative rational numbers. | Grade 6 | |

Alabama | 6.EE.19 | Students will: Write an inequality of the form 𝘹 > 𝘤 or 𝘹 < 𝘤 to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form 𝘹 > 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 | |

Alabama | 6.EE.20 | Students will: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 | |

Alabama | 6.G.21 | Students will: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Alabama | 6.G.22 | Students will: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭𝘸𝘩 and 𝘝 = 𝐵𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 | |

Alabama | 6.G.23 | Students will: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Alabama | 6.G.24 | Students will: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Alabama | 6.RP.1 | Students will: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. | Grade 6 | |

Alabama | 6.RP.2 | Students will: Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 | |

Alabama | 6.RP.3 | Students will: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 | |

Alabama | 6.SP.25 | Students will: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. | Grade 6 | |

Alabama | 6.SP.26 | Students will: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. | Grade 6 | |

Alabama | 6.SP.27 | Students will: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. | Grade 6 | |

Alabama | 6.SP.28 | Students will: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. | Grade 6 | |

Alabama | 6.SP.29 | Students will: Summarize numerical data sets in relation to their context. | Grade 6 | |

Alabama | 6.NS.4 | Students will: Interpret and compute quotients of fractions, and solve word problems involving division of fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 | |

Alabama | 6.NS.5 | Students will: Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 | |

Alabama | 6.NS.6 | Students will: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 | |

Alabama | 6.NS.7 | Students will: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. | Grade 6 | |

Alabama | 6.NS.8 | Students will: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts explaining the meaning of 0 in each situation. | Grade 6 | |

Alabama | 6.NS.9 | Students will: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 | |

Alabama | 6.NS.10 | Students will: Understand ordering and absolute value of rational numbers. | Grade 6 | |

Alabama | 6.NS.11 | Students will: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 | |

Alabama | 7.EE.7 | Students will: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 | |

Alabama | 7.EE.8 | Students will: Understand that rewriting an expression in different forms in a problem context can shed light on the problem, and how the quantities in it are related. | Grade 7 | |

Alabama | 7.EE.9 | Students will: Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 | |

Alabama | 7.EE.10 | Students will: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 | |

Alabama | 7.G.11 | Students will: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 | |

Alabama | 7.G.12 | Students will: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 | |

Alabama | 7.G.13 | Students will: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 | |

Alabama | 7.G.14 | Students will: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 | |

Alabama | 7.G.15 | Students will: Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 | |

Alabama | 7.G.16 | Students will: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 | |

Alabama | 7.RP.1 | Students will: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. | Grade 7 | |

Alabama | 7.RP.2 | Students will: Recognize and represent proportional relationships between quantities. | Grade 7 | |

Alabama | 7.RP.3 | Students will: Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 | |

Alabama | 7.SP.17 | Students will: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. | Grade 7 | |

Alabama | 7.SP.18 | Students will: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. | Grade 7 | |

Alabama | 7.SP.19 | Students will: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. | Grade 7 | |

Alabama | 7.SP.20 | Students will: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. | Grade 7 | |

Alabama | 7.SP.21 | Students will: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. | Grade 7 | |

Alabama | 7.SP.22 | Students will: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. | Grade 7 | |

Alabama | 7.SP.23 | Students will: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. | Grade 7 | |

Alabama | 7.SP.24 | Students will: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. | Grade 7 | |

Alabama | 7.NS.4 | Students will: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 | |

Alabama | 7.NS.5 | Students will: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 | |

Alabama | 7.NS.6 | Students will: Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 | |

Alabama | 8.EE.3 | Students will: Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 | |

Alabama | 8.EE.4 | Students will: Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 | |

Alabama | 8.EE.5 | Students will: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 | |

Alabama | 8.EE.6 | Students will: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 | |

Alabama | 8.EE.7 | Students will: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 | |

Alabama | 8.EE.8 | Students will: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 | |

Alabama | 8.EE.9 | Students will: Solve linear equations in one variable. | Grade 8 | |

Alabama | 8.EE.10 | Students will: Analyze and solve pairs of simultaneous linear equations. | Grade 8 | |

Alabama | 8.F.11 | Students will: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 | |

Alabama | 8.F.12 | Students will: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 | |

Alabama | 8.F.13 | Students will: Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function whose graph is a straight line; give examples of functions that are not linear. | Grade 8 | |

Alabama | 8.F.14 | Students will: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values. | Grade 8 | |

Alabama | 8.F.15 | Students will: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 | |

Alabama | 8.G.16 | Students will: Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 | |

Alabama | 8.G.17 | Students will: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 | |

Alabama | 8.G.18 | Students will: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 | |

Alabama | 8.G.19 | Students will: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 | |

Alabama | 8.G.20 | Students will: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 | |

Alabama | 8.G.21 | Students will: Explain a proof of the Pythagorean Theorem and its converse. | Grade 8 | |

Alabama | 8.G.22 | Students will: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 | |

Alabama | 8.G.23 | Students will: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 | |

Alabama | 8.G.24 | Students will: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. | Grade 8 | |

Alabama | 8.SP.25 | Students will: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 | |

Alabama | 8.SP.26 | Students will: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 | |

Alabama | 8.SP.27 | Students will: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. | Grade 8 | |

Alabama | 8.SP.28 | Students will: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. | Grade 8 | |

Alabama | 8.NS.1 | Students will: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. | Grade 8 | |

Alabama | 8.NS.2 | Students will: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 | |

Alabama | A-SSE.7 | Students will: Interpret expressions that represent a quantity in terms of its context. | Algebra I | |

Alabama | A-SSE.8 | Students will: Use the structure of an expression to identify ways to rewrite it. | Algebra I | |

Alabama | A-SSE.9 | Students will: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra I | |

Alabama | A-APR.10 | Students will: Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Algebra I | |

Alabama | A-APR.11 | Students will: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. | Algebra I | |

Alabama | A-CED.12 | Students will: Create equations and inequalities in one variable, and use them to solve problems. | Algebra I | |

Alabama | A-CED.13 | Students will: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra I | |

Alabama | A-CED.14 | Students will: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context. | Algebra I | |

Alabama | A-CED.15 | Students will: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Algebra I | |

Alabama | A-REI.16 | Students will: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. | Algebra I | |

Alabama | A-REI.17 | Students will: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Algebra I | |

Alabama | A-REI.18 | Students will: Solve quadratic equations in one variable. | Algebra I | |

Alabama | A-REI.19 | Students will: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | Algebra I | |

Alabama | A-REI.20 | Students will: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | Algebra I | |

Alabama | A-REI.21 | Students will: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | Algebra I | |

Alabama | A-REI.22 | Students will: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). | Algebra I | |

Alabama | A-REI.23 | Students will: Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Algebra I | |

Alabama | A-REI.24 | Students will: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | Algebra I | |

Alabama | F-IF.25 | Students will: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹). | Algebra I | |

Alabama | F-IF.26 | Students will: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra I | |

Alabama | F-IF.27 | Students will: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | Algebra I | |

Alabama | F-IF.28 | Students will: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra I | |

Alabama | F-IF.29 | Students will: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Algebra I | |

Alabama | F-IF.30 | Students will: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | Algebra I | |

Alabama | F-IF.31 | Students will: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra I | |

Alabama | F-IF.32 | Students will: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | Algebra I | |

Alabama | F-IF.33 | Students will: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Algebra I | |

Alabama | F-BF.34 | Students will: Write a function that describes a relationship between two quantities. | Algebra I | |

Alabama | F-BF.35 | Students will: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | Algebra I | |

Alabama | F-BF.36 | Students will: Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. | Algebra I | |

Alabama | F-LE.37 | Students will: Distinguish between situations that can be modeled with linear functions and with exponential functions. | Algebra I | |

Alabama | F-LE.38 | Students will: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | Algebra I | |

Alabama | F-LE.39 | Students will: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | Algebra I | |

Alabama | F-LE.40 | Students will: Interpret the parameters in a linear or exponential function in terms of a context. | Algebra I | |

Alabama | N-RN.1 | Students will: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | Algebra I | |

Alabama | N-RN.2 | Students will: Rewrite expressions involving radicals and rational exponents using the properties of exponents. | Algebra I | |

Alabama | N-RN.3 | Students will: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | Algebra I | |

Alabama | N-Q.4 | Students will: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | Algebra I | |

Alabama | N-Q.5 | Students will: Define appropriate quantities for the purpose of descriptive modeling. | Algebra I | |

Alabama | N-Q.6 | Students will: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | Algebra I | |

Alabama | S-ID.41 | Students will: Represent data with plots on the real number line (dot plots, histograms, and box plots). | Algebra I | |

Alabama | S-ID.42 | Students will: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | Algebra I | |

Alabama | S-ID.43 | Students will: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | Algebra I | |

Alabama | S-ID.44 | Students will: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | Algebra I | |

Alabama | S-ID.45 | Students will: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra I | |

Alabama | S-ID.46 | Students will: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | Algebra I | |

Alabama | S-CP.47 | Students will: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | Algebra I | |

Alabama | G-CO.1 | Students will: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | Geometry | |

Alabama | G-CO.2 | Students will: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | Geometry | |

Alabama | G-CO.3 | Students will: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | Geometry | |

Alabama | G-CO.4 | Students will: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | Geometry | |

Alabama | G-CO.5 | Students will: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. | Geometry | |

Alabama | G-CO.6 | Students will: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. | Geometry | |

Alabama | G-CO.7 | Students will: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. | Geometry | |

Alabama | G-CO.8 | Students will: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | Geometry | |

Alabama | G-CO.9 | Students will: Prove theorems about lines and angles. | Geometry | |

Alabama | G-CO.10 | Students will: Prove theorems about triangles. | Geometry | |

Alabama | G-CO.11 | Students will: Prove theorems about parallelograms. | Geometry | |

Alabama | G-CO.12 | Students will: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). | Geometry | |

Alabama | G-CO.13 | Students will: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | Geometry | |

Alabama | G-SRT.14 | Students will: Verify experimentally the properties of dilations given by a center and a scale factor. | Geometry | |

Alabama | G-SRT.15 | Students will: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. | Geometry | |

Alabama | G-SRT.16 | Students will: Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar. | Geometry | |

Alabama | G-SRT.17 | Students will: Prove theorems about triangles. | Geometry | |

Alabama | G-SRT.18 | Students will: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | Geometry | |

Alabama | G-SRT.19 | Students will: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle leading to definitions of trigonometric ratios for acute angles. | Geometry | |

Alabama | G-SRT.20 | Students will: Explain and use the relationship between the sine and cosine of complementary angles. | Geometry | |

Alabama | G-SRT.21 | Students will: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | Geometry | |

Alabama | G-SRT.22 | Students will: Prove the Law of Sines and the Law of Cosines and use them to solve problems. | Geometry | |

Alabama | G-SRT.23 | Students will: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). | Geometry | |

Alabama | G-C.24 | Students will: Prove that all circles are similar. | Geometry | |

Alabama | G-C.25 | Students will: Identify and describe relationships among inscribed angles, radii, and chords. | Geometry | |

Alabama | G-C.26 | Students will: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | Geometry | |

Alabama | G-C.27 | Students will: Construct a tangent line from a point outside a given circle to the circle. | Geometry | |

Alabama | G-C.28 | Students will: Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. | Geometry | |

Alabama | G-GPE.29 | Students will: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | Geometry | |

Alabama | G-GPE.30 | Students will: Use coordinates to prove simple geometric theorems algebraically. | Geometry | |

Alabama | G-GPE.31 | Students will: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | Geometry | |

Alabama | G-GPE.32 | Students will: Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | Geometry | |

Alabama | G-GPE.33 | Students will: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. | Geometry | |

Alabama | G-GPE.34 | Students will: Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. | Geometry | |

Alabama | G-GMD.35 | Students will: Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. | Geometry | |

Alabama | G-GMD.36 | Students will: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | Geometry | |

Alabama | G-GMD.37 | Students will: Determine the relationship between surface areas of similar figures and volumes of similar figures. | Geometry | |

Alabama | G-GMD.38 | Students will: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | Geometry | |

Alabama | G-MG.39 | Students will: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | Geometry | |

Alabama | G-MG.40 | Students will: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot). | Geometry | |

Alabama | G-MG.41 | Students will: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios). | Geometry | |

Alabama | S-MD.42 | Students will: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Geometry | |

Alabama | S-MD.43 | Students will: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | Geometry | |

Alabama | A-MOD.1 | Students will: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. | Algebraic Connections | |

Alabama | A-MOD.2 | Students will: Solve application-based problems by developing and solving systems of linear equations and inequalities. | Algebraic Connections | |

Alabama | A-MOD.3 | Students will: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. | Algebraic Connections | |

Alabama | A-GRA.4 | Students will: Determine maximum and minimum values of a function using linear programming procedures. | Algebraic Connections | |

Alabama | A-GRA.5 | Students will: Determine approximate rates of change of nonlinear relationships from graphical and numerical data. | Algebraic Connections | |

Alabama | A-GRA.6 | Students will: Use the extreme value of a given quadratic function to solve applied problems. | Algebraic Connections | |

Alabama | A-FIN.7 | Students will: Use analytical, numerical, and graphical methods to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. | Algebraic Connections | |

Alabama | G-MOD.8 | Students will: Determine missing information in an application-based situation using properties of right triangles, including trigonometric ratios and the Pythagorean Theorem. | Algebraic Connections | |

Alabama | G-SYM.9 | Students will: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. | Algebraic Connections | |

Alabama | G-MEA.10 | Students will: Critique measurements in terms of precision, accuracy, and approximate error. | Algebraic Connections | |

Alabama | G-MEA.11 | Students will: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. | Algebraic Connections | |

Alabama | S-GRA.12 | Students will: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. | Algebraic Connections | |

Alabama | A-SSE.12 | Students will: Interpret expressions that represent a quantity in terms of its context. | Algebra II | |

Alabama | A-SSE.13 | Students will: Use the structure of an expression to identify ways to rewrite it. | Algebra II | |

Alabama | A-SSE.14 | Students will: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | Algebra II | |

Alabama | A-APR.15 | Students will: Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Algebra II | |

Alabama | A-APR.16 | Students will: Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹). | Algebra II | |

Alabama | A-APR.17 | Students will: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra II | |

Alabama | A-APR.18 | Students will: Prove polynomial identities and use them to describe numerical relationships. | Algebra II | |

Alabama | A-APR.19 | Students will: Rewrite simple rational expressions in different forms; write 𝘢(𝘹)/𝘣(𝘹) in the form 𝘲(𝘹) + 𝘳(𝘹)/𝘣(𝘹), where 𝘢(𝘹), 𝘣(𝘹), 𝘲(𝘹), and 𝘳(𝘹) are polynomials with the degree of 𝘳(𝘹) less than the degree of 𝘣(𝘹), using inspection, long division, or for the more complicated examples, a computer algebra system. | Algebra II | |

Alabama | A-CED.20 | Students will: Create equations and inequalities in one variable and use them to solve problems. | Algebra II | |

Alabama | A-CED.21 | Students will: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra II | |

Alabama | A-CED.22 | Students will: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. | Algebra II | |

Alabama | A-CED.23 | Students will: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Algebra II | |

Alabama | A-REI.24 | Students will: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | Algebra II | |

Alabama | A-REI.25 | Students will: Recognize when the quadratic formula gives complex solutions, and write them as a ± bi for real numbers a and b. | Algebra II | |

Alabama | A-REI.26 | Students will: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). | Algebra II | |

Alabama | A-REI.27 | Students will: Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Algebra II | |

Alabama | A-CS.28 | Students will: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations. | Algebra II | |

Alabama | F-IF.29 | Students will: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Algebra II | |

Alabama | F-IF.30 | Students will: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra II | |

Alabama | F-IF.31 | Students will: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | Algebra II | |

Alabama | F-IF.32 | Students will: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Algebra II | |

Alabama | F-BF.33 | Students will: Write a function that describes a relationship between two quantities. | Algebra II | |

Alabama | F-BF.34 | Students will: Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Algebra II | |

Alabama | F-BF.35 | Students will: Find inverse functions. | Algebra II | |

Alabama | F-LE.36 | Students will: For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology. | Algebra II | |

Alabama | N-CN.1 | Students will: Know there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 real. | Algebra II | |

Alabama | N-CN.2 | Students will: Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | Algebra II | |

Alabama | N-CN.3 | Students will: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. | Algebra II | |

Alabama | N-CN.4 | Students will: Solve quadratic equations with real coefficients that have complex solutions. | Algebra II | |

Alabama | N-CN.5 | Students will: Extend polynomial identities to the complex numbers. | Algebra II | |

Alabama | N-CN.6 | Students will: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | Algebra II | |

Alabama | N-VM.7 | Students will: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. | Algebra II | |

Alabama | N-VM.8 | Students will: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. | Algebra II | |

Alabama | N-VM.9 | Students will: Add, subtract, and multiply matrices of appropriate dimensions. | Algebra II | |

Alabama | N-VM.10 | Students will: Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. | Algebra II | |

Alabama | N-VM.11 | Students will: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. | Algebra II | |

Alabama | S-MD.37 | Students will: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Algebra II | |

Alabama | S-MD.38 | Students will: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | Algebra II | |

Alabama | S-CP.39 | Students will: Describe events as subsets of a sample space (the set of outcomes), using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). | Algebra II | |

Alabama | S-CP.40 | Students will: Understand the conditional probability of 𝘈 given 𝘉 as 𝘗(𝘈 and 𝘉)/𝘗(𝘉), and interpret independence of 𝘈 and 𝘉 as saying that the conditional probability of 𝘈 given 𝘉 is the same as the probability of 𝘈, and the conditional probability of 𝘉 given 𝘈 is the same as the probability of 𝘉. | Algebra II | |

Alabama | S-CP.41 | Students will: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | Algebra II | |

Alabama | S-CP.42 | Students will: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | Algebra II | |

Alabama | S-CP.43 | Students will: Find the conditional probability of 𝘈 given 𝘉 as the fraction of 𝘉’s outcomes that also belong to 𝘈, and interpret the answer in terms of the model. | Algebra II | |

Alabama | S-CP.44 | Students will: Apply the Addition Rule, 𝘗(𝘈 or 𝘉) = 𝘗(𝘈) + 𝘗(𝘉) – 𝘗(𝘈 and 𝘉), and interpret the answer in terms of the model. | Algebra II | |

Alabama | S-CP.45 | Students will: Apply the general Multiplication Rule in a uniform probability model, 𝘗(𝘈 and 𝘉) = 𝘗(𝘈)𝘗(𝘉|𝘈) = 𝘗(𝘉)𝘗(𝘈|𝘉), and interpret the answer in terms of the model. | Algebra II | |

Alabama | S-CP.46 | Students will: Use permutations and combinations to compute probabilities of compound events and solve problems. | Algebra II | |

Alabama | A-SSE.12 | Students will: Interpret expressions that represent a quantity in terms of its context. | Algebra II With Trigonometry | |

Alabama | A-SSE.13 | Students will: Use the structure of an expression to identify ways to rewrite it. | Algebra II With Trigonometry | |

Alabama | A-SSE.14 | Students will: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | Algebra II With Trigonometry | |

Alabama | A-APR.15 | Students will: Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Algebra II With Trigonometry | |

Alabama | A-APR.16 | Students will: Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹). | Algebra II With Trigonometry | |

Alabama | A-APR.17 | Students will: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra II With Trigonometry | |

Alabama | A-APR.18 | Students will: Prove polynomial identities and use them to describe numerical relationships. | Algebra II With Trigonometry | |

Alabama | A-APR.19 | Students will: Rewrite simple rational expressions in different forms; write 𝘢(𝘹)/𝘣(𝘹) in the form 𝘲(𝘹) + 𝘳(𝘹)/𝘣(𝘹), where 𝘢(𝘹), 𝘣(𝘹), 𝘲(𝘹), and 𝘳(𝘹) are polynomials with the degree of 𝘳(𝘹) less than the degree of 𝘣(𝘹), using inspection, long division, or for the more complicated examples, a computer algebra system. | Algebra II With Trigonometry | |

Alabama | A-CED.20 | Students will: Create equations and inequalities in one variable and use them to solve problems. | Algebra II With Trigonometry | |

Alabama | A-CED.21 | Students will: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra II With Trigonometry | |

Alabama | A-CED.22 | Students will: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. | Algebra II With Trigonometry | |

Alabama | A-CED.23 | Students will: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Algebra II With Trigonometry | |

Alabama | A-REI.24 | Students will: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | Algebra II With Trigonometry | |

Alabama | A-REI.25 | Students will: Recognize when the quadratic formula gives complex solutions, and write them as a ± bi for real numbers a and b. | Algebra II With Trigonometry | |

Alabama | A-REI.26 | Students will: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). | Algebra II With Trigonometry | |

Alabama | A-REI.27 | Students will: Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Algebra II With Trigonometry | |

Alabama | A-CS.28 | Students will: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations. | Algebra II With Trigonometry | |

Alabama | F-IF.29 | Students will: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Algebra II With Trigonometry | |

Alabama | F-IF.30 | Students will: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra II With Trigonometry | |

Alabama | F-IF.31 | Students will: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | Algebra II With Trigonometry | |

Alabama | F-IF.32 | Students will: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Algebra II With Trigonometry | |

Alabama | F-BF.33 | Students will: Write a function that describes a relationship between two quantities. | Algebra II With Trigonometry | |

Alabama | F-BF.34 | Students will: Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Algebra II With Trigonometry | |

Alabama | F-BF.35 | Students will: Find inverse functions. | Algebra II With Trigonometry | |

Alabama | F-LE.36 | Students will: For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology. | Algebra II With Trigonometry | |

Alabama | F-TF.37 | Students will: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | Algebra II With Trigonometry | |

Alabama | F-TF.38 | Students will: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | Algebra II With Trigonometry | |

Alabama | F-TF.39 | Students will: Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions. | Algebra II With Trigonometry | |

Alabama | F-TF.40 | Students will: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. | Algebra II With Trigonometry | |

Alabama | N-CN.1 | Students will: Know there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 real. | Algebra II With Trigonometry | |

Alabama | N-CN.2 | Students will: Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | Algebra II With Trigonometry | |

Alabama | N-CN.3 | Students will: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. | Algebra II With Trigonometry | |

Alabama | N-CN.4 | Students will: Solve quadratic equations with real coefficients that have complex solutions. | Algebra II With Trigonometry | |

Alabama | N-CN.5 | Students will: Extend polynomial identities to the complex numbers. | Algebra II With Trigonometry | |

Alabama | N-CN.6 | Students will: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | Algebra II With Trigonometry | |

Alabama | N-VM.7 | Students will: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. | Algebra II With Trigonometry | |

Alabama | N-VM.8 | Students will: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. | Algebra II With Trigonometry | |

Alabama | N-VM.9 | Students will: Add, subtract, and multiply matrices of appropriate dimensions. | Algebra II With Trigonometry | |

Alabama | N-VM.10 | Students will: Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. | Algebra II With Trigonometry | |

Alabama | N-VM.11 | Students will: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. | Algebra II With Trigonometry | |

Alabama | S-MD.41 | Students will: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Algebra II With Trigonometry | |

Alabama | S-MD.42 | Students will: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | Algebra II With Trigonometry | |

Alabama | S-CP.43 | Students will: Describe events as subsets of a sample space (the set of outcomes), using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). | Algebra II With Trigonometry | |

Alabama | S-CP.44 | Students will: Understand the conditional probability of 𝘈 given 𝘉 as 𝘗(𝘈 and 𝘉)/𝘗(𝘉), and interpret independence of 𝘈 and 𝘉 as saying that the conditional probability of 𝘈 given 𝘉 is the same as the probability of 𝘈, and the conditional probability of 𝘉 given 𝘈 is the same as the probability of 𝘉. | Algebra II With Trigonometry | |

Alabama | S-CP.45 | Students will: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | Algebra II With Trigonometry | |

Alabama | S-CP.46 | Students will: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | Algebra II With Trigonometry | |

Alabama | S-CP.47 | Students will: Find the conditional probability of 𝘈 given 𝘉 as the fraction of 𝘉’s outcomes that also belong to 𝘈, and interpret the answer in terms of the model. | Algebra II With Trigonometry | |

Alabama | S-CP.48 | Students will: Apply the Addition Rule, 𝘗(𝘈 or 𝘉) = 𝘗(𝘈) + 𝘗(𝘉) – 𝘗(𝘈 and 𝘉), and interpret the answer in terms of the model. | Algebra II With Trigonometry | |

Alabama | S-CP.49 | Students will: Apply the general Multiplication Rule in a uniform probability model, 𝘗(𝘈 and 𝘉) = 𝘗(𝘈)𝘗(𝘉|𝘈) = 𝘗(𝘉)𝘗(𝘈|𝘉), and interpret the answer in terms of the model. | Algebra II With Trigonometry | |

Alabama | S-CP.50 | Students will: Use permutations and combinations to compute probabilities of compound events and solve problems. | Algebra II With Trigonometry | |

Alabama | A.7.a | Develop optimal solutions of application-based problems using existing and student-created algorithms. | Discrete Mathematics | |

Alabama | A.8.a | Use shortest path techniques to find optimal shipping routes. | Discrete Mathematics | |

Alabama | A.5.a | Create a Fibonacci sequence when given two initial integers. | Mathematical Investigations | |

Alabama | A.5.b | Investigate Tartaglia’s formula for solving cubic equations. | Mathematical Investigations | |

Alabama | A.7.a | Summarize the significance of René Descartes’ Cartesian coordinate system. | Mathematical Investigations | |

Alabama | A.7.b | Interpret the foundation of analytic geometry with regard to geometric curves and algebraic relationships. | Mathematical Investigations | |

Alabama | G.9.a | Summarize the historical development of perspective in art and architecture. | Mathematical Investigations | |

Alabama | G.10.a | Construct multiple proofs of the Pythagorean Theorem. | Mathematical Investigations | |

Alabama | G.10.b | Solve problems involving figurate numbers, including triangular and pentagonal numbers. | Mathematical Investigations | |

Alabama | N.1.a | Determine relationships among mathematical achievements of ancient peoples, including the Sumerians, Babylonians, Egyptians, Mesopotamians, Chinese, Aztecs, and Incas. | Mathematical Investigations | |

Alabama | N.1.b | Explain origins of the Hindu-Arabic numeration system. | Mathematical Investigations | |

Alabama | N.2.a | Determine lengths of strings necessary to produce harmonic tones as in Pythagorean tuning. | Mathematical Investigations | |

Alabama | N.3.a | Identify transcendental numbers. | Mathematical Investigations | |

Alabama | N.4.a | Analyze contributions to the number system by well-known mathematicians, including Archimedes, John Napier, René Descartes, Sir Isaac Newton, Johann Carl Friedrich Gauss, and Julius Wilhelm Richard Dedekind. | Mathematical Investigations | |

Alabama | A-SSE.12 | Students will: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | Precalculus | |

Alabama | A-APR.13 | Students will: Know and apply the Binomial Theorem for the expansion of (𝘹 + 𝘺)ⁿ in powers of 𝘹 and y for a positive integer 𝘯, where 𝘹 and 𝘺 are any numbers, with coefficients determined, for example, by Pascal’s Triangle. | Precalculus | |

Alabama | A-REI.14 | Students will: Represent a system of linear equations as a single matrix equation in a vector variable. | Precalculus | |

Alabama | A-CS.15 | Students will: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations. | Precalculus | |

Alabama | F-IF.16 | Students will: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Precalculus | |

Alabama | F-IF.17 | Students will: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | Precalculus | |

Alabama | F-IF.18 | Students will: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Precalculus | |

Alabama | F-BF.19 | Students will: Compose functions. | Precalculus | |

Alabama | F-BF.20 | Students will: Determine the inverse of a function and a relation. | Precalculus | |

Alabama | F-BF.21 | Students will: Verify by composition that one function is the inverse of another. | Precalculus | |

Alabama | F-BF.22 | Students will: Read values of an inverse function from a graph or a table, given that the function has an inverse. | Precalculus | |

Alabama | F-BF.23 | Students will: Produce an invertible function from a non-invertible function by restricting the domain. | Precalculus | |

Alabama | F-BF.24 | Students will: Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. | Precalculus | |

Alabama | F-BF.25 | Students will: Compare effects of parameter changes on graphs of transcendental functions. | Precalculus | |

Alabama | F-TF.26 | Students will: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. | Precalculus | |

Alabama | F-TF.27 | Students will: Use the sum, difference, and half-angle identities to find the exact value of a trigonometric function. | Precalculus | |

Alabama | F-TF.28 | Students will: Utilize parametric equations by graphing and by converting to rectangular form. | Precalculus | |

Alabama | F-TF.29 | Students will: Use special triangles to determine geometrically the values of sine, cosine, and tangent for π/3, π/4, and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π – 𝘹, π + 𝘹, and 2π – 𝘹 in terms of their values for 𝘹, where 𝘹 is any real number. | Precalculus | |

Alabama | F-TF.30 | Students will: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. | Precalculus | |

Alabama | F-TF.31 | Students will: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. | Precalculus | |

Alabama | F-TF.32 | Students will: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. | Precalculus | |

Alabama | F-TF.33 | Students will: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1, and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. | Precalculus | |

Alabama | F-TF.34 | Students will: Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems. | Precalculus | |

Alabama | G-SRT.35 | Students will: Derive the formula 𝐴 = 1/2 𝘢𝘣 sin(𝐶) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | Precalculus | |

Alabama | G-GPE.36 | Students will: Derive the equation of a parabola given a focus and directrix. | Precalculus | |

Alabama | G-GPE.37 | Students will: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. | Precalculus | |

Alabama | G-GPE.38 | Students will: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. | Precalculus | |

Alabama | N-CN.1 | Students will: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. | Precalculus | |

Alabama | N-CN.2 | Students will: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. | Precalculus | |

Alabama | N-CN.3 | Students will: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. | Precalculus | |

Alabama | N-L.4 | Students will: Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity. | Precalculus | |

Alabama | N-VM.5 | Students will: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., 𝙫, |𝙫|, ||𝙫||, 𝘷). | Precalculus | |

Alabama | N-VM.6 | Students will: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. | Precalculus | |

Alabama | N-VM.7 | Students will: Solve problems involving velocity and other quantities that can be represented by vectors. | Precalculus | |

Alabama | N-VM.8 | Students will: Add and subtract vectors. | Precalculus | |

Alabama | N-VM.9 | Students will: Multiply a vector by a scalar. | Precalculus | |

Alabama | N-VM.10 | Students will: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. | Precalculus | |

Alabama | N-VM.11 | Students will: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. | Precalculus | |

Alabama | S-ID.39 | Students will: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | Precalculus | |

Alabama | S-ID.40 | Students will: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | Precalculus | |

Alabama | S-ID.41 | Students will: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | Precalculus | |

Alabama | S-ID.42 | Students will: Compute (using technology) and interpret the correlation coefficient of a linear fit. | Precalculus | |

Alabama | S-ID.43 | Students will: Distinguish between correlation and causation. | Precalculus | |

Alabama | S-IC.44 | Students will: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | Precalculus | |

Alabama | S-IC.45 | Students will: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. | Precalculus | |

Alabama | S-IC.46 | Students will: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | Precalculus | |

Alabama | S-IC.47 | Students will: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | Precalculus | |

Alabama | S-IC.48 | Students will: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | Precalculus | |

Alabama | S-IC.49 | Students will: Evaluate reports based on data. | Precalculus | |

Alabama | S-MD.50 | Students will: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. | Precalculus | |

Alabama | S-MD.51 | Students will: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. | Precalculus | |

Alabama | S-MD.52 | Students will: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. | Precalculus | |

Alabama | S-MD.53 | Students will: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. | Precalculus | |

Alabama | S-MD.54 | Students will: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. | Precalculus | |

Alabama | 8.a | Critiquing and comparing options for purchasing an automobile including leasing, purchasing by cash, and purchasing by loan | Algebra with Finance | |

Alabama | 8.b | Interpreting and analyzing various functions, graphs, graphs, and data analysis in order to make a responsible automobile purchase and to maintain the operation of an automobile | Algebra with Finance | |

Alabama | 8.c | Computing braking distance using the formula BD = 5(.1s)² | Algebra with Finance | |

Alabama | 8.d | Computing distance, rate, and time using D = RT, R = D/T, and = T = D/R | Algebra with Finance | |

Alabama | 8.e | Using geometry theorems involving chords intersecting in a circle and radii perpendicular to chords to determine yaw mark arc length | Algebra with Finance | |

Alabama | 8.f | Computing total stopping distance of an automobile | Algebra with Finance | |

Alabama | 8.g | Calculating miles per gallon and distance using the formula D = MPG(G) | Algebra with Finance | |

Alabama | 1.a | Calculating cost of credit card interest with benefits | Algebra with Finance | |

Alabama | 1.b | Utilizing and understanding amortization tables for loans | Algebra with Finance | |

Alabama | 3.a | Deriving formulas and use iteration to compute compound interest | Algebra with Finance | |

Alabama | 3.b | Creating, interpreting, and analyzing a graph, table, and equation to compare compound interest and simple interest | Algebra with Finance | |

Alabama | 3.c | Applying findings to short-term, long-term, single deposit and periodic deposit accounts | Algebra with Finance | |

Alabama | 3.d | Interpreting the limit notation | Algebra with Finance | |

Alabama | 3.e | Modeling an infinite series and finding a finite sum for an infinite series with common ratio ½ | Algebra with Finance | |

Alabama | 3.f | Computing limits of polynomial functions as x→∞ | Algebra with Finance | |

Alabama | 3.g | Computing Annual Percentage Yield (APY) where APY = (1 + r/n)ⁿ − 1, given the Annual Percentage Rate (APR) | Algebra with Finance | |

Alabama | 3.h | Adapting algebra from banking formulas for input into a spreadsheet | Algebra with Finance | |

Alabama | 15.a | Creating, evaluating, and interpreting algebraic proportions | Algebra with Finance | |

Alabama | 15.b | Determining the curve of best fit using linear, quadratic, or cubic regression equations | Algebra with Finance | |

Alabama | 15.c | Using exponential growth and decay equations that model given relationships between quantities | Algebra with Finance | |

Alabama | 15.d | Calculating finance charge at various percentages | Algebra with Finance | |

Alabama | 5.a | Critiquing gross pay and net pay to determine total salary deductions | Algebra with Finance | |

Alabama | 7.a | Identifying continuous and discontinuous functions by their graphs | Algebra with Finance | |

Alabama | 7.b | Graphing pay schedules | Algebra with Finance | |

Alabama | 7.c | Graphing continuously polynomial functions with multiple slopes and cusps | Algebra with Finance | |

Alabama | 17.a | Evaluating the various mortgage products available | Algebra with Finance | |

Alabama | 17.b | Computing monthly mortgage payments at various terms and interest rates | Algebra with Finance | |

Alabama | 17.c | Comparing mortgage payments and increasing resale value of a home using a future value of a periodic deposit formula | Algebra with Finance | |

Alabama | 17.d | Modeling rent increases using exponential relationships | Algebra with Finance | |

Alabama | 18.a | Determining surface area and volume of irregular shapes including spheres, cylinders, or cones | Algebra with Finance | |

Alabama | 18.b | Determining the circumferences of circles | Algebra with Finance | |

Alabama | 18.c | Determining area of various shapes including rectangles, squares, parallelograms, triangles, trapezoids, circles, regular polygons, irregular polygons | Algebra with Finance | |

Alabama | 4.a | Constructing, interpreting, and analyzing scatterplots by utilizing linear, quadratic, and regression equations to see a complete picture of supply, demand, revenue, and profit | Algebra with Finance | |

Alabama | 4.b | Constructing algebraic ratios and proportions | Algebra with Finance | |

Alabama | 4.c | Recognizing, representing, and solving proportional relationships using equations | Algebra with Finance | |

Alabama | 4.d | Determining percent increase/decrease of monetary amounts | Algebra with Finance | |

Alabama | 4.e | Constructing and interpreting scatterplots | Algebra with Finance | |

Alabama | 4.f | Identifying form, direction, and strength from a scatterplot | Algebra with Finance | |

Alabama | 4.g | Evaluating and using functions to model relationships between quantities | Algebra with Finance | |

Alabama | 4.h | Translating verbal situations into algebraic linear functions and quadratic function | Algebra with Finance | |

Alabama | 4.i | Creating algebraic formulas for use in spreadsheets | Algebra with Finance | |

Alabama | 4.j | Evaluating and using functions to model relationships between algebraic fractions, ratios, and proportions | Algebra with Finance | |

Alabama | 9.a | Using mathematical operations including addition and subtraction using negative numbers | Algebra with Finance | |

Alabama | 9.b | Solving problems that require multiple mathematical operations | Algebra with Finance | |

Alabama | 10.a | Finding a common denominator in fractions | Algebra with Finance | |

Alabama | 10.b | Finding equivalent fractions in lowest terms | Algebra with Finance | |

Alabama | 10.c | Multiplying mixed numbers | Algebra with Finance | |

Alabama | 12.a | Converting units of money and time from one form to another | Algebra with Finance | |

Alabama | 19.a | Analyzing overall debt, cash flow, and resources to determine net worth | Algebra with Finance | |

Alabama | 19.b | Using the future value of a periodic investment formula to predict balances in future years | Algebra with Finance | |

Alabama | 19.c | Identifying the effect that a change in multipliers has to the value of an algebraic expression | Algebra with Finance | |

Alabama | 19.d | Creating rational expressions to represent increase over time | Algebra with Finance | |

Alabama | 19.e | Creating and interpreting a graph showing linear and a piecewise function and determining the point of intersection | Algebra with Finance | |

Alabama | 19.f | Interpreting points on a budget line graph in the context of their relationship to the budget line | Algebra with Finance | |

Alabama | A-SSE.13 | Students will: Use the laws of Boolean Algebra to describe true/false circuits. Simplify Boolean expressions using the relationships between conjunction, disjunction, and negation operations. | Analytical Mathematics | |

Alabama | A-SSE.14 | Students will: Use logic symbols to write truth tables. | Analytical Mathematics | |

Alabama | A-APR.15 | Students will: Reduce the degree of either the numerator or denominator of a rational function by using partial fraction decomposition or partial fraction expansion. | Analytical Mathematics | |

Alabama | F-TF.16 | Students will: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. | Analytical Mathematics | |

Alabama | F-TF.17 | Students will: Prove the Law of Sines and the Law of Cosines and use them to solve problems. Understand Law of Sines = 2r, where r is the radius of the circumscribed circle of the triangle. Apply the Law of Tangents. | Analytical Mathematics | |

Alabama | F-TF.18 | Students will: Apply Euler’s and deMoivre’s formulas as links between complex numbers and trigonometry. | Analytical Mathematics | |

Alabama | N-VM.1 | Students will: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, │v│, ││v││), including the use of eigen-values and eigen-vectors. | Analytical Mathematics | |

Alabama | N-VM.2 | Students will: Solve problems involving velocity and other quantities that can be represented by vectors, including navigation (e.g., airplane, aerospace, oceanic). | Analytical Mathematics | |

Alabama | N-VM.3 | Students will: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Find the dot product and the cross product of vectors. | Analytical Mathematics | |

Alabama | N-VM.4 | Students will: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum, including vectors in complex vector spaces. | Analytical Mathematics | |

Alabama | N-VM.5 | Students will: Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise, including vectors in complex vector spaces. | Analytical Mathematics | |

Alabama | N-VM.6 | Students will: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network, including linear programming. | Analytical Mathematics | |

Alabama | N-VM.7 | Students will: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled, including rotation matrices. | Analytical Mathematics | |

Alabama | N-VM.8 | Students will: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. Solve matrix equations using augmented matrices. | Analytical Mathematics | |

Alabama | N-VM.9 | Students will: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors, including matrices larger than 2 × 2. | Analytical Mathematics | |

Alabama | N-VM.10 | Students will: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. Solve matrix application problems using reduced row echelon form. | Analytical Mathematics | |

Alabama | N-CN.11 | Students will: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Understand the importance of using complex numbers in graphing functions on the Cartesian or complex plane. | Analytical Mathematics | |

Alabama | N-L.12 | Students will: Calculate the limit of a sequence, of a function, and of an infinite series. | Analytical Mathematics | |

Alabama | 7.a | Utilize mathematical skills for trouble-shooting in business and industrial applications. | Career Mathematics | |

Alabama | 9.a | Calculate operation cost to maximize profit. | Career Mathematics | |

Alabama | 9.b | Calculate appropriate materials to use for an application. | Career Mathematics | |

Alabama | 13.a | Formulate tables from occupational outlook data to predict employment rates in various industrial areas. | Career Mathematics | |

Alabama | 13.b | Construct scatter plots to analyze data and develop a plan that is most suitable for the application. | Career Mathematics | |

Alabama | 14.a | Make decisions basis on probabilities. | Career Mathematics | |

Alabama | 3.a | Create graphs and tables related to personal finance and economics. The use of appropriate technology is encouraged for numerical and graphical investigations. | Career Mathematics | |

Alabama | 3.b | Analyze job opportunities and career pathways related to business or industry. | Career Mathematics | |

Alabama | 3.c | Evaluate the economics of establishing and owning a business. | Career Mathematics | |

Alabama | 3.d | Make inferences and justify conclusions from economic conditions that can affect hiring and layoff decisions. | Career Mathematics | |

Alabama | 4.a | Interpret depreciation cost of decay relationships. | Career Mathematics | |

Alabama | 5.a | Graph functions expressed in tables, equations, or classroom-generated data to model consumer costs and to predict future outcomes. | Career Mathematics | |

Alabama | 5.b | Analyze interest rates, depreciation, and tax rates in order to determine how each affects the cost of owning and/or operating a business. | Career Mathematics | |

Alabama | 6.a | Predict trends about population change that will affect employment rate. | Career Mathematics | |

Alabama | 6.b | Calculate pay scale based on occupational outlook projections. | Career Mathematics | |

Alabama | 6.c | Calculate operating costs, including cost of materials, supplies, equipment, license fees, and insurance fees. | Career Mathematics | |

Alabama | 6.d | Construct charts that reflect current demographics in various industries. | Career Mathematics | |

Alabama | 6.e | Forecast growth and decline of various career fields by interpreting data from charts and graphs. | Career Mathematics | |

Alabama | 10.a | Determine overall angles or dimensions while working with various materials. | Career Mathematics | |

Alabama | 10.b | Use trigonometric ratios to apply properties of a right triangle to drawings or blueprints. | Career Mathematics | |

Alabama | 11.a | Design drawings or blueprints to include pictorial, top, front, sides, back, and detailed views. | Career Mathematics | |

Alabama | 11.b | Construct a project from designed drawings. | Career Mathematics | |

Alabama | 12.a | Determine allowable geometric tolerance in various industrial applications. | Career Mathematics | |

Alabama | 1.a | Determine dimensions by scaling plans or blueprints. | Career Mathematics | |

Alabama | 1.b | Apply knowledge of fractions for reading a ruler to 1/16 inch. | Career Mathematics | |

Alabama | 1.c | Convert decimals to fractions for interpreting blue prints and measuring materials. | Career Mathematics | |

Alabama | 1.d | Compare Metric and English systems of measurements used in industry. | Career Mathematics | |

Alabama | 1.e | Identify various measuring tools and demonstrate their use to verify precision, accuracy, and approximate error. | Career Mathematics | |

Alabama | 2.a | Calculate area utilizing the Pythagorean Theorem. | Career Mathematics | |

Alabama | 2.b | Demonstrate an understanding of blueprints and drawings. | Career Mathematics | |

Alabama | 2.c | Calculate estimates for construction or repair projects. | Career Mathematics | |

Alaska | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten | |

Alaska | K.CC.2 | Count forward beginning from a given number within the known sequence. | Kindergarten | |

Alaska | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0 - 20 (with 0 representing a count of no objects). | Kindergarten | |

Alaska | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten | |

Alaska | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten | |

Alaska | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group (e.g., by using matching, counting, or estimating strategies). | Kindergarten | |

Alaska | K.CC.7 | Compare and order two numbers between 1 and 10 presented as written numerals. | Kindergarten | |

Alaska | K.G.1 | Describe objects in the environment using names of shapes and describe their relative positions (e.g., above, below, beside, in front of, behind, next to). | Kindergarten | |

Alaska | K.G.2 | Name shapes regardless of their orientation or overall size. | Kindergarten | |

Alaska | K.G.3 | Identify shapes as two-dimensional (flat) or three-dimensional (solid). | Kindergarten | |

Alaska | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices), and other attributes (e.g., having sides of equal lengths). | Kindergarten | |

Alaska | K.G.5 | Build shapes (e.g., using sticks and clay) and draw shapes. | Kindergarten | |

Alaska | K.G.6 | Put together two-dimensional shapes to form larger shapes (e.g., join two triangles with full sides touching to make a rectangle). | Kindergarten | |

Alaska | K.MD.1 | Describe measurable attributes of objects (e.g., length or weight). Match measuring tools to attribute (e.g., ruler to length). Describe several measurable attributes of a single object. | Kindergarten | |

Alaska | K.MD.2 | Make comparisons between two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten | |

Alaska | K.MD.3 | Classify objects into given categories (attributes). Count the number of objects in each category (limit category counts to be less than or equal to 10). | Kindergarten | |

Alaska | K.MD.4 | Name in sequence the days of the week. | Kindergarten | |

Alaska | K.MD.5 | Tell time to the hour using both analog and digital clocks. | Kindergarten | |

Alaska | K.MD.6 | Identify coins by name. | Kindergarten | |

Alaska | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones (e.g., by using objects or drawings) and record each composition and decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight or nine ones. | Kindergarten | |

Alaska | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps) acting out situations, verbal explanations, expressions, or equations. | Kindergarten | |

Alaska | K.OA.2 | Add or subtract whole numbers to 10 (e.g., by using objects or drawings to solve word problems). | Kindergarten | |

Alaska | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way (e.g., by using objects or drawings, and record each decomposition by a drawing or equation). | Kindergarten | |

Alaska | K.OA.4 | For any number from 1- 4, find the number that makes 5 when added to the given number and, for any number from 1- 9, find the number that makes 10 when added to the given number (e.g., by using objects, drawings or 10 frames) and record the answer with a drawing or equation. | Kindergarten | |

Alaska | K.OA.5 | Fluently add and subtract numbers up to 5. | Kindergarten | |

Alaska | K.OA.6 | Recognize, identify and continue simple patterns of color, shape, and size. | Kindergarten | |

Alaska | 1.CC.1 | Skip count by 2s and 5s. | Grade 1 | |

Alaska | 1.CC.2 | Use ordinal numbers correctly when identifying object position (e.g., first, second, third, etc.). | Grade 1 | |

Alaska | 1.CC.3 | Order numbers from 1 - 100. Demonstrate ability in counting forward and backward. | Grade 1 | |

Alaska | 1.CC.4 | Count a large quantity of objects by grouping into 10s and counting by 10s and 1s to find the quantity. | Grade 1 | |

Alaska | 1.CC.5 | Use the symbols for greater than, less than or equal to when comparing two numbers or groups of objects. | Grade 1 | |

Alaska | 1.CC.6 | Estimate how many and how much in a given set to 20 and then verify estimate by counting. | Grade 1 | |

Alaska | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes. Identify shapes that have non-defining attributes (e.g., color, orientation, overall size). Build and draw shapes given specified attributes. | Grade 1 | |

Alaska | 1.G.2 | Compose (put together) two-dimensional or three-dimensional shapes to create a larger, composite shape, and compose new shapes from the composite shape. | Grade 1 | |

Alaska | 1.G.3 | Partition circles and rectangles into two and four equal shares. Describe the shares using the words, halves, fourths, and quarters and phrases half of, fourth of and quarter of. Describe the whole as two of or four of the shares. Understand for these examples that decomposing (break apart) into more equal shares creates smaller shares. | Grade 1 | |

Alaska | 1.MD.1 | Measure and compare three objects using standard or non-standard units. | Grade 1 | |

Alaska | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 | |

Alaska | 1.MD.3 | Tell and write time in half hours using both analog and digital clocks. | Grade 1 | |

Alaska | 1.MD.4 | Read a calendar distinguishing yesterday, today and tomorrow. Read and write a date. | Grade 1 | |

Alaska | 1.MD.5 | Recognize and read money symbols including $ and ¢. | Grade 1 | |

Alaska | 1.MD.6 | Identify values of coins (e.g., nickel = 5 cents, quarter = 25 cents). Identify equivalent values of coins up to $1 (e.g., 5 pennies = 1 nickel, 5 nickels = 1 quarter). | Grade 1 | |

Alaska | 1.MD.7 | Organize, represent and interpret data with up to three categories. Ask and answer comparison and quantity questions about the data. | Grade 1 | |

Alaska | 1.NBT.1 | Count to 120. In this range, read, write and order numerals and represent a number of objects with a written numeral. | Grade 1 | |

Alaska | 1.NBT.2 | Model and identify place value positions of two digit numbers. | Grade 1 | |

Alaska | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, <. | Grade 1 | |

Alaska | 1.NBT.4 | Add using numbers up to 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10. | Grade 1 | |

Alaska | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 | |

Alaska | 1.NBT.6 | Subtract multiples of 10 up to 100. | Grade 1 | |

Alaska | 1.OA.1 | Use addition and subtraction strategies to solve word problems (using numbers up to 20), involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions, using a number line (e.g., by using objects, drawings and equations). Record and explain using equation symbols and a symbol for the unknown number to represent the problem. | Grade 1 | |

Alaska | 1.OA.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 (e.g., by using objects, drawings and equations). Record and explain using equation symbols and a symbol for the unknown number to represent the problem. | Grade 1 | |

Alaska | 1.OA.3 | Apply properties of operations as strategies to add and subtract. (Students need not know the name of the property.) | Grade 1 | |

Alaska | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 | |

Alaska | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 | |

Alaska | 1.OA.6 | Add and subtract using numbers up to 20, demonstrating fluency for addition and subtraction up to 10. | Grade 1 | |

Alaska | 1.OA.7 | Understand the meaning of the equal sign (e.g., read equal sign as “same as”) and determine if equations involving addition and subtraction are true or false. | Grade 1 | |

Alaska | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation. | Grade 1 | |

Alaska | 1.OA.9 | Identify, continue and label patterns (e.g., aabb, abab). Create patterns using number, shape, size, rhythm or color. | Grade 1 | |

Alaska | 2.G.1 | Identify and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces compared visually, not by measuring. Identify triangles, quadrilaterals, pentagons, hexagons and cubes. | Grade 2 | |

Alaska | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 | |

Alaska | 2.G.3 | Partition circles and rectangles into shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 | |

Alaska | 2.MD.1 | Measure the length of an object by selecting and using standard tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 | |

Alaska | 2.MD.2 | Measure the length of an object twice using different length units for the two measurements. Describe how the two measurements relate to the size of the unit chosen. | Grade 2 | |

Alaska | 2.MD.3 | Estimate, measure and draw lengths using whole units of inches, feet, yards, centimeters and meters. | Grade 2 | |

Alaska | 2.MD.4 | Measure to compare lengths of two objects, expressing the difference in terms of a standard length unit. | Grade 2 | |

Alaska | 2.MD.5 | Solve addition and subtraction word problems using numbers up to 100 involving length that are given in the same units (e.g., by using drawings of rulers). Write an equation with a symbol for the unknown to represent the problem. | Grade 2 | |

Alaska | 2.MD.6 | Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1,2, …, and represent whole-number sums and differences within 100 on a number line diagram. | Grade 2 | |

Alaska | 2.MD.7 | Tell and write time to the nearest five minutes using a.m. and p.m. from analog and digital clocks. | Grade 2 | |

Alaska | 2.MD.8 | Solve word problems involving dollar bills and coins using the $ and ¢ symbols appropriately. | Grade 2 | |

Alaska | 2.MD.9 | Collect, record, interpret, represent, and describe data in a table, graph or line plot. | Grade 2 | |

Alaska | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart and compare problems using information presented in a bar graph. | Grade 2 | |

Alaska | 2.NBT.1 | Model and identify place value positions of three digit numbers. | Grade 2 | |

Alaska | 2.NBT.2 | Count up to 1000, skip-count by 5s, 10s and 100s. | Grade 2 | |

Alaska | 2.NBT.3 | Read, write, order up to 1000 using base-ten numerals, number names and expanded form. | Grade 2 | |

Alaska | 2.NBT.4 | Compare two three-digit numbers based on the meanings of the hundreds, tens and ones digits, using >, =, < symbols to record the results. | Grade 2 | |

Alaska | 2.NBT.5 | Fluently add and subtract using numbers up to 100. | Grade 2 | |

Alaska | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 | |

Alaska | 2.NBT.7 | Add and subtract using numbers up to 1000. | Grade 2 | |

Alaska | 2.NBT.8 | Mentally add 10 or 100 to a given number 100-900 and mentally subtract 10 or 100 from a given number. | Grade 2 | |

Alaska | 2.NBT.9 | Explain or illustrate the processes of addition or subtraction and their relationship using place value and the properties of operations. | Grade 2 | |

Alaska | 2.OA.1 | Use addition and subtraction strategies to estimate, then solve one- and two-step word problems (using numbers up to 100) involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions (e.g., by using objects, drawings and equations). Record and explain using equation symbols and a symbol for the unknown number to represent the problem. | Grade 2 | |

Alaska | 2.OA.2 | Fluently add and subtract using numbers up to 20 using mental strategies. Know from memory all sums of two one-digit numbers. | Grade 2 | |

Alaska | 2.OA.3 | Determine whether a group of objects (up to 20) is odd or even (e.g., by pairing objects and comparing, counting by 2s). Model an even number as two equal groups of objects and then write an equation as a sum of two equal addends. | Grade 2 | |

Alaska | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. Write an equation to express the total as repeated addition (e.g., array of 4 by 5 would be 5 + 5 + 5 + 5 = 20). | Grade 2 | |

Alaska | 2.OA.5 | Identify, continue and label number patterns (e.g., aabb, abab). Describe a rule that determines and continues a sequence or pattern. | Grade 2 | |

Alaska | 3.G.1 | Categorize shapes by different attribute classifications and recognize that shared attributes can define a larger category. Generalize to create examples or non-examples. | Grade 3 | |

Alaska | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 | |

Alaska | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes or hours (e.g., by representing the problem on a number line diagram or clock). | Grade 3 | |

Alaska | 3.MD.2 | Estimate and measure liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm³ and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve and create one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale, to represent the problem). (Excludes multiplicative comparison problems [problems involving notions of “times as much.”]) | Grade 3 | |

Alaska | 3.MD.3 | Select an appropriate unit of English, metric, or non-standard measurement to estimate the length, time, weight, or temperature (L) | Grade 3 | |

Alaska | 3.MD.4 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 | |

Alaska | 3.MD.5 | Measure and record lengths using rulers marked with halves and fourths of an inch. Make a line plot with the data, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. | Grade 3 | |

Alaska | 3.MD.6 | Explain the classification of data from real-world problems shown in graphical representations. Use the terms minimum and maximum. (L) | Grade 3 | |

Alaska | 3.MD.7 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 | |

Alaska | 3.MD.8 | Measure areas by tiling with unit squares (square centimeters, square meters, square inches, square feet, and improvised units). | Grade 3 | |

Alaska | 3.MD.9 | Relate area to the operations of multiplication and addition. | Grade 3 | |

Alaska | 3.MD.10 | Solve real-world and mathematical problems involving perimeters of polygons, including: | Grade 3 | |

Alaska | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 | |

Alaska | 3.NBT.2 | Use strategies and/or algorithms to fluently add and subtract with numbers up to 1000, demonstrating understanding of place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 | |

Alaska | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 10 x 60) using strategies based on place value and properties of operations. | Grade 3 | |

Alaska | 3.NF.1 | Understand a fraction 1/𝑏 (e.g., 1/4) as the quantity formed by 1 part when a whole is partitioned into 𝑏 (e.g., 4) equal parts; understand a fraction 𝑎/𝑏 (e.g., 2/4) as the quantity formed by 𝑎 (e.g., 2) parts of size 1/𝑏. (e.g., 1/4) | Grade 3 | |

Alaska | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 | |

Alaska | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 | |

Alaska | 3.OA.1 | Interpret products of whole numbers (e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each). | Grade 3 | |

Alaska | 3.OA.2 | Interpret whole-number quotients of whole numbers (e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each). | Grade 3 | |

Alaska | 3.OA.3 | Use multiplication and division numbers up to 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). | Grade 3 | |

Alaska | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 | |

Alaska | 3.OA.5 | Make, test, support, draw conclusions and justify conjectures about properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) | Grade 3 | |

Alaska | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 | |

Alaska | 3.OA.7 | Fluently multiply and divide numbers up to 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 ×5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 | |

Alaska | 3.OA.8 | Solve and create two-step word problems using any of the four operations. Represent these problems using equations with a symbol (box, circle, question mark) standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 | |

Alaska | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. | Grade 3 | |

Alaska | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular, parallel, and intersecting line segments. Identify these in two-dimensional (plane) figures. | Grade 4 | |

Alaska | 4.G.2 | Classify two-dimensional (plane) figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 | |

Alaska | 4.G.3 | Recognize a line of symmetry for a two-dimensional (plane) figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 | |

Alaska | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 | |

Alaska | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 | |

Alaska | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. | Grade 4 | |

Alaska | 4.MD.4 | Solve real-world problems involving elapsed time between U.S. time zones (including Alaska Standard time). | Grade 4 | |

Alaska | 4.MD.5 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 | |

Alaska | 4.MD.6 | Explain the classification of data from real-world problems shown in graphical representations including the use of terms range and mode with a given set of data. | Grade 4 | |

Alaska | 4.MD.7 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. | Grade 4 | |

Alaska | 4.MD.8 | Measure and draw angles in whole-number degrees using a protractor. Estimate and sketch angles of specified measure. | Grade 4 | |

Alaska | 4.MD.9 | Recognize angle measure as additive. When an angle is divided into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). | Grade 4 | |

Alaska | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 | |

Alaska | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 | |

Alaska | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place using a variety of estimation methods; be able to describe, compare, and contrast solutions. | Grade 4 | |

Alaska | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using any algorithm. Verify the reasonableness of the results. | Grade 4 | |

Alaska | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Alaska | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Alaska | 4.NF.1 | Explain why a fraction 𝑎/𝑏 is equivalent to a fraction (𝑛 × 𝑎)/(𝑛 × 𝑏) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 | |

Alaska | 4.NF.2 | Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). | Grade 4 | |

Alaska | 4.NF.3 | Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of fractions 1/𝑏. | Grade 4 | |

Alaska | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 | |

Alaska | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 | |

Alaska | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 | |

Alaska | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual model). | Grade 4 | |

Alaska | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 groups of 7 and 7 groups of 5 (Commutative property). Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 | |

Alaska | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem or missing numbers in an array). Distinguish multiplicative comparison from additive comparison. | Grade 4 | |

Alaska | 4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 | |

Alaska | 4.OA.4 | Find all factor pairs for a whole number in the range 1–100. | Grade 4 | |

Alaska | 4.OA.5 | Generate a number, shape pattern, table, t-chart, or input/output function that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Be able to express the pattern in algebraic terms. | Grade 4 | |

Alaska | 4.OA.6 | Extend patterns that use addition, subtraction, multiplication, division or symbols, up to 10 terms, represented by models (function machines), tables, sequences, or in problem situations. | Grade 4 | |

Alaska | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝑥-axis and 𝑥-coordinate, 𝑦-axis and 𝑦-coordinate). | Grade 5 | |

Alaska | 5.G.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 | |

Alaska | 5.G.3 | Understand that attributes belonging to a category of two-dimensional (plane) figures also belong to all subcategories of that category. | Grade 5 | |

Alaska | 5.G.4 | Classify two-dimensional (plane) figures in a hierarchy based on attributes and properties. | Grade 5 | |

Alaska | 5.MD.1 | Identify, estimate measure, and convert equivalent measures within systems English length (inches, feet, yards, miles) weight (ounces, pounds, tons) volume (fluid ounces, cups, pints, quarts, gallons) temperature (Fahrenheit) Metric length (millimeters, centimeters, meters, kilometers) volume (milliliters, liters), temperature (Celsius), (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems using appropriate tools. | Grade 5 | |

Alaska | 5.MD.2 | Solve real-world problems involving elapsed time between world time zones. | Grade 5 | |

Alaska | 5.MD.3 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving information presented in line plots. | Grade 5 | |

Alaska | 5.MD.4 | Explain the classification of data from real-world problems shown in graphical representations including the use of terms mean and median with a given set of data. | Grade 5 | |

Alaska | 5.MD.5 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 | |

Alaska | 5.MD.6 | Estimate and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and non-standard units. | Grade 5 | |

Alaska | 5.MD.7 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 | |

Alaska | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 | |

Alaska | 5.NBT.2 | Explain and extend the patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain and extend the patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 | |

Alaska | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 | |

Alaska | 5.NBT.4 | Use place values understanding to round decimals to any place. | Grade 5 | |

Alaska | 5.NBT.5 | Fluently multiply multi-digit whole numbers using a standard algorithm. | Grade 5 | |

Alaska | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, number lines, real life situations, and/or area models. | Grade 5 | |

Alaska | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between the operations. Relate the strategy to a written method and explain their reasoning in getting their answers. | Grade 5 | |

Alaska | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 | |

Alaska | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models or equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and check the reasonableness of answers. | Grade 5 | |

Alaska | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers (e.g., by using visual fraction models or equations to represent the problem). | Grade 5 | |

Alaska | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 | |

Alaska | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 | |

Alaska | 5.NF.6 | Solve real-world problems involving multiplication of fractions and mixed numbers (e.g., by using visual fraction models or equations to represent the problem). | Grade 5 | |

Alaska | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 | |

Alaska | 5.OA.1 | Use parentheses to construct numerical expressions, and evaluate numerical expressions with these symbols. | Grade 5 | |

Alaska | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 | |

Alaska | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 | |

Alaska | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 | |

Alaska | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 | |

Alaska | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. Model (e.g., manipulatives, graph paper) and apply the distributive, commutative, identity, and inverse properties with integers and variables by writing equivalent expressions. | Grade 6 | |

Alaska | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 | |

Alaska | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 | |

Alaska | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 | |

Alaska | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞 for cases in which 𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers. | Grade 6 | |

Alaska | 6.EE.8 | Write an inequality of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 | |

Alaska | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 | |

Alaska | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing or decomposing into other polygons (e.g., rectangles and triangles). Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Alaska | 6.G.2 | Apply the standard formulas to find volumes of prisms. Use the attributes and properties (including shapes of bases) of prisms to identify, compare or describe three-dimensional figures including prisms and cylinders. | Grade 6 | |

Alaska | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; determine the length of a side joining the coordinates of vertices with the same first or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Alaska | 6.G.4 | Represent three-dimensional figures (e.g., prisms) using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Alaska | 6.G.5 | Identify, compare or describe attributes and properties of circles (radius, and diameter). | Grade 6 | |

Alaska | 6.RP.1 | Write and describe the relationship in real life context between two quantities using ratio language. | Grade 6 | |

Alaska | 6.RP.2 | Understand the concept of a unit rate (𝑎/𝑏 associated with a ratio 𝑎:𝑏 with 𝑏 ≠ 0, and use rate language in the context of a ratio relationship) and apply it to solve real-world problems (e.g., unit pricing, constant speed). | Grade 6 | |

Alaska | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). | Grade 6 | |

Alaska | 6.SP.1 | Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. | Grade 6 | |

Alaska | 6.SP.2 | Understand that a set of data has a distribution that can be described by its center (mean, median, or mode), spread (range), and overall shape and can be used to answer a statistical question. | Grade 6 | |

Alaska | 6.SP.3 | Recognize that a measure of center (mean, median, or mode) for a numerical data set summarizes all of its values with a single number, while a measure of variation (range) describes how its values vary with a single number. | Grade 6 | |

Alaska | 6.SP.4 | Display numerical data in plots on a number line, including dot or line plots, histograms and box (box and whisker) plots. | Grade 6 | |

Alaska | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 | |

Alaska | 6.SP.6 | Analyze whether a game is mathematically fair or unfair by explaining the probability of all possible outcomes. | Grade 6 | |

Alaska | 6.SP.7 | Solve or identify solutions to problems involving possible combinations (e.g., if ice cream sundaes come in 3 flavors with 2 possible toppings, how many different sundaes can be made using only one flavor of ice cream with one topping?) | Grade 6 | |

Alaska | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions (e.g., by using visual fraction models and equations to represent the problem). | Grade 6 | |

Alaska | 6.NS.2 | Fluently multiply and divide multi-digit whole numbers using the standard algorithm. Express the remainder as a whole number, decimal, or simplified fraction; explain or justify your choice based on the context of the problem. | Grade 6 | |

Alaska | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Express the remainder as a terminating decimal, or a repeating decimal, or rounded to a designated place value. | Grade 6 | |

Alaska | 6.NS.4 | Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. | Grade 6 | |

Alaska | 6.NS.5 | Understand that positive and negative numbers describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explain the meaning of 0 in each situation. | Grade 6 | |

Alaska | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 | |

Alaska | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 | |

Alaska | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 | |

Alaska | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, expand and simplify linear expressions with rational coefficients. | Grade 7 | |

Alaska | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 | |

Alaska | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 | |

Alaska | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct multi-step equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 | |

Alaska | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 | |

Alaska | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes including polygons and circles with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 | |

Alaska | 7.G.3 | Describe the two-dimensional figures, i.e., cross-section, that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 | |

Alaska | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 | |

Alaska | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 | |

Alaska | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 | |

Alaska | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 | |

Alaska | 7.RP.2 | Recognize and represent proportional relationships between quantities. Make basic inferences or logical predictions from proportional relationships. | Grade 7 | |

Alaska | 7.RP.3 | Use proportional relationships to solve multi-step ratio and percent problems. | Grade 7 | |

Alaska | 7.SP.1 | Understand that statistics can be used to gain information about a population by examining a reasonably sized sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. | Grade 7 | |

Alaska | 7.SP.2 | Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. | Grade 7 | |

Alaska | 7.SP.3 | Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. | Grade 7 | |

Alaska | 7.SP.4 | Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. | Grade 7 | |

Alaska | 7.SP.5 | Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. | Grade 7 | |

Alaska | 7.SP.6 | Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. | Grade 7 | |

Alaska | 7.SP.7 | Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. | Grade 7 | |

Alaska | 7.SP.8 | Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. | Grade 7 | |

Alaska | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 | |

Alaska | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers and use equivalent representations. | Grade 7 | |

Alaska | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) | Grade 7 | |

Alaska | 8.EE.1 | Apply the properties (product, quotient, power, zero, negative exponents, and rational exponents) of integer exponents to generate equivalent numerical expressions. | Grade 8 | |

Alaska | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝑥² = 𝑝 and 𝑥³ = 𝑝, where 𝑝 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 | |

Alaska | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 | |

Alaska | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both standard notation and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 | |

Alaska | 8.EE.5 | Graph linear equations such as 𝑦 = 𝑚𝑥 + 𝑏, interpreting 𝑚 as the slope or rate of change of the graph and 𝑏 as the 𝑦-intercept or starting value. Compare two different proportional relationships represented in different ways. | Grade 8 | |

Alaska | 8.EE.6 | Use similar triangles to explain why the slope 𝑚 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝑦 = 𝑚𝑥 for a line through the origin and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line intercepting the vertical axis at 𝑏. | Grade 8 | |

Alaska | 8.EE.7 | Solve linear equations in one variable. | Grade 8 | |

Alaska | 8.EE.8 | Analyze and solve systems of linear equations. | Grade 8 | |

Alaska | 8.F.1 | Understand that a function is a rule that assigns to each input (the domain) exactly one output (the range). The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. For example, use the vertical line test to determine functions and non-functions. | Grade 8 | |

Alaska | 8.F.2 | Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 | |

Alaska | 8.F.3 | Interpret the equation 𝑦 = 𝑚𝑥 + 𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 | |

Alaska | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥, 𝑦) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 | |

Alaska | 8.F.5 | Given a verbal description between two quantities, sketch a graph. Conversely, given a graph, describe a possible real-world example. | Grade 8 | |

Alaska | 8.G.1 | Through experimentation, verify the properties of rotations, reflections, and translations (transformations) to figures on a coordinate plane). | Grade 8 | |

Alaska | 8.G.2 | Demonstrate understanding of congruence by applying a sequence of translations, reflections, and rotations on two-dimensional figures. Given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 | |

Alaska | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 | |

Alaska | 8.G.4 | Demonstrate understanding of similarity, by applying a sequence of translations, reflections, rotations, and dilations on two-dimensional figures. Describe a sequence that exhibits the similarity between them. | Grade 8 | |

Alaska | 8.G.5 | Justify using informal arguments to establish facts about | Grade 8 | |

Alaska | 8.G.6 | Explain the Pythagorean Theorem and its converse. | Grade 8 | |

Alaska | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 | |

Alaska | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 | |

Alaska | 8.G.9 | Identify and apply the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 | |

Alaska | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 | |

Alaska | 8.SP.2 | Explain why straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 | |

Alaska | 8.SP.3 | Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and 𝑦-intercept. | Grade 8 | |

Alaska | 8.SP.4 | Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects and use relative frequencies to describe possible association between the two variables. | Grade 8 | |

Alaska | 8.NS.1 | Classify real numbers as either rational (the ratio of two integers, a terminating decimal number, or a repeating decimal number) or irrational. | Grade 8 | |

Alaska | 8.NS.2 | Order real numbers, using approximations of irrational numbers, locating them on a number line. | Grade 8 | |

Alaska | 8.NS.3 | Identify or write the prime factorization of a number using exponents. | Grade 8 | |

Alaska | N-Q.1 | Use units as a way to understand problems and to guide the solution of multi‐step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | High School | |

Alaska | N-Q.2 | Define appropriate quantities for the purpose of descriptive modeling. | High School | |

Alaska | N-Q.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | High School | |

Alaska | N-CN.1 | Know there is a complex number 𝑖 such that 𝑖² = –1, and every complex number has the form 𝑎 + 𝑏𝑖 with 𝑎 and 𝑏 real. | High School | |

Alaska | N-CN.2 | Use the relation 𝑖² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | High School | |

Alaska | N-CN.3 | Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. | High School | |

Alaska | N-CN.4 | Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. | High School | |

Alaska | N-CN.5 | Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. | High School | |

Alaska | N-CN.6 | Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. | High School | |

Alaska | N-CN.7 | Solve quadratic equations with real coefficients that have complex solutions. | High School | |

Alaska | N-CN.8 | Extend polynomial identities to the complex numbers. For example, rewrite 𝑥² + 4 as (𝑥 + 2𝑖)(𝑥 – 2𝑖). | High School | |

Alaska | N-CN.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | High School | |

Alaska | N-RN.1 | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | High School | |

Alaska | N-RN.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | High School | |

Alaska | N-RN.3 | Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | High School | |

Alaska | N-VM.1 | Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., 𝙫, |𝙫|, ||𝙫||, 𝙫). | High School | |

Alaska | N-VM.2 | Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. | High School | |

Alaska | N-VM.3 | Solve problems involving velocity and other quantities that can be represented by vectors. | High School | |

Alaska | N-VM.4 | Add and subtract vectors. | High School | |

Alaska | N-VM.5 | Multiply a vector by a scalar. | High School | |

Alaska | N-VM.6 | Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. | High School | |

Alaska | N-VM.7 | Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. | High School | |

Alaska | N-VM.8 | Add, subtract, and multiply matrices of appropriate dimensions. | High School | |

Alaska | N-VM.9 | Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. | High School | |

Alaska | N-VM.10 | Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. | High School | |

Alaska | N-VM.11 | Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. | High School | |

Alaska | N-VM.12 | Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area. | High School | |

Alaska | A-APR.1 | Add, subtract, and multiply polynomials. Understand that polynomials form a system similar to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication. | High School | |

Alaska | A-APR.2 | Know and apply the Remainder Theorem: For a polynomial 𝑝(𝑥) and a number 𝑎, the remainder on division by 𝑥 – 𝑎 is 𝑝(𝑎), so 𝑝(𝑎) = 0 if and only if (𝑥 – 𝑎) is a factor of 𝑝(𝑥). | High School | |

Alaska | A-APR.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School | |

Alaska | A-APR.4 | Prove polynomial identities and use them to describe numerical relationships. | High School | |

Alaska | A-APR.5 | Know and apply the Binomial Theorem for the expansion of (𝑥 + 𝑦)ⁿ in powers of 𝑥 and 𝑦 for a positive integer 𝑛, where 𝑥 and 𝑦 are any numbers, with coefficients determined for example by Pascal’s Triangle. | High School | |

Alaska | A-APR.6 | Rewrite simple rational expressions in different forms; write 𝑎(𝑥)/𝑏(𝑥) in the form 𝑞(𝑥) + 𝑟(𝑥)/𝑏(𝑥), where 𝑎(𝑥), 𝑏(𝑥), 𝑞(𝑥), and 𝑟(𝑥) are polynomials with the degree of 𝑟(𝑥) less than the degree of 𝑏(𝑥), using inspection, long division, or, for the more complicated examples, a computer algebra system. | High School | |

Alaska | A-APR.7 | Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system similar to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression. | High School | |

Alaska | A-CED.1 | Create equations and inequalities in one variable and use them to solve problems. | High School | |

Alaska | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School | |

Alaska | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. | High School | |

Alaska | A-CED.4 | Rearrange formulas (literal equations) to highlight a quantity of interest, using the same reasoning as in solving equations. | High School | |

Alaska | A-REI.1 | Apply properties of mathematics to justify steps in solving equations in one variable. | High School | |

Alaska | A-REI.2 | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | High School | |

Alaska | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School | |

Alaska | A-REI.4 | Solve quadratic equations in one variable. | High School | |

Alaska | A-REI.5 | Show that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | High School | |

Alaska | A-REI.6 | Solve systems of linear equations exactly and approximately, e.g., with graphs or algebraically, focusing on pairs of linear equations in two variables. | High School | |

Alaska | A-REI.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | High School | |

Alaska | A-REI.8 | Represent a system of linear equations as a single matrix equation in a vector variable. | High School | |

Alaska | A-REI.9 | Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). | High School | |

Alaska | A-REI.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). | High School | |

Alaska | A-REI.11 | Explain why the 𝑥‐coordinates of the points where the graphs of the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | High School | |

Alaska | A-REI.12 | Graph the solutions to a linear inequality in two variables as a half‐plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half‐planes. | High School | |

Alaska | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | High School | |

Alaska | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School | |

Alaska | A-SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School | |

Alaska | A-SSE.4 | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | High School | |

Alaska | F-BF.1 | Write a function that describes a relationship between two quantities. | High School | |

Alaska | F-BF.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | High School | |

Alaska | F-BF.3 | Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of 𝑘 (both positive and negative); find the value of 𝑘 given the graphs. | High School | |

Alaska | F-BF.4 | Find inverse functions. | High School | |

Alaska | F-BF.5 | Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. | High School | |

Alaska | F-IF.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝑓 is a function and 𝑥 is an element of its domain, then 𝑓(𝑥) denotes the output of 𝑓 corresponding to the input 𝑥. The graph of 𝑓 is the graph of the equation 𝑦 = 𝑓(𝑥). | High School | |

Alaska | F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School | |

Alaska | F-IF.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | High School | |

Alaska | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School | |

Alaska | F-IF.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | High School | |

Alaska | F-IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | High School | |

Alaska | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School | |

Alaska | F-IF.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | High School | |

Alaska | F-IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions). | High School | |

Alaska | F-LE.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. | High School | |

Alaska | F-LE.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or input‐output table of values. | High School | |

Alaska | F-LE.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | High School | |

Alaska | F-LE.4 | For exponential models, express as a logarithm the solution to 𝑎𝑏𝑐𝑡 = 𝑑 where 𝑎, 𝑐, and 𝑑 are numbers and the base 𝑏 is 2, 10, or 𝑒; evaluate the logarithm using technology. | High School | |

Alaska | F-LE.5 | Interpret the parameters in a linear or exponential function in terms of a context. | High School | |

Alaska | F-TF.1 | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | High School | |

Alaska | F-TF.2 | Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | High School | |

Alaska | F-TF.3 | Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for π – 𝑥, π + 𝑥, and 2π – 𝑥 in terms of their values for 𝑥, where 𝑥 is any real number. | High School | |

Alaska | F-TF.4 | Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. | High School | |

Alaska | F-TF.5 | Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. | High School | |

Alaska | F-TF.6 | Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. | High School | |

Alaska | F-TF.7 | Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. | High School | |

Alaska | F-TF.8 | Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to calculate trigonometric ratios. | High School | |

Alaska | F-TF.9 | Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. | High School | |

Alaska | G-C.1 | Prove that all circles are similar. | High School | |

Alaska | G-C.2 | Identify and describe relationships among inscribed angles, radii, and chords. | High School | |

Alaska | G-C.3 | Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | High School | |

Alaska | G-C.4 | Construct a tangent line from a point outside a given circle to the circle. | High School | |

Alaska | G-C.5 | Use and apply the concepts of arc length and areas of sectors of circles. Determine or derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. | High School | |

Alaska | G-CO.1 | Demonstrates understanding of key geometrical definitions, including angle, circle, perpendicular line, parallel line, line segment, and transformations in Euclidian geometry. Understand undefined notions of point, line, distance along a line, and distance around a circular arc. | High School | |

Alaska | G-CO.2 | Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | High School | |

Alaska | G-CO.3 | Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | High School | |

Alaska | G-CO.4 | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | High School | |

Alaska | G-CO.5 | Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. | High School | |

Alaska | G-CO.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. | High School | |

Alaska | G-CO.7 | Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. | High School | |

Alaska | G-CO.8 | Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS, and HL) follow from the definition of congruence in terms of rigid motions. | High School | |

Alaska | G-CO.9 | Using methods of proof including direct, indirect, and counter examples to prove theorems about lines and angles. | High School | |

Alaska | G-CO.10 | Using methods of proof including direct, indirect, and counter examples to prove theorems about triangles. | High School | |

Alaska | G-CO.11 | Using methods of proof including direct, indirect, and counter examples to prove theorems about parallelograms. | High School | |

Alaska | G-CO.12 | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. | High School | |

Alaska | G-CO.13 | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | High School | |

Alaska | G-GPE.1 | Determine or derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | High School | |

Alaska | G-GPE.2 | Determine or derive the equation of a parabola given a focus and directrix. | High School | |

Alaska | G-GPE.3 | Derive the equations of ellipses and hyperbolas given foci and directrices. | High School | |

Alaska | G-GPE.4 | Perform simple coordinate proofs. | High School | |

Alaska | G-GPE.5 | Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | High School | |

Alaska | G-GPE.6 | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | High School | |

Alaska | G-GPE.7 | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. | High School | |

Alaska | G-GMD.1 | Explain how to find the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. | High School | |

Alaska | G-GMD.2 | Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. | High School | |

Alaska | G-GMD.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | High School | |

Alaska | G-GMD.4 | Identify the shapes of two‐dimensional cross‐sections of three‐dimensional objects, and identify three‐dimensional objects generated by rotations of two‐dimensional objects. | High School | |

Alaska | G-MG.1 | Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | High School | |

Alaska | G-MG.2 | Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). | High School | |

Alaska | G-MG.3 | Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). | High School | |

Alaska | G-SRT.1 | Verify experimentally the properties of dilations given by a center and a scale factor: | High School | |

Alaska | G-SRT.2 | Given two figures, use the definition of similarity in terms of transformations to explain whether or not they are similar. | High School | |

Alaska | G-SRT.3 | Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. | High School | |

Alaska | G-SRT.4 | Prove theorems about triangles. | High School | |

Alaska | G-SRT.5 | Apply congruence and similarity properties and prove relationships involving triangles and other geometric figures. | High School | |

Alaska | G-SRT.6 | Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. | High School | |

Alaska | G-SRT.7 | Explain and use the relationship between the sine and cosine of complementary angles. | High School | |

Alaska | G-SRT.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | High School | |

Alaska | G-SRT.9 | Derive the formula 𝐴 = 1/2 𝑎𝑏 sin(𝐶) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | High School | |

Alaska | G-SRT.10 | Prove the Laws of Sines and Cosines and use them to solve problems. | High School | |

Alaska | G-SRT.11 | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non‐right triangles (e.g., surveying problems, resultant forces). | High School | |

Alaska | S-CP.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). | High School | |

Alaska | S-CP.2 | Understand that two events 𝐴 and 𝐵 are independent if the probability of 𝐴 and 𝐵 occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | High School | |

Alaska | S-CP.3 | Understand the conditional probability of 𝐴 given 𝐵 as 𝑃(𝐴 and 𝐵)/𝑃(𝐵), and interpret independence of 𝐴 and 𝐵 as saying that the conditional probability of 𝐴 given 𝐵 is the same as the probability of 𝐴, and the conditional probability of 𝐵 given 𝐴 is the same as the probability of 𝐵. | High School | |

Alaska | S-CP.4 | Construct and interpret two‐way frequency tables of data when two categories are associated with each object being classified. Use the two‐way table as a sample space to decide if events are independent and to approximate conditional probabilities. | High School | |

Alaska | S-CP.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | High School | |

Alaska | S-CP.6 | Find the conditional probability of 𝐴 given 𝐵 as the fraction of 𝐵’s outcomes that also belong to 𝐴, and interpret the answer in terms of the model. | High School | |

Alaska | S-CP.7 | Apply the Addition Rule, 𝑃(𝐴 or 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) – 𝑃(𝐴 and 𝐵), and interpret the answer in terms of the model. | High School | |

Alaska | S-CP.8 | Apply the general Multiplication Rule in a uniform probability model, 𝑃(𝐴 and 𝐵) = 𝑃(𝐴)𝑃(𝐵|𝐴) = 𝑃(𝐵)𝑃(𝐴|𝐵), and interpret the answer in terms of the model. | High School | |

Alaska | S-CP.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. | High School | |

Alaska | S-ID.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). | High School | |

Alaska | S-ID.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | High School | |

Alaska | S-ID.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | High School | |

Alaska | S-ID.4 | Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | High School | |

Alaska | S-ID.5 | Summarize categorical data for two categories in two‐way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | High School | |

Alaska | S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School | |

Alaska | S-ID.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | High School | |

Alaska | S-ID.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | High School | |

Alaska | S-ID.9 | Distinguish between correlation and causation. | High School | |

Alaska | S-IC.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | High School | |

Alaska | S-IC.2 | Decide if a specified model is consistent with results from a given data‐generating process, e.g., using simulation. | High School | |

Alaska | S-IC.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | High School | |

Alaska | S-IC.4 | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | High School | |

Alaska | S-IC.5 | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | High School | |

Alaska | S-IC.6 | Evaluate reports based on data. | High School | |

Alaska | S-MD.1 | Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. | High School | |

Alaska | S-MD.2 | Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. | High School | |

Alaska | S-MD.3 | Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. | High School | |

Alaska | S-MD.4 | Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. | High School | |

Alaska | S-MD.5 | Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. | High School | |

Alaska | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | High School | |

Alaska | S-MD.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | High School | |

Arizona | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra | |

Arizona | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra | |

Arizona | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra | |

Arizona | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra | |

Arizona | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra | |

Arizona | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra | |

Arizona | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra | |

Arizona | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra | |

Arizona | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra | |

Arizona | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 | |

Arizona | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 | |

Arizona | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 | |

Arizona | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones - called a 'ten.'. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 | |

Arizona | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols. | Grade 1 | |

Arizona | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 | |

Arizona | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 | |

Arizona | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 | |

Arizona | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) | Grade 1 | |

Arizona | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. | Grade 1 | |

Arizona | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 | |

Arizona | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 | |

Arizona | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 | |

Arizona | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. | Grade 1 | |

Arizona | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 | |

Arizona | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 | |

Arizona | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 | |

Arizona | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 | |

Arizona | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a 'hundred.'. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 | |

Arizona | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 | |

Arizona | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 | |

Arizona | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons. | Grade 2 | |

Arizona | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 | |

Arizona | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 | |

Arizona | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 | |

Arizona | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 | |

Arizona | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 | |

Arizona | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 | |

Arizona | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 | |

Arizona | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 | |

Arizona | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step √±how many more√Æ and √±how many less√Æ problems using information presented in scaled bar graphs. | Grade 3 | |

Arizona | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 | |

Arizona | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 | |

Arizona | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 | |

Arizona | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 | |

Arizona | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 | |

Arizona | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 | |

Arizona | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 _ 80, 5 _ 60) using strategies based on place value and properties of operations. | Grade 3 | |

Arizona | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 | |

Arizona | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 | |

Arizona | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 3 | |

Arizona | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 _ 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 _ 7. | Grade 3 | |

Arizona | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ¬Ö 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ¬Ö 8. | Grade 3 | |

Arizona | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 | |

Arizona | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 _ ? = 48, 5 = _ ¬Ö 3, 6 _ 6 = ? | Grade 3 | |

Arizona | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 _ 4 = 24 is known, then 4 _ 6 = 24 is also known. (Commutative property of multiplication.) 3 _ 5 _ 2 can be found by 3 _ 5 = 15, then 15 _ 2 = 30, or by 5 _ 2 = 10, then 3 _ 10 = 30. (Associative property of multiplication.) Knowing that 8 _ 5 = 40 and 8 _ 2 = 16, one can find 8 _ 7 as 8 _ (5 + 2) = (8 _ 5) + (8 _ 2) = 40 + 16 = 56. (Distributive property.) | Grade 3 | |

Arizona | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32 ¬Ö 8 by finding the number that makes 32 when multiplied by 8. | Grade 3 | |

Arizona | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 _ 5 = 40, one knows 40 ¬Ö 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 | |

Arizona | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 | |

Arizona | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 | |

Arizona | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 | |

Arizona | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 | |

Arizona | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 | |

Arizona | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 | |

Arizona | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 | |

Arizona | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 | |

Arizona | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. | Grade 4 | |

Arizona | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 | |

Arizona | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 | |

Arizona | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 | |

Arizona | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Arizona | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Arizona | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 | |

Arizona | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or | Grade 4 | |

Arizona | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 | |

Arizona | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) / b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 | |

Arizona | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 | |

Arizona | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 | |

Arizona | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 4 | |

Arizona | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 | |

Arizona | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 | |

Arizona | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 ¬Ñ 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 | |

Arizona | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 | |

Arizona | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 | |

Arizona | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 | |

Arizona | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 | |

Arizona | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 | |

Arizona | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 | |

Arizona | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 | |

Arizona | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 | |

Arizona | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 | |

Arizona | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 | |

Arizona | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 | |

Arizona | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 | |

Arizona | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 | |

Arizona | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 | |

Arizona | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 | |

Arizona | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | Grade 5 | |

Arizona | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 | |

Arizona | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 | |

Arizona | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 | |

Arizona | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule √±Add 3√Æ and the starting number 0, and given the rule √±Add 6√Æ and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 | |

Arizona | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 | |

Arizona | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 | |

Arizona | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 | |

Arizona | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 | |

Arizona | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 | |

Arizona | 6.EE.B.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 | |

Arizona | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 | |

Arizona | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 | |

Arizona | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 | |

Arizona | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 | |

Arizona | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 | |

Arizona | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 | |

Arizona | 6.NS.C.7 | Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. | Grade 6 | |

Arizona | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 | |

Arizona | 6.NS.C.9 | Convert between expressions for positive rational numbers, including fractions, decimals, and percents. | Grade 6 | |

Arizona | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 | |

Arizona | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. | Grade 6 | |

Arizona | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 | |

Arizona | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 | |

Arizona | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 | |

Arizona | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 | |

Arizona | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 | |

Arizona | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 | |

Arizona | 7.NS.A.1 | Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. | Grade 7 | |

Arizona | 7.NS.A.2 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. | Grade 7 | |

Arizona | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 | |

Arizona | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/3 hour, compute the unit rate as the complex fraction 1/2 divided by 1/4 per hour, equivalently 2 miles per hour. | Grade 7 | |

Arizona | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 | |

Arizona | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 | |

Arizona | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 | |

Arizona | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 | |

Arizona | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 | |

Arizona | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 | |

Arizona | 8.EE.C.7 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 | |

Arizona | 8.EE.C.8 | Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. | Grade 8 | |

Arizona | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 | |

Arizona | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 | |

Arizona | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 | |

Arizona | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 | |

Arizona | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 | |

Arizona | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 | |

Arizona | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 | |

Arizona | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 | |

Arizona | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 | |

Arizona | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 | |

Arizona | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 | |

Arizona | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 | |

Arizona | K.CC.A.1 | Count to 100 by ones and by tens | Kindergarten | |

Arizona | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten | |

Arizona | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten | |

Arizona | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten | |

Arizona | K.CC.B.5 | Count to answer 'how many' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten | |

Arizona | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten | |

Arizona | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten | |

Arizona | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten | |

Arizona | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten | |

Arizona | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten | |

Arizona | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten | |

Arizona | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten | |

Arizona | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten | |

Arkansas | K.CC.A.1 | Count to 100 by ones, fives, and tens. | Kindergarten | |

Arkansas | K.CC.A.2 | Count forward, by ones, from any given number up to 100. | Kindergarten | |

Arkansas | K.CC.A.3 | Read, write, and represent numerals from 0 to 20. | Kindergarten | |

Arkansas | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten | |

Arkansas | K.CC.B.5 | Count to answer how many; count up to 20 objects in an arrangement, count up to 10 objects in a scattered configuration, given a number from 1-20 count out that many objects. | Kindergarten | |

Arkansas | K.CC.C.6 | Identify whether the number of objects in one group from 0-10 is greater than (more, most), less than (less, fewer, least), or equal to (same as) the number of objects in another group of 0-10. | Kindergarten | |

Arkansas | K.CC.C.7 | Compare two numbers between 0 and 20 presented as written numerals. | Kindergarten | |

Arkansas | K.CC.C.8 | Quickly identify a number of items in a set from 0-10 without counting (e.g., dominoes, dot cubes, tally marks, ten-frames). | Kindergarten | |

Arkansas | K.G.A.1 | Describe the positions of objects in the environment and geometric shapes in space using names of shapes, and describe the relative positions of these objects. | Kindergarten | |

Arkansas | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten | |

Arkansas | K.G.A.3 | Identify shapes as two-dimensional or three-dimensional. | Kindergarten | |

Arkansas | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/‚Äúcorners‚Äù) and other attributes (e.g., having sides of equal length). | Kindergarten | |

Arkansas | K.G.B.5 | Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. | Kindergarten | |

Arkansas | K.G.B.6 | Compose two-dimensional shapes to form larger two-dimensional shapes. | Kindergarten | |

Arkansas | K.MD.A.1 | Describe several measurable attributes of a single object, including but not limited to length, weight, height, and temperature . | Kindergarten | |

Arkansas | K.MD.A.2 | Describe the difference when comparing two objects (side-by-side) with a measurable attribute in common, to see which object has more of or less of the common attribute. | Kindergarten | |

Arkansas | K.MD.B.3 | Classify, sort, and count objects using both measureable and non-measureable attributes such as size, number, color, or shape. | Kindergarten | |

Arkansas | K.MD.C.4 | Understand concepts of time including morning, afternoon, evening, today, yesterday, tomorrow, day, week, month and year. Understand that clocks, both analog and digital, and calendars are tools thatmeasure time. | Kindergarten | |

Arkansas | K.MD.C.5 | Read time to the hour on digital and analog clocks. | Kindergarten | |

Arkansas | K.MD.C.6 | Identify pennies, nickels, and dimes, and know the vlaue of each. | Kindergarten | |

Arkansas | K.NBT.A.1 | Develop initial understanding of place value and the base-ten number system by showing equivalent forms of whole numbers from 11 to 19 as groups of tens and ones using objects and drawings. | Kindergarten | |

Arkansas | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten | |

Arkansas | K.OA.A.2 | Solve real-world problems that involve addition and subtraction within 10 (e.g., by using objects or drawings to represent the problem). | Kindergarten | |

Arkansas | K.OA.A.3 | Use objects or drawings to decompose (break apart) numbers less than or equal to 10 into pairs in more than one way, and record each decomposition (part) by a drawing or an equation. | Kindergarten | |

Arkansas | K.OA.A.4 | Find the number that makes 10 when added to the given number (e.g., by using objects or drawings) and record the answer with a drawing or equation. | Kindergarten | |

Arkansas | K.OA.A.5 | Fluently add and subtract within 10 by using various strategies and manipulatives. | Kindergarten | |

Arkansas | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 | |

Arkansas | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 | |

Arkansas | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 | |

Arkansas | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 | |

Arkansas | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 | |

Arkansas | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 | |

Arkansas | 1.MD.B.4 | Identify and know the value of a penny, nickel, dime and quarter. | Grade 1 | |

Arkansas | 1.MD.B.5 | Count collections of like coins (pennies, nickels, and dimes). | Grade 1 | |

Arkansas | 1.MD.C.6 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 | |

Arkansas | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 | |

Arkansas | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones - called a 'ten.'. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 | |

Arkansas | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols. | Grade 1 | |

Arkansas | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 | |

Arkansas | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 | |

Arkansas | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 | |

Arkansas | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. | Grade 1 | |

Arkansas | 1.OA.A.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 . | Grade 1 | |

Arkansas | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) | Grade 1 | |

Arkansas | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. | Grade 1 | |

Arkansas | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 | |

Arkansas | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 | |

Arkansas | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 | |

Arkansas | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. | Grade 1 | |

Arkansas | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 | |

Arkansas | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 | |

Arkansas | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 | |

Arkansas | 2.G.A.4 | Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 | |

Arkansas | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 | |

Arkansas | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 | |

Arkansas | 2.MD.A.3 | Estimate lengths using units of inches, feet, centimeters, and meters. | Grade 2 | |

Arkansas | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 | |

Arkansas | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 | |

Arkansas | 2.MD.B.6 | Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram. | Grade 2 | |

Arkansas | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 | |

Arkansas | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¬¢ symbols appropriately. | Grade 2 | |

Arkansas | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 | |

Arkansas | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 | |

Arkansas | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a 'hundred.'. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 | |

Arkansas | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 | |

Arkansas | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 | |

Arkansas | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons. | Grade 2 | |

Arkansas | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 | |

Arkansas | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 | |

Arkansas | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 | |

Arkansas | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 | |

Arkansas | 2.NBT.B.9 | Explain why addition and subtraction strategies work, using place value and the properties of operations. | Grade 2 | |

Arkansas | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 | |

Arkansas | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 | |

Arkansas | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 | |

Arkansas | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 | |

Arkansas | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 | |

Arkansas | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 | |

Arkansas | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 | |

Arkansas | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 | |

Arkansas | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ‚Äúhow many more‚Äù and ‚Äúhow many less‚Äù problems using information presented in scaled bar graphs. | Grade 3 | |

Arkansas | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 | |

Arkansas | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 | |

Arkansas | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 | |

Arkansas | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 | |

Arkansas | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 | |

Arkansas | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 | |

Arkansas | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 | |

Arkansas | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 | |

Arkansas | 3.NBT.A.4 | Understand that the four digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones. | Grade 3 | |

Arkansas | 3.NBT.A.5 | Read and write numbers to 10,000 using base-ten numerals, number names, and expanded form(s). | Grade 3 | |

Arkansas | 3.NBT.A.6 | Compare two four-digit numbers based on meanings of thousands, hundreds, tens, and ones digits using symbols (<, >, =) to record the results of comparisons. | Grade 3 | |

Arkansas | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 | |

Arkansas | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 | |

Arkansas | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 3 | |

Arkansas | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. | Grade 3 | |

Arkansas | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. | Grade 3 | |

Arkansas | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 | |

Arkansas | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ? | Grade 3 | |

Arkansas | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) | Grade 3 | |

Arkansas | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. | Grade 3 | |

Arkansas | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 | |

Arkansas | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 | |

Arkansas | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 | |

Arkansas | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 | |

Arkansas | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 | |

Arkansas | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 | |

Arkansas | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 | |

Arkansas | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 | |

Arkansas | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 | |

Arkansas | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 | |

Arkansas | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 | |

Arkansas | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 | |

Arkansas | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 | |

Arkansas | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. | Grade 4 | |

Arkansas | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 | |

Arkansas | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 | |

Arkansas | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 | |

Arkansas | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Arkansas | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Arkansas | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 | |

Arkansas | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 | |

Arkansas | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 | |

Arkansas | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) / b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 | |

Arkansas | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 | |

Arkansas | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 | |

Arkansas | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 | |

Arkansas | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 | |

Arkansas | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 | |

Arkansas | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 | |

Arkansas | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 ‚Äî 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 | |

Arkansas | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 | |

Arkansas | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 | |

Arkansas | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 | |

Arkansas | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 | |

Arkansas | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 | |

Arkansas | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 | |

Arkansas | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 | |

Arkansas | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 | |

Arkansas | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 | |

Arkansas | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 | |

Arkansas | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 | |

Arkansas | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 | |

Arkansas | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 | |

Arkansas | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 | |

Arkansas | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 | |

Arkansas | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 | |

Arkansas | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 | |

Arkansas | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 | |

Arkansas | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 | |

Arkansas | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 | |

Arkansas | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 | |

Arkansas | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | Grade 5 | |

Arkansas | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 | |

Arkansas | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 | |

Arkansas | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 | |

Arkansas | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 | |

Arkansas | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ‚ÄúAdd 3‚Äù and the starting number 0, and given the rule ‚ÄúAdd 6‚Äù and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 | |

Arkansas | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 | |

Arkansas | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 | |

Arkansas | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 | |

Arkansas | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 | |

Arkansas | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 | |

Arkansas | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 | |

Arkansas | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 | |

Arkansas | 6.EE.B.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 | |

Arkansas | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 | |

Arkansas | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Arkansas | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas ùòù = ùò≠ ùò∏ ùò© and ùòù = ùò£ ùò© to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 | |

Arkansas | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 | |

Arkansas | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Arkansas | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 | |

Arkansas | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 | |

Arkansas | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 | |

Arkansas | 6.NS.B.4 | Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1‚Äì100 with a common factor as a multiple of a sum of two whole numbers with no common factor. | Grade 6 | |

Arkansas | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 | |

Arkansas | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 | |

Arkansas | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 | |

Arkansas | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 | |

Arkansas | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 | |

Arkansas | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. | Grade 6 | |

Arkansas | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 | |

Arkansas | 6.SP.A.1 | Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. | Grade 6 | |

Arkansas | 6.SP.A.2 | Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. | Grade 6 | |

Arkansas | 6.SP.A.3 | Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. | Grade 6 | |

Arkansas | 6.SP.B.4 | Display numerical data in plots on a number line, including dot plots, histograms, and box plots. | Grade 6 | |

Arkansas | 6.SP.B.5 | Summarize numerical data sets in relation to their context. | Grade 6 | |

Arkansas | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 | |

Arkansas | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 | |

Arkansas | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 | |

Arkansas | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 | |

Arkansas | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 | |

Arkansas | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 | |

Arkansas | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 | |

Arkansas | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 | |

Arkansas | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 | |

Arkansas | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 | |

Arkansas | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 | |

Arkansas | 7.NS.A.2 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. | Grade 7 | |

Arkansas | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 | |

Arkansas | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/3 hour, compute the unit rate as the complex fraction 1/2 divided by 1/4 per hour, equivalently 2 miles per hour. | Grade 7 | |

Arkansas | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 | |

Arkansas | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 | |

Arkansas | 7.SP.A.1 | Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. | Grade 7 | |

Arkansas | 7.SP.A.2 | Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. | Grade 7 | |

Arkansas | 7.SP.B.3 | Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. | Grade 7 | |

Arkansas | 7.SP.B.4 | Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. | Grade 7 | |

Arkansas | 7.SP.C.5 | Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. | Grade 7 | |

Arkansas | 7.SP.C.6 | Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. | Grade 7 | |

Arkansas | 7.SP.C.7 | Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. | Grade 7 | |

Arkansas | 7.SP.C.8 | Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. | Grade 7 | |

Arkansas | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 | |

Arkansas | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form ùòπ¬≤ = ùò± and ùòπ¬≥ = ùò±, where ùò± is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that ‚àö2 is irrational. | Grade 8 | |

Arkansas | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 | |

Arkansas | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 | |

Arkansas | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 | |

Arkansas | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 | |

Arkansas | 8.EE.C.7 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 | |

Arkansas | 8.EE.C.8 | Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. | Grade 8 | |

Arkansas | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 | |

Arkansas | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 | |

Arkansas | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 | |

Arkansas | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 | |

Arkansas | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 | |

Arkansas | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 | |

Arkansas | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 | |

Arkansas | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 | |

Arkansas | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 | |

Arkansas | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 | |

Arkansas | 8.G.B.6 | Explain a proof of the Pythagorean Theorem and its converse. | Grade 8 | |

Arkansas | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 | |

Arkansas | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 | |

Arkansas | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 | |

Arkansas | 8.NS.A.1 | Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. | Grade 8 | |

Arkansas | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., œÄ¬≤). | Grade 8 | |

Arkansas | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 | |

Arkansas | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 | |

Arkansas | 8.SP.A.3 | Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. | Grade 8 | |

Arkansas | 8.SP.A.4 | Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. | Grade 8 | |

Arkansas | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra | |

Arkansas | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra | |

Arkansas | A-REI.C.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | Algebra | |

Arkansas | A-REI.C.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = ‚Äì3x and the circle x^2 + y^2 = 3. | Algebra | |

Arkansas | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra | |

Arkansas | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra | |

Arkansas | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra | |

Arkansas | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra | |

Arkansas | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra | |

Arkansas | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra | |

Arkansas | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra | |

Arkansas | S-ID.C.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | Algebra | |

California | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten | |

California | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten | |

California | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten | |

California | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten | |

California | K.CC.5 | Count to answer ‚Äúhow many?‚Äù questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten | |

California | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten | |

California | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten | |

California | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten | |

California | K.G.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten | |

California | K.G.3 | Identify shapes as two-dimensional (lying in a plane, ‚Äúflat‚Äù) or three-dimensional (‚Äúsolid‚Äù). | Kindergarten | |

California | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/‚Äúcorners‚Äù) and other attributes (e.g., having sides of equal length). | Kindergarten | |

California | K.G.5 | Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. | Kindergarten | |

California | K.G.6 | Compose simple shapes to form larger shapes. | Kindergarten | |

California | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten | |

California | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has ‚Äúmore of‚Äù/‚Äúless of‚Äù the attribute, and describe the difference. | Kindergarten | |

California | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten | |

California | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten | |

California | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten | |

California | K.OA.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten | |

California | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten | |

California | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten | |

California | K.OA.5 | Fluently add and subtract within 5. | Kindergarten | |

California | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 | |

California | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 | |

California | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 | |

California | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 | |

California | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 | |

California | 1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 | |

California | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 | |

California | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 | |

California | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | Grade 1 | |

California | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 | |

California | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 | |

California | 1.NBT.5 | Grade 1 | ||

California | 1.NBT.6 | Subtract multiples of 10 in the range 10‚Äì90 from multiples of 10 in the range 10‚Äì90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 | |

California | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 | |

California | 1.OA.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 | |

California | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 | |

California | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 | |

California | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 | |

California | 1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 | |

California | 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 | |

California | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 | |

California | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 | |

California | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 | |

California | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 | |

California | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 | |

California | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 | |

California | 2.MD.3 | Estimate lengths using units of inches, feet, centimeters, and meters. | Grade 2 | |

California | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 | |

California | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 | |

California | 2.MD.6 | Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, . . . , and represent whole-number sums and differences within 100 on a number line diagram. | Grade 2 | |

California | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year). | Grade 2 | |

California | 2.MD.8 | Solve word problems involving combinations of dollar bills, quarters, dimes, nickels, and pennies, using $ and ¬¢ symbols appropriately. | Grade 2 | |

California | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 | |

California | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 | |

California | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | Grade 2 | |

California | 2.NBT.2 | Count within 1000; skip-count by 2s, 5s, 10s, and 100s. | Grade 2 | |

California | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 | |

California | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 | |

California | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 | |

California | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 | |

California | 2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 | |

California | 2.NBT.7.1 | Use estimation strategies to make reasonable estimates in problem solving. | Grade 2 | |

California | 2.NBT.8 | Mentally add 10 or 100 to a given number 100‚Äì900, and mentally subtract 10 or 100 from a given number 100‚Äì900. | Grade 2 | |

California | 2.NBT.9 | Explain why addition and subtraction strategies work, using place value and the properties of operations. | Grade 2 | |

California | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 | |

California | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 | |

California | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 | |

California | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 | |

California | 3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 | |

California | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 | |

California | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 | |

California | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 | |

California | 3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ‚Äúhow many more‚Äù and ‚Äúhow many less‚Äù problems using information presented in scaled bar graphs. | Grade 3 | |

California | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 | |

California | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 | |

California | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 | |

California | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 | |

California | 3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 | |

California | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 | |

California | 3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 | |

California | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10‚Äì90 (e.g., 9 √ó 80, 5 √ó 60) using strategies based on place value and properties of operations. | Grade 3 | |

California | 3.NF.1 | Understand a fraction 1/ùò£ as the quantity formed by 1 part when a whole is partitioned into ùò£ equal parts; understand a fraction ùò¢/ùëè as the quantity formed by ùò¢ parts of size 1/ùò£. | Grade 3 | |

California | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 | |

California | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 | |

California | 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 √ó 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 | |

California | 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 √∑ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 | |

California | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 | |

California | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 | |

California | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 | |

California | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 | |

California | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 √ó 5 = 40, one knows 40 √∑ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 | |

California | 3.OA.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 | |

California | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 | |

California | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 | |

California | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two-dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.) | Grade 4 | |

California | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 | |

California | 4.MD.1 | Grade 4 | ||

California | 4.MD.2 | Grade 4 | ||

California | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. | Grade 4 | |

California | 4.MD.4 | Grade 4 | ||

California | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 | |

California | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 | |

California | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 | |

California | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 | |

California | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 | |

California | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 | |

California | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 | |

California | 4.NBT.5 | Grade 4 | ||

California | 4.NBT.6 | Grade 4 | ||

California | 4.NF.1 | Explain why a fraction ùò¢/ùò£ is equivalent to a fraction (ùòØ √ó ùò¢)/(ùòØ √ó ùò£) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 | |

California | 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 | |

California | 4.NF.3 | Understand a fraction ùò¢/ùò£ with ùò¢ > 1 as a sum of fractions 1/ùò£. | Grade 4 | |

California | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 | |

California | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 | |

California | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 | |

California | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model. | Grade 4 | |

California | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 √ó 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 | |

California | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 | |

California | 4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 | |

California | 4.OA.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 | |

California | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 | |

California | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., ùòπ-axis and ùòπ-coordinate, ùò∫-axis and ùò∫-coordinate). | Grade 5 | |

California | 5.G.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 | |

California | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 | |

California | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 | |

California | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. | Grade 5 | |

California | 5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 | |

California | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 | |

California | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 | |

California | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 | |

California | 5.NBT.1 | Grade 5 | ||

California | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 | |

California | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 | |

California | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 | |

California | 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 | |

California | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 | |

California | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 | |

California | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 | |

California | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 | |

California | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (ùò¢/ùò£ = ùò¢ √∑ ùò£). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 | |

California | 5.NF.4 | Grade 5 | ||

California | 5.NF.5 | Interpret multiplication as scaling (resizing), by: | Grade 5 | |

California | 5.NF.6 | Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 | |

California | 5.NF.7 | Grade 5 | ||

California | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 | |

California | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 | |

California | 5.OA.2.1 | Express a whole number in the range 2-50 as a product of its prime factors. | Grade 5 | |

California | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 | |

California | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 | |

California | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 | |

California | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 | |

California | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 | |

California | 6.EE.5 | Grade 6 | ||

California | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 | |

California | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form ùòπ + ùò± = ùò≤ and ùò±ùòπ = ùò≤ for cases in which ùò±, ùò≤ and ùòπ are all nonnegative rational numbers. | Grade 6 | |

California | 6.EE.8 | Write an inequality of the form ùòπ > ùò§ or ùòπ < ùò§ to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form ùòπ > ùò§ or ùòπ < ùò§ have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 | |

California | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 | |

California | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

California | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas ùòù = ùò≠ ùò∏ ùò© and ùòù = ùò£ ùò© to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 | |

California | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

California | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

California | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 | |

California | 6.RP.2 | Understand the concept of a unit rate ùò¢/ùò£ associated with a ratio ùò¢:ùò£ with ùò£ ‚â† 0, and use rate language in the context of a ratio relationship. | Grade 6 | |

California | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 | |

California | 6.SP.1 | Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. | Grade 6 | |

California | 6.SP.2 | Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. | Grade 6 | |

California | 6.SP.3 | Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. | Grade 6 | |

California | 6.SP.4 | Display numerical data in plots on a number line, including dot plots, histograms, and box plots. | Grade 6 | |

California | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 | |

California | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 | |

California | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 | |

California | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 | |

California | 6.NS.4 | Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1‚Äì100 with a common factor as a multiple of a sum of two whole numbers with no common factor. | Grade 6 | |

California | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 | |

California | 6.NS.6 | Grade 6 | ||

California | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 | |

California | 6.NS.8 | Grade 6 | ||

California | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 | |

California | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 | |

California | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 | |

California | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 | |

California | 7.G.1 | Grade 7 | ||

California | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 | |

California | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 | |

California | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 | |

California | 7.G.5 | Grade 7 | ||

California | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 | |

California | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 | |

California | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 | |

California | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 | |

California | 7.SP.1 | Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. | Grade 7 | |

California | 7.SP.2 | Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. | Grade 7 | |

California | 7.SP.3 | Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. | Grade 7 | |

California | 7.SP.4 | Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. | Grade 7 | |

California | 7.SP.5 | Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. | Grade 7 | |

California | 7.SP.6 | Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. | Grade 7 | |

California | 7.SP.7 | Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. | Grade 7 | |

California | 7.SP.8 | Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. | Grade 7 | |

California | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 | |

California | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 | |

California | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 | |

California | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 | |

California | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form ùòπ¬≤ = ùò± and ùòπ¬≥ = ùò±, where ùò± is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that ‚àö2 is irrational. | Grade 8 | |

California | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 | |

California | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 | |

California | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 | |

California | 8.EE.6 | Use similar triangles to explain why the slope ùòÆ is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation ùò∫ = ùòÆùòπ for a line through the origin and the equation ùò∫ = ùòÆùòπ + ùò£ for a line intercepting the vertical axis at ùò£. | Grade 8 | |

California | 8.EE.7 | Solve linear equations in one variable. | Grade 8 | |

California | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 | |

California | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 | |

California | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 | |

California | 8.F.3 | Interpret the equation ùò∫ = ùòÆùòπ + ùò£ as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 | |

California | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (ùòπ, ùò∫) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 | |

California | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 | |

California | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 | |

California | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 | |

California | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 | |

California | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 | |

California | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 | |

California | 8.G.6 | Explain a proof of the Pythagorean Theorem and its converse. | Grade 8 | |

California | 8.G.7 | Grade 8 | ||

California | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 | |

California | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 | |

California | 8.SP.1 | Grade 8 | ||

California | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 | |

California | 8.SP.3 | Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. | Grade 8 | |

California | 8.SP.4 | Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. | Grade 8 | |

California | 8.NS.1 | Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. | Grade 8 | |

California | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., œÄ¬≤). | Grade 8 | |

California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Algebra I | |

California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra I | |

California | A-SSE.3 | Algebra I | ||

California | A-APR.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Algebra I | |

California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. | Algebra I | |

California | A-CED.2 | Algebra I | ||

California | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Algebra I | |

California | A-CED.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Algebra I | |

California | A-REI.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. | Algebra I | |

California | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Algebra I | |

California | A-REI.3.1 | Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. | Algebra I | |

California | A-REI.4 | Solve quadratic equations in one variable. | Algebra I | |

California | A-REI.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | Algebra I | |

California | A-REI.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | Algebra I | |

California | A-REI.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | Algebra I | |

California | A-REI.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). | Algebra I | |

California | A-REI.11 | Explain why the ùòπ-coordinates of the points where the graphs of the equations ùò∫ = ùòß(ùòπ) and ùò∫ = ùëî(ùòπ) intersect are the solutions of the equation ùòß(ùòπ) = ùëî(ùòπ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ùòß(ùòπ) and/or ùëî(ùòπ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Algebra I | |

California | A-REI.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | Algebra I | |

California | F-IF.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ùòß is a function and ùòπ is an element of its domain, then ùòß(ùòπ) denotes the output of ùòß corresponding to the input ùòπ. The graph of ùòß is the graph of the equation ùò∫ = ùòß(ùòπ). | Algebra I | |

California | F-IF.2 | Algebra I | ||

California | F-IF.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | Algebra I | |

California | F-IF.4 | Algebra I | ||

California | F-IF.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Algebra I | |

California | F-IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | Algebra I | |

California | F-IF.7 | Algebra I | ||

California | F-IF.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | Algebra I | |

California | F-IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Algebra I | |

California | F-BF.1 | Write a function that describes a relationship between two quantities. | Algebra I | |

California | F-BF.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | Algebra I | |

California | F-BF.3 | Identify the effect on the graph of replacing ùòß(ùòπ) by ùòß(ùòπ) + ùò¨, ùò¨ ùòß(ùòπ), ùòß(ùò¨ùòπ), and ùòß(ùòπ + ùò¨) for specific values of ùò¨ (both positive and negative); find the value of ùò¨ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Algebra I | |

California | F-BF.4 | Find inverse functions. | Algebra I | |

California | F-LE.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. | Algebra I | |

California | F-LE.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | Algebra I | |

California | F-LE.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | Algebra I | |

California | F-LE.5 | Interpret the parameters in a linear or exponential function in terms of a context. | Algebra I | |

California | F-LE.6 | Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. | Algebra I | |

California | N-RN.1 | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | Algebra I | |

California | N-RN.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | Algebra I | |

California | N-RN.3 | Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | Algebra I | |

California | N-Q.1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | Algebra I | |

California | N-Q.2 | Define appropriate quantities for the purpose of descriptive modeling. | Algebra I | |

California | N-Q.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | Algebra I | |

California | S-ID.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). | Algebra I | |

California | S-ID.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | Algebra I | |

California | S-ID.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | Algebra I | |

California | S-ID.5 | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | Algebra I | |

California | S-ID.6 | Algebra I | ||

California | S-ID.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | Algebra I | |

California | S-ID.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | Algebra I | |

California | S-ID.9 | Distinguish between correlation and causation. | Algebra I | |

California | G-CO.1 | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | Geometry | |

California | G-CO.2 | Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | Geometry | |

California | G-CO.3 | Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | Geometry | |

California | G-CO.4 | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | Geometry | |

California | G-CO.5 | Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. | Geometry | |

California | G-CO.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. | Geometry | |

California | G-CO.7 | Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. | Geometry | |

California | G-CO.8 | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | Geometry | |

California | G-CO.9 | Prove theorems about lines and angles. | Geometry | |

California | G-CO.10 | Prove theorems about triangles. | Geometry | |

California | G-CO.11 | Prove theorems about parallelograms. | Geometry | |

California | G-CO.12 | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). | Geometry | |

California | G-CO.13 | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | Geometry | |

California | G-SRT.1 | Verify experimentally the properties of dilations given by a center and a scale factor: | Geometry | |

California | G-SRT.2 | Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. | Geometry | |

California | G-SRT.3 | Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar. | Geometry | |

California | G-SRT.4 | Prove theorems about triangles. | Geometry | |

California | G-SRT.5 | Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | Geometry | |

California | G-SRT.6 | Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. | Geometry | |

California | G-SRT.7 | Explain and use the relationship between the sine and cosine of complementary angles. | Geometry | |

California | G-SRT.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | Geometry | |

California | G-SRT.8.1 | Derive and use the trigonometric ratios for special right triangles (30¬∞, 60¬∞, 90¬∞ and 45¬∞, 45¬∞, 90¬∞). | Geometry | |

California | G-SRT.9 | Derive the formula ùê¥ = 1/2 ùò¢ùò£ sin(ùê∂) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | Geometry | |

California | G-SRT.10 | Prove the Laws of Sines and Cosines and use them to solve problems. | Geometry | |

California | G-SRT.11 | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). | Geometry | |

California | G-C.1 | Prove that all circles are similar. | Geometry | |

California | G-C.2 | Identify and describe relationships among inscribed angles, radii, and chords. | Geometry | |

California | G-C.3 | Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | Geometry | |

California | G-C.4 | Construct a tangent line from a point outside a given circle to the circle. | Geometry | |

California | G-C.5 | Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. | Geometry | |

California | G-GPE.1 | Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | Geometry | |

California | G-GPE.2 | Derive the equation of a parabola given a focus and directrix. | Geometry | |

California | G-GPE.4 | Use coordinates to prove simple geometric theorems algebraically. | Geometry | |

California | G-GPE.5 | Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | Geometry | |

California | G-GPE.6 | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | Geometry | |

California | G-GPE.7 | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. | Geometry | |

California | G-GMD.1 | Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. | Geometry | |

California | G-GMD.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | Geometry | |

California | G-GMD.4 | Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | Geometry | |

California | G-GMD.5 | Know that the effect of a scale factor ùëò greater than zero on length, area, and volume is to multiply each by ùëò, ùëò¬≤, and ùëò¬≥, respectively; determine length, area and volume measures using scale factors. | Geometry | |

California | G-GMD.6 | Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real-world and mathematical problems. | Geometry | |

California | G-MG.1 | Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | Geometry | |

California | G-MG.2 | Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). | Geometry | |

California | G-MG.3 | Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). | Geometry | |

California | S-CP.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (‚Äúor,‚Äù ‚Äúand,‚Äù ‚Äúnot‚Äù). | Geometry | |

California | S-CP.2 | Understand that two events ùòà and ùòâ are independent if the probability of ùòà and ùòâ occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | Geometry | |

California | S-CP.3 | Understand the conditional probability of ùòà given ùòâ as ùòó(ùòà and ùòâ)/ùòó(ùòâ), and interpret independence of ùòà and ùòâ as saying that the conditional probability of ùòà given ùòâ is the same as the probability of ùòà, and the conditional probability of ùòâ given ùòà is the same as the probability of ùòâ. | Geometry | |

California | S-CP.4 | Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | Geometry | |

California | S-CP.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | Geometry | |

California | S-CP.6 | Find the conditional probability of ùòà given ùòâ as the fraction of ùòâ‚Äôs outcomes that also belong to ùòà, and interpret the answer in terms of the model. | Geometry | |

California | S-CP.7 | Apply the Addition Rule, ùòó(ùòà or ùòâ) = ùòó(ùòà) + ùòó(ùòâ) ‚Äì ùòó(ùòà and ùòâ), and interpret the answer in terms of the model. | Geometry | |

California | S-CP.8 | Apply the general Multiplication Rule in a uniform probability model, ùòó(ùòà and ùòâ) = ùòó(ùòà)ùòó(ùòâ|ùòà) = ùòó(ùòâ)ùòó(ùòà|ùòâ), and interpret the answer in terms of the model. | Geometry | |

California | S-CP.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. | Geometry | |

California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Geometry | |

California | S-MD.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | Geometry | |

California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Algebra II | |

California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra II | |

California | A-SSE.4 | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | Algebra II | |

California | A-APR.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Algebra II | |

California | A-APR.2 | Know and apply the Remainder Theorem: For a polynomial ùò±(ùòπ) and a number ùò¢, the remainder on division by ùòπ ‚Äì ùò¢ is ùò±(ùò¢), so ùò±(ùò¢) = 0 if and only if (ùòπ ‚Äì ùò¢) is a factor of ùò±(ùòπ). | Algebra II | |

California | A-APR.3 | Algebra II | ||

California | A-APR.4 | Prove polynomial identities and use them to describe numerical relationships. | Algebra II | |

California | A-APR.5 | Know and apply the Binomial Theorem for the expansion of (ùòπ + ùò∫)‚Åø in powers of ùòπ and y for a positive integer ùòØ, where ùòπ and ùò∫ are any numbers, with coefficients determined for example by Pascal‚Äôs Triangle. | Algebra II | |

California | A-APR.6 | Rewrite simple rational expressions in different forms; write ùò¢(ùòπ)/ùò£(ùòπ) in the form ùò≤(ùòπ) + ùò≥(ùòπ)/ùò£(ùòπ), where ùò¢(ùòπ), ùò£(ùòπ), ùò≤(ùòπ), and ùò≥(ùòπ) are polynomials with the degree of ùò≥(ùòπ) less than the degree of ùò£(ùòπ), using inspection, long division, or, for the more complicated examples, a computer algebra system. | Algebra II | |

California | A-APR.7 | Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. | Algebra II | |

California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. | Algebra II | |

California | A-CED.2 | Algebra II | ||

California | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Algebra II | |

California | A-CED.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Algebra II | |

California | A-REI.2 | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | Algebra II | |

California | A-REI.3.1 | Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. | Algebra II | |

California | A-REI.11 | Explain why the ùòπ-coordinates of the points where the graphs of the equations ùò∫ = ùòß(ùòπ) and ùò∫ = ùëî(ùòπ) intersect are the solutions of the equation ùòß(ùòπ) = ùëî(ùòπ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ùòß(ùòπ) and/or ùëî(ùòπ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Algebra II | |

California | F-IF.4 | Algebra II | ||

California | F-IF.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | Algebra II | |

California | F-IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | Algebra II | |

California | F-IF.7 | Algebra II | ||

California | F-IF.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | Algebra II | |

California | F-IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Algebra II | |

California | F-BF.1 | Write a function that describes a relationship between two quantities. | Algebra II | |

California | F-BF.3 | Identify the effect on the graph of replacing ùòß(ùòπ) by ùòß(ùòπ) + ùò¨, ùò¨ ùòß(ùòπ), ùòß(ùò¨ùòπ), and ùòß(ùòπ + ùò¨) for specific values of ùò¨ (both positive and negative); find the value of ùò¨ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Algebra II | |

California | F-BF.4 | Find inverse functions. | Algebra II | |

California | F-LE.4 | For exponential models, express as a logarithm the solution to ùò¢ùò£ to the ùò§ùòµ power = ùò• where ùò¢, ùò§, and ùò• are numbers and the base ùò£ is 2, 10, or ùò¶; evaluate the logarithm using technology. | Algebra II | |

California | F-LE.4.1 | Prove simple laws of logarithms. | Algebra II | |

California | F-LE.4.2 | Use the definition of logarithms to translate between logarithms in any base. | Algebra II | |

California | F-LE.4.3 | Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. | Algebra II | |

California | F-TF.1 | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | Algebra II | |

California | F-TF.2 | Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | Algebra II | |

California | F-TF.2.1 | Graph all 6 basic trigonometric functions. | Algebra II | |

California | F-TF.5 | Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. | Algebra II | |

California | F-TF.8 | Prove the Pythagorean identity sin¬≤(Œ∏) + cos¬≤(Œ∏) = 1 and use it to find sin(Œ∏), cos(Œ∏), or tan(Œ∏) given sin(Œ∏), cos(Œ∏), or tan(Œ∏) and the quadrant of the angle. | Algebra II | |

California | G-GPE.3.1 | Given a quadratic equation of the form ax¬≤ + by2 + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola, and graph the equation. | Algebra II | |

California | N-CN.1 | Know there is a complex number ùò™ such that ùò™¬≤ = ‚Äì1, and every complex number has the form ùò¢ + ùò£ùò™ with ùò¢ and ùò£ real. | Algebra II | |

California | N-CN.2 | Use the relation ùò™¬≤ = ‚Äì1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | Algebra II | |

California | N-CN.7 | Solve quadratic equations with real coefficients that have complex solutions. | Algebra II | |

California | N-CN.8 | Extend polynomial identities to the complex numbers. | Algebra II | |

California | N-CN.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | Algebra II | |

California | S-ID.4 | Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | Algebra II | |

California | S-IC.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | Algebra II | |

California | S-IC.2 | Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. | Algebra II | |

California | S-IC.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | Algebra II | |

California | S-IC.4 | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | Algebra II | |

California | S-IC.5 | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | Algebra II | |

California | S-IC.6 | Evaluate reports based on data. | Algebra II | |

California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Algebra II | |

California | S-MD.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | Algebra II | |

California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Mathematics I | |

California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. | Mathematics I | |

California | A-CED.2 | Mathematics I | ||

California | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Mathematics I | |

California | A-CED.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | Mathematics I | |

California | A-REI.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. | Mathematics I | |

California | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Mathematics I | |

California | A-REI.3.1 | Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. | Mathematics I | |

California | A-REI.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | Mathematics I | |

California | A-REI.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | Mathematics I | |

California | A-REI.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). | Mathematics I | |

California | A-REI.11 | Explain why the ùòπ-coordinates of the points where the graphs of the equations ùò∫ = ùòß(ùòπ) and ùò∫ = ùëî(ùòπ) intersect are the solutions of the equation ùòß(ùòπ) = ùëî(ùòπ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ùòß(ùòπ) and/or ùëî(ùòπ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | Mathematics I | |

California | A-REI.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | Mathematics I | |

California | F-IF.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ùòß is a function and ùòπ is an element of its domain, then ùòß(ùòπ) denotes the output of ùòß corresponding to the input ùòπ. The graph of ùòß is the graph of the equation ùò∫ = ùòß(ùòπ). | Mathematics I | |

California | F-IF.2 | Mathematics I | ||

California | F-IF.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | Mathematics I | |

California | F-IF.4 | Mathematics I | ||

California | F-IF.5 | Mathematics I | ||

California | F-IF.6 | Mathematics I | ||

California | F-IF.7 | Mathematics I | ||

California | F-IF.9 | Mathematics I | ||

California | F-BF.1 | Write a function that describes a relationship between two quantities. | Mathematics I | |

California | F-BF.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | Mathematics I | |

California | F-BF.3 | Identify the effect on the graph of replacing ùòß(ùòπ) by ùòß(ùòπ) + ùò¨, ùò¨ ùòß(ùòπ), ùòß(ùò¨ùòπ), and ùòß(ùòπ + ùò¨) for specific values of ùò¨ (both positive and negative); find the value of ùò¨ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. | Mathematics I | |

California | F-LE.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. | Mathematics I | |

California | F-LE.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | Mathematics I | |

California | F-LE.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | Mathematics I | |

California | F-LE.5 | Interpret the parameters in a linear or exponential function in terms of a context. | Mathematics I | |

California | G-CO.1 | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | Mathematics I | |

California | G-CO.2 | Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | Mathematics I | |

California | G-CO.3 | Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | Mathematics I | |

California | G-CO.4 | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | Mathematics I | |

California | G-CO.5 | Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. | Mathematics I | |

California | G-CO.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. | Mathematics I | |

California | G-CO.7 | Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. | Mathematics I | |

California | G-CO.8 | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | Mathematics I | |

California | G-CO.12 | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). | Mathematics I | |

California | G-CO.13 | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | Mathematics I | |

California | G-GPE.4 | Use coordinates to prove simple geometric theorems algebraically. | Mathematics I | |

California | G-GPE.5 | Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | Mathematics I | |

California | G-GPE.7 | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. | Mathematics I | |

California | N-Q.1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | Mathematics I | |

California | N-Q.2 | Define appropriate quantities for the purpose of descriptive modeling. | Mathematics I | |

California | N-Q.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | Mathematics I | |

California | S-ID.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). | Mathematics I | |

California | S-ID.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | Mathematics I | |

California | S-ID.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | Mathematics I | |

California | S-ID.5 | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | Mathematics I | |

California | S-ID.6 | Mathematics I | ||

California | S-ID.7 | Mathematics I | ||

California | S-ID.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | Mathematics I | |

California | S-ID.9 | Distinguish between correlation and causation. | Mathematics I | |

California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Mathematics II | |

California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | Mathematics II | |

California | A-SSE.3 | Mathematics II | ||

California | A-APR.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | Mathematics II | |

California | A-CED.1 | Mathematics II | ||

California | A-CED.2 | Mathematics II | ||

California | A-CED.4 | Mathematics II | ||

California | A-REI.4 | Solve quadratic equations in one variable. | Mathematics II | |

California | A-REI.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | Mathematics II | |

California | F-IF.4 | Mathematics II | ||

California | F-IF.5 | Mathematics II | ||

California | F-IF.6 | Mathematics II | ||

California | F-IF.7 | Mathematics II | ||

California | F-IF.8 | Mathematics II | ||

California | F-IF.9 | Mathematics II | ||

California | F-BF.1 | Write a function that describes a relationship between two quantities. | Mathematics II | |

California | F-BF.3 | Mathematics II | ||

California | F-BF.4 | Find inverse functions. | Mathematics II | |

California | F-LE.3 | Mathematics II | ||

California | F-LE.6 | Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. | Mathematics II | |

California | F-TF.8 | Prove the Pythagorean identity sin¬≤(Œ∏) + cos¬≤(Œ∏) = 1 and use it to find sin(Œ∏), cos(Œ∏), or tan(Œ∏) given sin(Œ∏), cos(Œ∏), or tan(Œ∏) and the quadrant of the angle. | Mathematics II | |

California | G-CO.9 | Prove theorems about lines and angles. | Mathematics II | |

California | G-CO.10 | Prove theorems about triangles. | Mathematics II | |

California | G-CO.11 | Prove theorems about parallelograms. | Mathematics II | |

California | G-SRT.1 | Verify experimentally the properties of dilations given by a center and a scale factor: | Mathematics II | |

California | G-SRT.2 | Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. | Mathematics II | |

California | G-SRT.3 | Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar. | Mathematics II | |

California | G-SRT.4 | Prove theorems about triangles. | Mathematics II | |

California | G-SRT.5 | Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | Mathematics II | |

California | G-SRT.6 | Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. | Mathematics II | |

California | G-SRT.7 | Explain and use the relationship between the sine and cosine of complementary angles. | Mathematics II | |

California | G-SRT.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | Mathematics II | |

California | G-SRT.8.1 | Derive and use the trigonometric ratios for special right triangles (30¬∞, 60¬∞, 90¬∞ and 45¬∞, 45¬∞, 90¬∞). | Mathematics II | |

California | G-C.1 | Prove that all circles are similar. | Mathematics II | |

California | G-C.2 | Identify and describe relationships among inscribed angles, radii, and chords. | Mathematics II | |

California | G-C.3 | Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | Mathematics II | |

California | G-C.4 | Construct a tangent line from a point outside a given circle to the circle. | Mathematics II | |

California | G-C.5 | Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. | Mathematics II | |

California | G-GPE.1 | Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | Mathematics II | |

California | G-GPE.2 | Derive the equation of a parabola given a focus and directrix. | Mathematics II | |

California | G-GPE.4 | Use coordinates to prove simple geometric theorems algebraically. | Mathematics II | |

California | G-GPE.6 | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | Mathematics II | |

California | G-GMD.1 | Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. | Mathematics II | |

California | G-GMD.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | Mathematics II | |

California | G-GMD.5 | Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k¬≤, and k¬≥, respectively; determine length, area and volume measures using scale factors. | Mathematics II | |

California | G-GMD.6 | Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real-world and mathematical problems. | Mathematics II | |

California | N-RN.1 | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | Mathematics II | |

California | N-RN.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | Mathematics II | |

California | N-RN.3 | Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | Mathematics II | |

California | N-CN.1 | Know there is a complex number ùò™ such that ùò™¬≤ = ‚Äì1, and every complex number has the form ùò¢ + ùò£ùò™ with ùò¢ and ùò£ real. | Mathematics II | |

California | N-CN.2 | Use the relation ùò™¬≤ = ‚Äì1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | Mathematics II | |

California | N-CN.7 | Solve quadratic equations with real coefficients that have complex solutions. | Mathematics II | |

California | N-CN.8 | Extend polynomial identities to the complex numbers. | Mathematics II | |

California | N-CN.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | Mathematics II | |

California | S-CP.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (‚Äúor,‚Äù ‚Äúand,‚Äù ‚Äúnot‚Äù). | Mathematics II | |

California | S-CP.2 | Understand that two events ùòà and ùòâ are independent if the probability of ùòà and ùòâ occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | Mathematics II | |

California | S-CP.3 | Understand the conditional probability of ùòà given ùòâ as ùòó(ùòà and ùòâ)/ùòó(ùòâ), and interpret independence of ùòà and ùòâ as saying that the conditional probability of ùòà given ùòâ is the same as the probability of ùòà, and the conditional probability of ùòâ given ùòà is the same as the probability of ùòâ. | Mathematics II | |

California | S-CP.4 | Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | Mathematics II | |

California | S-CP.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | Mathematics II | |

California | S-CP.6 | Find the conditional probability of ùòà given ùòâ as the fraction of ùòâ‚Äôs outcomes that also belong to ùòà, and interpret the answer in terms of the model. | Mathematics II | |

California | S-CP.7 | Apply the Addition Rule, ùòó(ùòà or ùòâ) = ùòó(ùòà) + ùòó(ùòâ) ‚Äì ùòó(ùòà and ùòâ), and interpret the answer in terms of the model. | Mathematics II | |

California | S-CP.8 | Apply the general Multiplication Rule in a uniform probability model, ùòó(ùòà and ùòâ) = ùòó(ùòà)ùòó(ùòâ|ùòà) = ùòó(ùòâ)ùòó(ùòà|ùòâ), and interpret the answer in terms of the model. | Mathematics II | |

California | S-CP.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. | Mathematics II | |

California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Mathematics II | |

California | S-MD.7 | Mathematics II | ||

California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | Mathematics III | |

California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | Mathematics III | |

California | A-SSE.4 | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | Mathematics III | |

California | A-APR.1 | Mathematics III | ||

California | A-APR.2 | Know and apply the Remainder Theorem: For a polynomial ùò±(ùòπ) and a number ùò¢, the remainder on division by ùòπ ‚Äì ùò¢ is ùò±(ùò¢), so ùò±(ùò¢) = 0 if and only if (ùòπ ‚Äì ùò¢) is a factor of ùò±(ùòπ). | Mathematics III | |

California | A-APR.3 | Mathematics III | ||

California | A-APR.4 | Prove polynomial identities and use them to describe numerical relationships. | Mathematics III | |

California | A-APR.5 | Know and apply the Binomial Theorem for the expansion of (ùòπ + ùò∫)‚Åø in powers of ùòπ and y for a positive integer ùòØ, where ùòπ and ùò∫ are any numbers, with coefficients determined for example by Pascal‚Äôs Triangle. | Mathematics III | |

California | A-APR.6 | Rewrite simple rational expressions in different forms; write ùò¢(ùòπ)/ùò£(ùòπ) in the form ùò≤(ùòπ) + ùò≥(ùòπ)/ùò£(ùòπ), where ùò¢(ùòπ), ùò£(ùòπ), ùò≤(ùòπ), and ùò≥(ùòπ) are polynomials with the degree of ùò≥(ùòπ) less than the degree of ùò£(ùòπ), using inspection, long division, or, for the more complicated examples, a computer algebra system. | Mathematics III | |

California | A-APR.7 | Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. | Mathematics III | |

California | A-CED.1 | Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. | Mathematics III | |

California | A-CED.2 | Mathematics III | ||

California | A-CED.3 | Mathematics III | ||

California | A-CED.4 | Mathematics III | ||

California | A-REI.2 | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | Mathematics III | |

California | A-REI.11 | Mathematics III | ||

California | F-IF.4 | Mathematics III | ||

California | F-IF.5 | Mathematics III | ||

California | F-IF.6 | Mathematics III | ||

California | F-IF.7 | Mathematics III | ||

California | F-IF.8 | Mathematics III | ||

California | F-IF.9 | Mathematics III | ||

California | F-BF.1 | Write a function that describes a relationship between two quantities. | Mathematics III | |

California | F-BF.3 | Mathematics III | ||

California | F-BF.4 | Find inverse functions. | Mathematics III | |

California | F-LE.4 | For exponential models, express as a logarithm the solution to ùò¢ùò£ to the ùò§ùòµ power = ùò• where ùò¢, ùò§, and ùò• are numbers and the base ùò£ is 2, 10, or ùò¶; evaluate the logarithm using technology. | Mathematics III | |

California | F-LE.4.1 | Prove simple laws of logarithms. | Mathematics III | |

California | F-LE.4.2 | Use the definition of logarithms to translate between logarithms in any base. | Mathematics III | |

California | F-LE.4.3 | Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. | Mathematics III | |

California | F-TF.1 | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | Mathematics III | |

California | F-TF.2 | Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | Mathematics III | |

California | F-TF.2.1 | Graph all 6 basic trigonometric functions. | Mathematics III | |

California | F-TF.5 | Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. | Mathematics III | |

California | G-SRT.9 | Derive the formula ùê¥ = 1/2 ùò¢ùò£ sin(ùê∂) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | Mathematics III | |

California | G-SRT.10 | Prove the Laws of Sines and Cosines and use them to solve problems. | Mathematics III | |

California | G-SRT.11 | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). | Mathematics III | |

California | G-GPE.3.1 | Given a quadratic equation of the form ax¬≤ + by¬≤ + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola, and graph the equation | Mathematics III | |

California | G-GMD.4 | Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | Mathematics III | |

California | G-MG.1 | Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | Mathematics III | |

California | G-MG.2 | Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). | Mathematics III | |

California | G-MG.3 | Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). | Mathematics III | |

California | N-CN.8 | Extend polynomial identities to the complex numbers. | Mathematics III | |

California | N-CN.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | Mathematics III | |

California | S-ID.4 | Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | Mathematics III | |

California | S-IC.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | Mathematics III | |

California | S-IC.2 | Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. | Mathematics III | |

California | S-IC.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | Mathematics III | |

California | S-IC.4 | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | Mathematics III | |

California | S-IC.5 | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | Mathematics III | |

California | S-IC.6 | Evaluate reports based on data. | Mathematics III | |

California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | Mathematics III | |

California | S-MD.7 | Mathematics III | ||

California | N-Q.1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | High School - Number and Quantity | |

California | N-Q.2 | Define appropriate quantities for the purpose of descriptive modeling. | High School - Number and Quantity | |

California | N-Q.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | High School - Number and Quantity | |

California | N-CN.1 | Know there is a complex number ùò™ such that ùò™¬≤ = ‚Äì1, and every complex number has the form ùò¢ + ùò£ùò™ with ùò¢ and ùò£ real. | High School - Number and Quantity | |

California | N-CN.2 | Use the relation ùò™¬≤ = ‚Äì1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | High School - Number and Quantity | |

California | N-CN.3 | Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. | High School - Number and Quantity | |

California | N-CN.4 | Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. | High School - Number and Quantity | |

California | N-CN.5 | Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. | High School - Number and Quantity | |

California | N-CN.6 | Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. | High School - Number and Quantity | |

California | N-CN.7 | Solve quadratic equations with real coefficients that have complex solutions. | High School - Number and Quantity | |

California | N-CN.8 | Extend polynomial identities to the complex numbers. | High School - Number and Quantity | |

California | N-CN.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | High School - Number and Quantity | |

California | N-RN.1 | High School - Number and Quantity | ||

California | N-RN.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | High School - Number and Quantity | |

California | N-RN.3 | High School - Number and Quantity | ||

California | N-VM.1 | Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., ùô´, |ùô´|, ||ùô´||, ùô´). | High School - Number and Quantity | |

California | N-VM.2 | Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. | High School - Number and Quantity | |

California | N-VM.3 | Solve problems involving velocity and other quantities that can be represented by vectors. | High School - Number and Quantity | |

California | N-VM.4 | Add and subtract vectors. | High School - Number and Quantity | |

California | N-VM.5 | Multiply a vector by a scalar. | High School - Number and Quantity | |

California | N-VM.6 | Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. | High School - Number and Quantity | |

California | N-VM.7 | Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. | High School - Number and Quantity | |

California | N-VM.8 | Add, subtract, and multiply matrices of appropriate dimensions. | High School - Number and Quantity | |

California | N-VM.9 | Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. | High School - Number and Quantity | |

California | N-VM.10 | Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. | High School - Number and Quantity | |

California | N-VM.11 | Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. | High School - Number and Quantity | |

California | N-VM.12 | Work with 2 √ó 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. | High School - Number and Quantity | |

California | A-APR.1 | High School - Algebra | ||

California | A-APR.2 | Know and apply the Remainder Theorem: For a polynomial ùò±(ùòπ) and a number ùò¢, the remainder on division by ùòπ ‚Äì ùò¢ is ùò±(ùò¢), so ùò±(ùò¢) = 0 if and only if (ùòπ ‚Äì ùò¢) is a factor of ùò±(ùòπ). | High School - Algebra | |

California | A-APR.3 | High School - Algebra | ||

California | A-APR.4 | Prove polynomial identities and use them to describe numerical relationships. | High School - Algebra | |

California | A-APR.5 | Know and apply the Binomial Theorem for the expansion of (ùòπ + ùò∫)‚Åø in powers of ùòπ and y for a positive integer ùòØ, where ùòπ and ùò∫ are any numbers, with coefficients determined for example by Pascal‚Äôs Triangle. | High School - Algebra | |

California | A-APR.6 | Rewrite simple rational expressions in different forms; write ùò¢(ùòπ)/ùò£(ùòπ) in the form ùò≤(ùòπ) + ùò≥(ùòπ)/ùò£(ùòπ), where ùò¢(ùòπ), ùò£(ùòπ), ùò≤(ùòπ), and ùò≥(ùòπ) are polynomials with the degree of ùò≥(ùòπ) less than the degree of ùò£(ùòπ), using inspection, long division, or, for the more complicated examples, a computer algebra system. | High School - Algebra | |

California | A-APR.7 | Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. | High School - Algebra | |

California | A-CED.1 | High School - Algebra | ||

California | A-CED.2 | High School - Algebra | ||

California | A-CED.3 | High School - Algebra | ||

California | A-CED.4 | High School - Algebra | ||

California | A-REI.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. | High School - Algebra | |

California | A-REI.2 | High School - Algebra | ||

California | A-REI.3 | High School - Algebra | ||

California | A-REI.3.1 | High School - Algebra | ||

California | A-REI.4 | Solve quadratic equations in one variable. | High School - Algebra | |

California | A-REI.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | High School - Algebra | |

California | A-REI.6 | High School - Algebra | ||

California | A-REI.7 | High School - Algebra | ||

California | A-REI.8 | Represent a system of linear equations as a single matrix equation in a vector variable. | High School - Algebra | |

California | A-REI.9 | Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 √ó 3 or greater). | High School - Algebra | |

California | A-REI.10 | High School - Algebra | ||

California | A-REI.11 | High School - Algebra | ||

California | A-REI.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | High School - Algebra | |

California | A-SSE.1 | Interpret expressions that represent a quantity in terms of its context. | High School - Algebra | |

California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School - Algebra | |

California | A-SSE.3 | High School - Algebra | ||

California | A-SSE.4 | High School - Algebra | ||

California | F-BF.1 | Write a function that describes a relationship between two quantities. | High School - Functions | |

California | F-BF.2 | High School - Functions | ||

California | F-BF.3 | High School - Functions | ||

California | F-BF.4 | Find inverse functions. | High School - Functions | |

California | F-BF.5 | Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. | High School - Functions | |

California | F-IF.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ùòß is a function and ùòπ is an element of its domain, then ùòß(ùòπ) denotes the output of ùòß corresponding to the input ùòπ. The graph of ùòß is the graph of the equation ùò∫ = ùòß(ùòπ). | High School - Functions | |

California | F-IF.2 | High School - Functions | ||

California | F-IF.3 | High School - Functions | ||

California | F-IF.4 | High School - Functions | ||

California | F-IF.5 | High School - Functions | ||

California | F-IF.6 | High School - Functions | ||

California | F-IF.7 | High School - Functions | ||

California | F-IF.8 | High School - Functions | ||

California | F-IF.9 | High School - Functions | ||

California | F-IF.10 | Demonstrate an understanding of functions and equations defined parametrically and graph them. | High School - Functions | |

California | F-IF.11 | Graph polar coordinates and curves. Convert between polar and rectangular coordinate systems. | High School - Functions | |

California | F-LE.1 | High School - Functions | ||

California | F-LE.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | High School - Functions | |

California | F-LE.3 | High School - Functions | ||

California | F-LE.4 | For exponential models, express as a logarithm the solution to ùò¢ùò£ to the ùò§ùòµ power = ùò• where ùò¢, ùò§, and ùò• are numbers and the base ùò£ is 2, 10, or ùò¶; evaluate the logarithm using technology. | High School - Functions | |

California | F-LE.4.1 | Prove simple laws of logarithms. | High School - Functions | |

California | F-LE.4.2 | Use the definition of logarithms to translate between logarithms in any base. | High School - Functions | |

California | F-LE.4.3 | Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. | High School - Functions | |

California | F-LE.5 | Interpret the parameters in a linear or exponential function in terms of a context. | High School - Functions | |

California | F-LE.6 | Apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. | High School - Functions | |

California | F-TF.1 | High School - Functions | ||

California | F-TF.2 | High School - Functions | ||

California | F-TF.2.1 | Graph all 6 basic trigonometric functions. | High School - Functions | |

California | F-TF.3 | Use special triangles to determine geometrically the values of sine, cosine, tangent for œÄ/3, œÄ/4 and œÄ/6, and use the unit circle to express the values of sine, cosine, and tangent for œÄ‚Äìùòπ, œÄ+ùòπ, and 2œÄ‚Äìùòπ in terms of their values for ùòπ, where ùòπ is any real number. | High School - Functions | |

California | F-TF.4 | Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. | High School - Functions | |

California | F-TF.5 | High School - Functions | ||

California | F-TF.6 | Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. | High School - Functions | |

California | F-TF.7 | Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. | High School - Functions | |

California | F-TF.8 | Prove the Pythagorean identity sin¬≤(Œ∏) + cos¬≤(Œ∏) = 1 and use it to find sin(Œ∏), cos(Œ∏), or tan(Œ∏) given sin(Œ∏), cos(Œ∏), or tan(Œ∏) and the quadrant of the angle. | High School - Functions | |

California | F-TF.9 | Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. | High School - Functions | |

California | F-TF.10 | Prove the half angle and double angle identities for sine and cosine and use them to solve problems. | High School - Functions | |

California | G-C.1 | Prove that all circles are similar. | High School - Geometry | |

California | G-C.2 | Identify and describe relationships among inscribed angles, radii, and chords. | High School - Geometry | |

California | G-C.3 | High School - Geometry | ||

California | G-C.4 | Construct a tangent line from a point outside a given circle to the circle. | High School - Geometry | |

California | G-C.5 | Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. | High School - Geometry | |

California | G-CO.1 | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | High School - Geometry | |

California | G-CO.2 | High School - Geometry | ||

California | G-CO.3 | High School - Geometry | ||

California | G-CO.4 | High School - Geometry | ||

California | G-CO.5 | High School - Geometry | ||

California | G-CO.6 | High School - Geometry | ||

California | G-CO.7 | High School - Geometry | ||

California | G-CO.8 | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | High School - Geometry | |

California | G-CO.9 | Prove theorems about lines and angles. | High School - Geometry | |

California | G-CO.10 | Prove theorems about triangles. | High School - Geometry | |

California | G-CO.11 | Prove theorems about parallelograms. | High School - Geometry | |

California | G-CO.12 | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). | High School - Geometry | |

California | G-CO.13 | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | High School - Geometry | |

California | G-GPE.1 | Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | High School - Geometry | |

California | G-GPE.2 | Derive the equation of a parabola given a focus and directrix. | High School - Geometry | |

California | G-GPE.3 | Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. | High School - Geometry | |

California | G-GPE.3.1 | Given a quadratic equation of the form ax¬≤ + by¬≤ + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola, and graph the equation. | High School - Geometry | |

California | G-GPE.4 | Use coordinates to prove simple geometric theorems algebraically. | High School - Geometry | |

California | G-GPE.5 | High School - Geometry | ||

California | G-GPE.6 | High School - Geometry | ||

California | G-GPE.7 | High School - Geometry | ||

California | G-GMD.1 | Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. | High School - Geometry | |

California | G-GMD.2 | Give an informal argument using Cavalieri‚Äôs principle for the formulas for the volume of a sphere and other solid figures. | High School - Geometry | |

California | G-GMD.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | High School - Geometry | |

California | G-GMD.4 | Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | High School - Geometry | |

California | G-GMD.5 | Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k¬≤, and k¬≥, respectively; determine length, area and volume measures using scale factors. | High School - Geometry | |

California | G-GMD.6 | Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real-world and mathematical problems. | High School - Geometry | |

California | G-MG.1 | High School - Geometry | ||

California | G-MG.2 | High School - Geometry | ||

California | G-MG.3 | High School - Geometry | ||

California | G-SRT.1 | Verify experimentally the properties of dilations given by a center and a scale factor: | High School - Geometry | |

California | G-SRT.2 | Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. | High School - Geometry | |

California | G-SRT.3 | Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. | High School - Geometry | |

California | G-SRT.4 | Prove theorems about triangles. | High School - Geometry | |

California | G-SRT.5 | Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | High School - Geometry | |

California | G-SRT.6 | High School - Geometry | ||

California | G-SRT.7 | Explain and use the relationship between the sine and cosine of complementary angles. | High School - Geometry | |

California | G-SRT.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | High School - Geometry | |

California | G-SRT.8.1 | Derive and use the trigonometric ratios for special right triangles (30¬∞, 60¬∞, 90¬∞ and 45¬∞, 45¬∞, 90¬∞). | High School - Geometry | |

California | G-SRT.9 | Derive the formula ùê¥ = 1/2 ùò¢ùò£ sin(ùê∂) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | High School - Geometry | |

California | G-SRT.10 | Prove the Laws of Sines and Cosines and use them to solve problems. | High School - Geometry | |

California | G-SRT.11 | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). | High School - Geometry | |

California | S-CP.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (‚Äúor,‚Äù ‚Äúand,‚Äù ‚Äúnot‚Äù). | High School - Statistics and Probability | |

California | S-CP.2 | Understand that two events ùòà and ùòâ are independent if the probability of ùòà and ùòâ occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | High School - Statistics and Probability | |

California | S-CP.3 | Understand the conditional probability of ùòà given ùòâ as ùòó(ùòà and ùòâ)/ùòó(ùòâ), and interpret independence of ùòà and ùòâ as saying that the conditional probability of ùòà given ùòâ is the same as the probability of ùòà, and the conditional probability of ùòâ given ùòà is the same as the probability of ùòâ. | High School - Statistics and Probability | |

California | S-CP.4 | Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | High School - Statistics and Probability | |

California | S-CP.5 | High School - Statistics and Probability | ||

California | S-CP.6 | Find the conditional probability of ùòà given ùòâ as the fraction of ùòâ‚Äôs outcomes that also belong to ùòà, and interpret the answer in terms of the model. | High School - Statistics and Probability | |

California | S-CP.7 | Apply the Addition Rule, ùòó(ùòà or ùòâ) = ùòó(ùòà) + ùòó(ùòâ) ‚Äì ùòó(ùòà and ùòâ), and interpret the answer in terms of the model. | High School - Statistics and Probability | |

California | S-CP.8 | Apply the general Multiplication Rule in a uniform probability model, ùòó(ùòà and ùòâ) = ùòó(ùòà)ùòó(ùòâ|ùòà) = ùòó(ùòâ)ùòó(ùòà|ùòâ), and interpret the answer in terms of the model. | High School - Statistics and Probability | |

California | S-CP.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. | High School - Statistics and Probability | |

California | S-ID.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). | High School - Statistics and Probability | |

California | S-ID.2 | High School - Statistics and Probability | ||

California | S-ID.3 | High School - Statistics and Probability | ||

California | S-ID.4 | High School - Statistics and Probability | ||

California | S-ID.5 | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | High School - Statistics and Probability | |

California | S-ID.6 | High School - Statistics and Probability | ||

California | S-ID.7 | High School - Statistics and Probability | ||

California | S-ID.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | High School - Statistics and Probability | |

California | S-ID.9 | Distinguish between correlation and causation. | High School - Statistics and Probability | |

California | S-IC.1 | High School - Statistics and Probability | ||

California | S-IC.2 | Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. | High School - Statistics and Probability | |

California | S-IC.3 | High School - Statistics and Probability | ||

California | S-IC.4 | High School - Statistics and Probability | ||

California | S-IC.5 | High School - Statistics and Probability | ||

California | S-IC.6 | Evaluate reports based on data. | High School - Statistics and Probability | |

California | S-MD.1 | Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. | High School - Statistics and Probability | |

California | S-MD.2 | Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. | High School - Statistics and Probability | |

California | S-MD.3 | Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. | High School - Statistics and Probability | |

California | S-MD.4 | Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. | High School - Statistics and Probability | |

California | S-MD.5 | Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. | High School - Statistics and Probability | |

California | S-MD.6 | Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | High School - Statistics and Probability | |

California | S-MD.7 | High School - Statistics and Probability | ||

CCSSM | A-APR.B.3 | Algebra | ||

CCSSM | A-CED.A.2 | Algebra | ||

CCSSM | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra | |

CCSSM | A-SSE.B.3 | Algebra | ||

CCSSM | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra | |

CCSSM | F-IF.A.2 | Algebra | ||

CCSSM | F-IF.B.4 | Algebra | ||

CCSSM | F-IF.C.7 | Algebra | ||

CCSSM | S-ID.B.6 | Algebra | ||

CCSSM | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 | |

CCSSM | 1.MD.C.4 | Grade 1 | ||

CCSSM | 1.NBT.A.1 | Grade 1 | ||

CCSSM | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones - called a 'ten.'. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 | |

CCSSM | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols. | Grade 1 | |

CCSSM | 1.NBT.C.4 | Grade 1 | ||

CCSSM | 1.NBT.C.5 | Grade 1 | ||

CCSSM | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 | |

CCSSM | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) | Grade 1 | |

CCSSM | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. | Grade 1 | |

CCSSM | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 | |

CCSSM | 1.OA.C.6 | Grade 1 | ||

CCSSM | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 | |

CCSSM | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. | Grade 1 | |

CCSSM | 2.G.A.1 | Grade 2 | ||

CCSSM | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 | |

CCSSM | 2.MD.D.10 | Grade 2 | ||

CCSSM | 2.MD.D.9 | Grade 2 | ||

CCSSM | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a 'hundred.'. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 | |

CCSSM | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 | |

CCSSM | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 | |

CCSSM | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons. | Grade 2 | |

CCSSM | 2.NBT.B.5 | Grade 2 | ||

CCSSM | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 | |

CCSSM | 2.NBT.B.7 | Grade 2 | ||

CCSSM | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 | |

CCSSM | 2.OA.A.1 | Grade 2 | ||

CCSSM | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 | |

CCSSM | 3.G.A.1 | Grade 3 | ||

CCSSM | 3.MD.A.1 | Grade 3 | ||

CCSSM | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step √±how many more√Æ and √±how many less√Æ problems using information presented in scaled bar graphs. | Grade 3 | |

CCSSM | 3.MD.B.4 | Grade 3 | ||

CCSSM | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 | |

CCSSM | 3.MD.C.6 | Grade 3 | ||

CCSSM | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 | |

CCSSM | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 | |

CCSSM | 3.NBT.A.2 | Grade 3 | ||

CCSSM | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 _ 80, 5 _ 60) using strategies based on place value and properties of operations. | Grade 3 | |

CCSSM | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 | |

CCSSM | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 | |

CCSSM | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 3 | |

CCSSM | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 _ 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 _ 7. | Grade 3 | |

CCSSM | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ¬Ö 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ¬Ö 8. | Grade 3 | |

CCSSM | 3.OA.A.3 | Grade 3 | ||

CCSSM | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 _ ? = 48, 5 = _ ¬Ö 3, 6 _ 6 = ? | Grade 3 | |

CCSSM | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 _ 4 = 24 is known, then 4 _ 6 = 24 is also known. (Commutative property of multiplication.) 3 _ 5 _ 2 can be found by 3 _ 5 = 15, then 15 _ 2 = 30, or by 5 _ 2 = 10, then 3 _ 10 = 30. (Associative property of multiplication.) Knowing that 8 _ 5 = 40 and 8 _ 2 = 16, one can find 8 _ 7 as 8 _ (5 + 2) = (8 _ 5) + (8 _ 2) = 40 + 16 = 56. (Distributive property.) | Grade 3 | |

CCSSM | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32 ¬Ö 8 by finding the number that makes 32 when multiplied by 8. | Grade 3 | |

CCSSM | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 _ 5 = 40, one knows 40 ¬Ö 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 | |

CCSSM | 4.G.A.1 | Grade 4 | ||

CCSSM | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 | |

CCSSM | 4.MD.A.1 | Grade 4 | ||

CCSSM | 4.MD.A.2 | Grade 4 | ||

CCSSM | 4.MD.B.4 | Grade 4 | ||

CCSSM | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 | |

CCSSM | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 | |

CCSSM | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 | |

CCSSM | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. | Grade 4 | |

CCSSM | 4.NBT.A.2 | Grade 4 | ||

CCSSM | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 | |

CCSSM | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 | |

CCSSM | 4.NBT.B.5 | Grade 4 | ||

CCSSM | 4.NBT.B.6 | Grade 4 | ||

CCSSM | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 | |

CCSSM | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or | Grade 4 | |

CCSSM | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 | |

CCSSM | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) / b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 | |

CCSSM | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 | |

CCSSM | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 | |

CCSSM | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or | Grade 4 | |

CCSSM | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 | |

CCSSM | 4.OA.A.2 | Grade 4 | ||

CCSSM | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 ¬Ñ 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 | |

CCSSM | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 | |

CCSSM | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 | |

CCSSM | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 | |

CCSSM | 5.G.B.3 | Grade 5 | ||

CCSSM | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 | |

CCSSM | 5.MD.B.2 | Grade 5 | ||

CCSSM | 5.NBT.A.1 | Grade 5 | ||

CCSSM | 5.NBT.A.2 | Grade 5 | ||

CCSSM | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 | |

CCSSM | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 | |

CCSSM | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 | |

CCSSM | 5.NBT.B.6 | Grade 5 | ||

CCSSM | 5.NBT.B.7 | Grade 5 | ||

CCSSM | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 | |

CCSSM | 5.NF.B.4 | Grade 5 | ||

CCSSM | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | Grade 5 | |

CCSSM | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 | |

CCSSM | 5.NF.B.7 | Grade 5 | ||

CCSSM | 5.OA.A.1 | Grade 5 | ||

CCSSM | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule √±Add 3√Æ and the starting number 0, and given the rule √±Add 6√Æ and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 | |

CCSSM | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 | |

CCSSM | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 | |

CCSSM | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 | |

CCSSM | 6.EE.B.5 | Grade 6 | ||

CCSSM | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 | |

CCSSM | 6.EE.B.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 | |

CCSSM | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 | |

CCSSM | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 | |

CCSSM | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 | |

CCSSM | 6.NS.B.3 | Grade 6 | ||

CCSSM | 6.NS.C.5 | Grade 6 | ||

CCSSM | 6.NS.C.6 | Grade 6 | ||

CCSSM | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 | |

CCSSM | 6.NS.C.8 | Grade 6 | ||

CCSSM | 6.RP.A.1 | Grade 6 | ||

CCSSM | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. | Grade 6 | |

CCSSM | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 | |

CCSSM | 7.EE.A.1 | Grade 7 | ||

CCSSM | 7.EE.B.3 | Grade 7 | ||

CCSSM | 7.G.A.1 | Grade 7 | ||

CCSSM | 7.G.A.2 | Grade 7 | ||

CCSSM | 7.G.B.5 | Grade 7 | ||

CCSSM | 7.NS.A.1 | Grade 7 | ||

CCSSM | 7.NS.A.2 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. | Grade 7 | |

CCSSM | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 | |

CCSSM | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/3 hour, compute the unit rate as the complex fraction 1/2 divided by 1/4 per hour, equivalently 2 miles per hour. | Grade 7 | |

CCSSM | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 | |

CCSSM | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 | |

CCSSM | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 | |

CCSSM | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 | |

CCSSM | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 | |

CCSSM | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 | |

CCSSM | 8.EE.C.7 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 | |

CCSSM | 8.EE.C.8 | Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. | Grade 8 | |

CCSSM | 8.F.A.1 | Grade 8 | ||

CCSSM | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 | |

CCSSM | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 | |

CCSSM | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 | |

CCSSM | 8.F.B.5 | Grade 8 | ||

CCSSM | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 | |

CCSSM | 8.G.A.2 | Grade 8 | ||

CCSSM | 8.G.A.4 | Grade 8 | ||

CCSSM | 8.G.B.7 | Grade 8 | ||

CCSSM | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 | |

CCSSM | 8.SP.A.1 | Grade 8 | ||

CCSSM | 8.SP.A.2 | Grade 8 | ||

CCSSM | K.CC.A.1 | Count to 100 by ones and by tens | Kindergarten | |

CCSSM | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten | |

CCSSM | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten | |

CCSSM | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten | |

CCSSM | K.CC.B.5 | Count to answer 'how many' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten | |

CCSSM | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten | |

CCSSM | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten | |

CCSSM | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten | |

CCSSM | K.OA.A.1 | Kindergarten | ||

CCSSM | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten | |

CCSSM | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten | |

CCSSM | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten | |

CCSSM | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten | |

Colorado | MP4 | Prepared graduates: Model with mathematics. | Prekindergarten | |

Colorado | P.OA.A.1 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Represent addition and subtraction in different ways, such as with fingers, objects, and drawings. | Prekindergarten | |

Colorado | P.OA.A.2 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Solve addition and subtraction problems set in simple contexts. Add and subtract up to at least five to or from a given number to find a sum or difference up to 10. | Prekindergarten | |

Colorado | P.OA.A.3 | By the end of the preschool experience (approximately 60 months/5 years old), students may: With adult assistance, begin to use counting on (adding 1 or 2, for example) from the larger number for addition. | Prekindergarten | |

Colorado | 1 | Children may: Add a group of three and a group of two, counting ‚ÄúOne, two three ‚Ä¶‚Äù and then counting on ‚ÄúFour, five!‚Äù while keeping track using their fingers. | Prekindergarten | |

Colorado | 2 | Children may: Take three away from five, counting ‚ÄúFive, four, three ‚Ä¶ two!‚Äù while keeping track using their fingers. | Prekindergarten | |

Colorado | 3 | Children may: Say after receiving more crackers at snack time, ‚ÄúI had two and now I have four.‚Äù | Prekindergarten | |

Colorado | 4 | Children may: Predict what will happen when one more object is taken away from a group of five or fewer objects, and then verify their prediction by taking the object away and counting the remaining objects. | Prekindergarten | |

Colorado | MP8 | Prepared graduates: Look for and express regularity in repeated reasoning. | Prekindergarten | |

Colorado | P.OA.B.4 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Fill in missing elements of simple patterns. | Prekindergarten | |

Colorado | P.OA.B.5 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Duplicate simple patterns in a different location than demonstrated, such as making the same alternating color pattern with blocks at a table that was demonstrated on the rug. Extend patterns, such as making an eight-block tower of the same pattern that was demonstrated with four blocks. | Prekindergarten | |

Colorado | P.OA.B.6 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Identify the core unit of sequentially repeating patterns, such as color in a sequence of alternating red and blue blocks. | Prekindergarten | |

Colorado | MP1 | Prepared graduates: Make sense of problems and persevere in solving them. | Prekindergarten | |

Colorado | P.MD.A.1 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Use comparative language, such as shortest, heavier, biggest, or later. | Prekindergarten | |

Colorado | P.MD.A.2 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Compare or order up to five objects based on their measurable attributes, such as height or weight. | Prekindergarten | |

Colorado | P.MD.A.3 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Measure using the same unit, such as putting together snap cubes to see how tall a book is. | Prekindergarten | |

Colorado | MP3 | Prepared graduates: Construct viable arguments and critique the reasoning of others. | Prekindergarten | |

Colorado | P.G.A.1 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Name and describe shapes in terms of length of sides, number of sides, and number of angles/corners. | Prekindergarten | |

Colorado | P.G.A.2 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Correctly name basic shapes (circle, square, rectangle, triangle) regardless of size and orientation. | Prekindergarten | |

Colorado | P.G.A.3 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Analyze, compare, and sort two-and three-dimensional shapes and objects in different sizes. Describe their similarities, differences, and other attributes, such as size and shape. | Prekindergarten | |

Colorado | P.G.A.4 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Compose simple shapes to form larger shapes. | Prekindergarten | |

Colorado | MP6 | Prepared graduates: Attend to precision. | Prekindergarten | |

Colorado | P.G.B.5 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Understand and use language related to directionality, order, and the position of objects, including up/down and in front/behind. | Prekindergarten | |

Colorado | P.G.B.6 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Correctly follow directions involving their own position in space, such as ‚ÄúStand up‚Äù and ‚ÄúMove forward.‚Äù | Prekindergarten | |

Colorado | P.CC.A.1 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Count verbally or sign to at least 20 by ones. | Prekindergarten | |

Colorado | MP2 | Prepared graduates: Reason abstractly and quantitatively. | Prekindergarten | |

Colorado | P.CC.B.2 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Instantly recognize, without counting, small quantities of up to five objects and say or sign the number. | Prekindergarten | |

Colorado | P.CC.C.3 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Say or sign the number names in order when counting, pairing one number word that corresponds with one object, up to at least 10. | Prekindergarten | |

Colorado | P.CC.C.4 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Use the number name of the last object counted to answer ‚ÄúHow many?‚Äù questions for up to approximately 10 objects. | Prekindergarten | |

Colorado | P.CC.C.5 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Accurately count as many as five objects in a scattered configuration or out of a collection of more than five objects. | Prekindergarten | |

Colorado | P.CC.C.6 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Understand that each successive number name refers to a quantity that is one larger. | Prekindergarten | |

Colorado | MP7 | Prepared graduates: Look for and make use of structure. | Prekindergarten | |

Colorado | P.CC.D.7 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Identify whether the number of objects in one group is more than, less than or the same as objects in another group for up to at least five objects. | Prekindergarten | |

Colorado | P.CC.D.8 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Identify and use numbers related to order or position from first to fifth. | Prekindergarten | |

Colorado | MP5 | Prepared graduates: Use appropriate tools strategically. | Prekindergarten | |

Colorado | P.CC.E.9 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Associate a number of objects with a written numeral 0-5. | Prekindergarten | |

Colorado | P.CC.E.10 | By the end of the preschool experience (approximately 60 months/5 years old), students may: Recognize and, with support, write some numerals up to 10. | Prekindergarten | |

Colorado | K.OA.A.1 | Students can: Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten | |

Colorado | K.OA.A.2 | Students can: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten | |

Colorado | K.OA.A.3 | Students can: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten | |

Colorado | K.OA.A.4 | Students can: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten | |

Colorado | K.OA.A.5 | Students can: Fluently add and subtract within 5. | Kindergarten | |

Colorado | K.MD.A.1 | Students can: Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten | |

Colorado | K.MD.A.2 | Students can: Directly compare two objects with a measurable attribute in common, to see which object has ‚Äúmore of‚Äù/‚Äúless of‚Äù the attribute, and describe the difference. | Kindergarten | |

Colorado | K.MD.B.3 | Students can: Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.) | Kindergarten | |

Colorado | K.G.A.1 | Students can: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten | |

Colorado | K.G.A.2 | Students can: Correctly name shapes regardless of their orientations or overall size. | Kindergarten | |

Colorado | K.G.A.3 | Students can: Identify shapes as two-dimensional (lying in a plane, ‚Äúflat‚Äù) or three-dimensional (‚Äúsolid‚Äù). | Kindergarten | |

Colorado | K.G.B.4 | Students can: Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/‚Äúcorners‚Äù) and other attributes (e.g., having sides of equal length). | Kindergarten | |

Colorado | K.G.B.5 | Students can: Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. | Kindergarten | |

Colorado | K.G.B.6 | Students can: Compose simple shapes to form larger shapes. | Kindergarten | |

Colorado | K.CC.A.1 | Students can: Count to 100 by ones and by tens. | Kindergarten | |

Colorado | K.CC.A.2 | Students can: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten | |

Colorado | K.CC.A.3 | Students can: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten | |

Colorado | K.CC.B.4 | Students can: Apply the relationship between numbers and quantities and connect counting to cardinality. | Kindergarten | |

Colorado | K.CC.B.5 | Students can: Count to answer ‚Äúhow many?‚Äù questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten | |

Colorado | K.CC.C.6 | Students can: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to 10 objects.) | Kindergarten | |

Colorado | K.CC.C.7 | Students can: Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten | |

Colorado | K.NBT.A.1 | Students can: Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10+8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten | |

Colorado | 1.OA.A.1 | Students can: Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 | |

Colorado | 1.OA.A.2 | Students can: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 | |

Colorado | 1.OA.B.3 | Students can: Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) | Grade 1 | |

Colorado | 1.OA.B.4 | Students can: Understand subtraction as an unknown-addend problem. | Grade 1 | |

Colorado | 1.OA.C.5 | Students can: Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 | |

Colorado | 1.OA.C.6 | Students can: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 ‚àí 4 = 13 ‚àí 3 ‚àí 1 = 10‚àí1=9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 ‚àí 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 | |

Colorado | 1.OA.D.7 | Students can: Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 | |

Colorado | 1.OA.D.8 | Students can: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 | |

Colorado | 1.MD.A.1 | Students can: Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 | |

Colorado | 1.MD.A.2 | Students can: Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. | Grade 1 | |

Colorado | 1.MD.B.3 | Students can: Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 | |

Colorado | 1.MD.C.4 | Students can: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 | |

Colorado | 1.G.A.1 | Students can: Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 | |

Colorado | 1.G.A.2 | Students can: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names, such as ‚Äúright rectangular prisms.‚Äù) | Grade 1 | |

Colorado | 1.G.A.3 | Students can: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 | |

Colorado | 1.NBT.A.1 | Students can: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 | |

Colorado | 1.NBT.B.2 | Students can: Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 | |

Colorado | 1.NBT.B.3 | Students can: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 | |

Colorado | 1.NBT.C.4 | Students can: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 | |

Colorado | 1.NBT.C.5 | Students can: Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 | |

Colorado | 1.NBT.C.6 | Students can: Subtract multiples of 10 in the range 10‚Äì90 from multiples of 10 in the range 10‚Äì90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 | |

Colorado | 2.OA.A.1 | Students can: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 | |

Colorado | 2.OA.B.2 | Students can: Fluently add and subtract within 20 using mental strategies. (See 1.OA.C.6 for a list of strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 | |

Colorado | 2.OA.C.3 | Students can: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 | |

Colorado | 2.OA.C.4 | Students can: Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 | |

Colorado | 2.MD.A.1 | Students can: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 | |

Colorado | 2.MD.A.2 | Students can: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 | |

Colorado | 2.MD.A.3 | Students can: Estimate lengths using units of inches, feet, centimeters, and meters. | Grade 2 | |

Colorado | 2.MD.A.4 | Students can: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 | |

Colorado | 2.MD.B.5 | Students can: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 | |

Colorado | 2.MD.B.6 | Students can: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,‚Ä¶, and represent whole-number sums and differences within 100 on a number line diagram. | Grade 2 | |

Colorado | 2.MD.C.7 | Students can: Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 | |

Colorado | 2.MD.C.8 | Students can: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¬¢ symbols appropriately. | Grade 2 | |

Colorado | 2.MD.D.9 | Students can: Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 | |

Colorado | 2.MD.D.10 | Students can: Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 | |

Colorado | 2.G.A.1 | Students can: Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 | |

Colorado | 2.G.A.2 | Students can: Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 | |

Colorado | 2.G.A.3 | Students can: Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 | |

Colorado | 2.NBT.A.1 | Students can: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 | |

Colorado | 2.NBT.A.2 | Students can: Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 | |

Colorado | 2.NBT.A.3 | Students can: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 | |

Colorado | 2.NBT.A.4 | Students can: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 | |

Colorado | 2.NBT.B.5 | Students can: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 | |

Colorado | 2.NBT.B.6 | Students can: Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 | |

Colorado | 2.NBT.B.7 | Students can: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 | |

Colorado | 2.NBT.B.8 | Students can: Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 | |

Colorado | 2.NBT.B.9 | Students can: Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.) | Grade 2 | |

Colorado | 3.OA.A.1 | Students can: Interpret products of whole numbers, e.g., interpret 5 √ó 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 | |

Colorado | 3.OA.A.2 | Students can: Interpret whole-number quotients of whole numbers, e.g., interpret 56 √∑ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 | |

Colorado | 3.OA.A.3 | Students can: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 | |

Colorado | 3.OA.A.4 | Students can: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 | |

Colorado | 3.OA.B.5 | Students can: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) | Grade 3 | |

Colorado | 3.OA.B.6 | Students can: Interpret division as an unknown-factor problem. | Grade 3 | |

Colorado | 3.OA.C.7 | Students can: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 √ó 5 = 40, one knows 40 √∑ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 | |

Colorado | 3.OA.D.8 | Students can: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This evidence outcome is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order of operations when there are no parentheses to specify a particular order.) | Grade 3 | |

Colorado | 3.OA.D.9 | Students can: Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. | Grade 3 | |

Colorado | 3.MD.A.1 | Students can: Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 | |

Colorado | 3.MD.A.2 | Students can: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (This excludes compound units such as cm¬≥ and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 | |

Colorado | 3.MD.B.3 | Students can: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ‚Äúhow many more‚Äù and ‚Äúhow many less‚Äù problems using information presented in scaled bar graphs. | Grade 3 | |

Colorado | 3.MD.B.4 | Students can: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 | |

Colorado | 3.MD.C.5 | Students can: Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 | |

Colorado | 3.MD.C.6 | Students can: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 | |

Colorado | 3.MD.C.7 | Students can: Use concepts of area and relate area to the operations of multiplication and addition. | Grade 3 | |

Colorado | 3.MD.D.8 | Students can: Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 | |

Colorado | 3.G.A.1 | Students can: Explain that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 | |

Colorado | 3.G.A.2 | Students can: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 | |

Colorado | 3.NBT.A.1 | Students can: Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 | |

Colorado | 3.NBT.A.2 | Students can: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 | |

Colorado | 3.NBT.A.3 | Students can: Multiply one-digit whole numbers by multiples of 10 in the range 10 - 90 (e.g., 9 √ó 80, 5 √ó 60) using strategies based on place value and properties of operations. | Grade 3 | |

Colorado | 3.NF.A.1 | Students can: Describe a fraction 1/ùëè as the quantity formed by 1 part when a whole is partitioned into ùëè equal parts; understand a fraction ùëé/ùëè as the quantity formed by ùëé parts of size 1/ùëè. | Grade 3 | |

Colorado | 3.NF.A.2 | Students can: Describe a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 | |

Colorado | 3.NF.A.3 | Students can: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 | |

Colorado | 4.OA.A.1 | Students can: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 √ó 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 | |

Colorado | 4.OA.A.2 | Students can: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 | |

Colorado | 4.OA.A.3 | Students can: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 | |

Colorado | 4.OA.B.4 | Students can: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 | |

Colorado | 4.OA.C.5 | Students can: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 | |

Colorado | 4.MD.A.1 | Students can: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 | |

Colorado | 4.MD.A.2 | Students can: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 | |

Colorado | 4.MD.A.3 | Students can: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. | Grade 4 | |

Colorado | 4.MD.B.4 | Students Can: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 | |

Colorado | 4.MD.C.5 | Students can: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 | |

Colorado | 4.MD.C.6 | Students can: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 | |

Colorado | 4.MD.C.7 | Students can: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 | |

Colorado | 4.G.A.1 | Students can: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 | |

Colorado | 4.G.A.2 | Students can: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 | |

Colorado | 4.G.A.3 | Students can: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 | |

Colorado | 4.NBT.A.1 | Students can: Explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 | |

Colorado | 4.NBT.A.2 | Students can: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 | |

Colorado | 4.NBT.A.3 | Students can: Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 | |

Colorado | 4.NBT.B.4 | Students can: Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 | |

Colorado | 4.NBT.B.5 | Students can: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Colorado | 4.NBT.B.6 | Students can: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 | |

Colorado | 4.NF.A.1 | Students can: Explain why a fraction ùëé/ùëè is equivalent to a fraction (ùëõ √ó ùëé)/(ùëõ √ó ùëè) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 | |

Colorado | 4.NF.A.2 | Students can: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 | |

Colorado | 4.NF.B.3 | Students can: Understand a fraction ùëé/ùëè with ùëé > 1 as a sum of fractions 1/ùëè. | Grade 4 | |

Colorado | 4.NF.B.4 | Students can: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 | |

Colorado | 4.NF.C.5 | Students can: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) | Grade 4 | |

Colorado | 4.NF.C.6 | Students can: Use decimal notation for fractions with denominators 10 or 100. | Grade 4 | |

Colorado | 4.NF.C.7 | Students can: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 | |

Colorado | 5.OA.A.1 | Students can: Use grouping symbols (parentheses, brackets, or braces) in numerical expressions, and evaluate expressions with these symbols. | Grade 5 | |

Colorado | 5.OA.A.2 | Students can: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 | |

Colorado | 5.OA.B.3 | Students can: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 | |

Colorado | 5.MD.A.1 | Students can: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. | Grade 5 | |

Colorado | 5.MD.B.2 | Students can: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 | |

Colorado | 5.MD.C.3 | Students can: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 | |

Colorado | 5.MD.C.4 | Students can: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 | |

Colorado | 5.MD.C.5 | Students can: Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 | |

Colorado | 5.G.A.1 | Students can: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., ùë•-axis and ùë•-coordinate, ùë¶-axis and ùë¶-coordinate). | Grade 5 | |

Colorado | 5.G.A.2 | Students can: Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 | |

Colorado | 5.G.B.3 | Students can: Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 | |

Colorado | 5.G.B.4 | Students can: Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 | |

Colorado | 5.NBT.A.1 | Students can: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 | |

Colorado | 5.NBT.A.2 | Students can: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 | |

Colorado | 5.NBT.A.3 | Students can: Read, write, and compare decimals to thousandths. | Grade 5 | |

Colorado | 5.NBT.A.4 | Students can: Use place value understanding to round decimals to any place. | Grade 5 | |

Colorado | 5.NBT.B.5 | Students can: Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 | |

Colorado | 5.NBT.B.6 | Students can: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 | |

Colorado | 5.NBT.B.7 | Students can: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 | |

Colorado | 5.NF.A.1 | Students can: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 | |

Colorado | 5.NF.A.2 | Students can: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 | |

Colorado | 5.NF.B.3 | Students can: Interpret a fraction as division of the numerator by the denominator (ùëé/ùëè = ùëé √∑ ùëè). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 | |

Colorado | 5.NF.B.4 | Students can: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 | |

Colorado | 5.NF.B.5 | Students can: Interpret multiplication as scaling (resizing). | Grade 5 | |

Colorado | 5.NF.B.6 | Students can: Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 | |

Colorado | 5.NF.B.7 | Students can: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.) | Grade 5 | |

Colorado | 6.EE.A.1 | Students can: Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 | |

Colorado | 6.EE.A.2 | Students can: Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 | |

Colorado | 6.EE.A.3 | Students can: Apply the properties of operations to generate equivalent expressions. | Grade 6 | |

Colorado | 6.EE.A.4 | Students can: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 | |

Colorado | 6.EE.B.5 | Students can: Describe solving an equation or inequality as a process of answering a question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 | |

Colorado | 6.EE.B.6 | Students can: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 | |

Colorado | 6.EE.B.7 | Students can: Solve real-world and mathematical problems by writing and solving equations of the form ùë• ¬± ùëù = ùëû and ùëùùë• = ùëû for cases in which ùëù, ùëû and ùë• are all nonnegative rational numbers. | Grade 6 | |

Colorado | 6.EE.B.8 | Students can: Write an inequality of the form ùë• > ùëê, ùë• ‚â• ùëê, ùë• < ùëê, or ùë• ‚â§ ùëê to represent a constraint or condition in a real-world or mathematical problem. Show that inequalities of the form ùë• > ùëê, ùë• ‚â• ùëê, ùë• < ùëê, or ùë• ‚â§ ùëê have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 | |

Colorado | 6.EE.C.9 | Students can: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 | |

Colorado | 6.SP.A.1 | Students can: Identify a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. | Grade 6 | |

Colorado | 6.SP.A.2 | Students can: Demonstrate that a set of data collected to answer a statistical question has a distribution that can be described by its center, spread, and overall shape. | Grade 6 | |

Colorado | 6.SP.A.3 | Students can: Explain that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. | Grade 6 | |

Colorado | 6.SP.B.4 | Students can: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. | Grade 6 | |

Colorado | 6.SP.B.5 | Students can: Summarize numerical data sets in relation to their context, such as by: | Grade 6 | |

Colorado | 6.G.A.1 | Students can: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Colorado | 6.G.A.2 | Students can: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas ùëâ = ùëôùë§‚Ñé and ùëâ = ùëè‚Ñé to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 | |

Colorado | 6.G.A.3 | Students can: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Colorado | 6.G.A.4 | Students can: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 | |

Colorado | 6.RP.A.1 | Students can: Apply the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 | |

Colorado | 6.RP.A.2 | Students can: Apply the concept of a unit rate ùëé/ùëè associated with a ratio ùëé:ùëè with ùëè ‚â† 0, and use rate language in the context of a ratio relationship. | Grade 6 | |

Colorado | 6.RP.A.3 | Students can: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 | |

Colorado | 6.NS.A.1 | Students can: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 | |

Colorado | 6.NS.B.2 | Students can: Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 | |

Colorado | 6.NS.B.3 | Students can: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 | |

Colorado | 6.NS.B.4 | Students can: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. | Grade 6 | |

Colorado | 6.NS.C.5 | Students can: Explain why positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 | |

Colorado | 6.NS.C.6 | Students can: Describe a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 | |

Colorado | 6.NS.C.7 | Students can: Order and find absolute value of rational numbers. | Grade 6 | |

Colorado | 6.NS.C.8 | Students can: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 | |

Colorado | 7.EE.A.1 | Students can: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 | |

Colorado | 7.EE.A.2 | Students can: Demonstrate that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 | |

Colorado | 7.EE.B.3 | Students can: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 | |

Colorado | 7.EE.B.4 | Students can: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 | |

Colorado | 7.SP.A.1 | Students can: Understand that statistics can be used to gain information about a population by examining a sample of the population; explain that generalizations about a population from a sample are valid only if the sample is representative of that population. Explain that random sampling tends to produce representative samples and support valid inferences. | Grade 7 | |

Colorado | 7.SP.A.2 | Students can: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. | Grade 7 | |

Colorado | 7.SP.B.3 | Students can: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. | Grade 7 | |

Colorado | 7.SP.B.4 | Students can: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. | Grade 7 | |

Colorado | 7.SP.C.5 | Students can: Explain that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. | Grade 7 | |

Colorado | 7.SP.C.6 | Students can: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. | Grade 7 | |

Colorado | 7.SP.C.7 | Students can: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. | Grade 7 | |

Colorado | 7.SP.C.8 | Students can: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. | Grade 7 | |

Colorado | 7.G.A.1 | Students can: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 | |

Colorado | 7.G.A.2 | Students can: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 | |

Colorado | 7.G.A.3 | Students can: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in cross sections of right rectangular prisms and right rectangular pyramids. | Grade 7 | |

Colorado | 7.G.B.4 | Students can: State the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 | |

Colorado | 7.G.B.5 | Students can: Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 | |

Colorado | 7.G.B.6 | Students can: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 | |

Colorado | 7.RP.A.1 | Students can: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. | Grade 7 | |

Colorado | 7.RP.A.2 | Students can: Identify and represent proportional relationships between quantities. | Grade 7 | |

Colorado | 7.RP.A.3 | Students can: Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 | |

Colorado | 7.NS.A.1 | Students can: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 | |

Colorado | 7.NS.A.2 | Students can: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 | |

Colorado | 7.NS.A.3 | Students can: Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) | Grade 7 | |

Colorado | 8.EE.A.1 | Students can: Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 | |

Colorado | 8.EE.A.2 | Students can: Use square root and cube root symbols to represent solutions to equations of the form ùë•¬≤ = ùëù and ùë•¬≥ = ùëù, where ùëù is a positive rational number. Evaluate square roots of small perfect squares (up to 100) and cube roots of small perfect cubes (up to 64). Know that ‚àö2 is irrational. | Grade 8 | |

Colorado | 8.EE.A.3 | Students can: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 | |

Colorado | 8.EE.A.4 | Students can: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 | |

Colorado | 8.EE.B.5 | Students can: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 | |

Colorado | 8.EE.B.6 | Students can: Use similar triangles to explain why the slope ùëö is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation ùë¶ = ùëöùë• for a line through the origin and the equation ùë¶ = ùëöùë• + ùëè for a line intercepting the vertical axis at ùëè. | Grade 8 | |

Colorado | 8.EE.C.7 | Students can: Solve linear equations in one variable. | Grade 8 | |

Colorado | 8.EE.C.8 | Students can: Analyze and solve pairs of simultaneous linear equations. | Grade 8 | |

Colorado | 8.F.A.1 | Students can: Define a function as a rule that assigns to each input exactly one output. Show that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required for Grade 8.) | Grade 8 | |

Colorado | 8.F.A.2 | Students can: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 | |

Colorado | 8.F.A.3 | Students can: Interpret the equation ùë¶ = ùëöx + ùëè as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 | |

Colorado | 8.F.B.4 | Students can: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (ùë•, ùë¶) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 | |

Colorado | 8.F.B.5 | Students can: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 | |

Colorado | 8.SP.A.1 | Students can: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 | |

Colorado | 8.SP.A.2 | Students can: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 | |

Colorado | 8.SP.A.3 | Students can: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. | Grade 8 | |

Colorado | 8.SP.A.4 | Students can: Explain that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. | Grade 8 | |

Colorado | 8.G.A.1 | Students can: Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 | |

Colorado | 8.G.A.2 | Students can: Demonstrate that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 | |

Colorado | 8.G.A.3 | Students can: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 | |

Colorado | 8.G.A.4 | Students can: Demonstrate that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 | |

Colorado | 8.G.A.5 | Students can: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 | |

Colorado | 8.G.B.6 | Students can: Explain a proof of the Pythagorean Theorem and its converse. | Grade 8 | |

Colorado | 8.G.B.7 | Students can: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 | |

Colorado | 8.G.B.8 | Students can: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 | |

Colorado | 8.G.C.9 | Students can: State the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 | |

Colorado | 8.NS.A.1 | Students can: Demonstrate informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Define irrational numbers as numbers that are not rational. | Grade 8 | |

Colorado | 8.NS.A.2 | Students can: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., ùúã¬≤). | Grade 8 | |

Colorado | HS.A-SSE.A.1 | Students can: Interpret expressions that represent a quantity in terms of its context. | High School | |

Colorado | HS.A-SSE.A.2 | Students can: Use the structure of an expression to identify ways to rewrite it. | High School | |

Colorado | HS.A-SSE.B.3 | Students can: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School | |

Colorado | HS.A-SSE.B.4 | Students can: Use the formula for the sum of a finite geometric series (when the common ratio is not 1) to solve problems. | High School | |

Colorado | HS.A-APR.A.1 | Students can: Explain that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | High School | |

Colorado | HS.A-APR.B.2 | Students can: Know and apply the Remainder Theorem. For a polynomial ùëù(ùë•) and a number ùëé, the remainder on division by ùë• ‚Äì ùëé is ùëù(ùëé), so ùëù(ùëé) = 0 if and only if (ùë• ‚Äì ùëé) is a factor of ùëù(ùë•). (Students need not apply the Remainder Theorem to polynomials of degree greater than 4.) | High School | |

Colorado | HS.A-APR.B.3 | Students can: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School | |

Colorado | HS.A-APR.C.4 | Students can: Prove polynomial identities and use them to describe numerical relationships. | High School | |

Colorado | HS.A-APR.C.5 | Students can: Know and apply the Binomial Theorem for the expansion of in powers of ùë• and ùë¶ for a positive integer ùëõ, where ùë• and ùë¶ are any numbers, with coefficients determined for example by Pascal‚Äôs Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.) | High School | |

Colorado | HS.A-APR.D.6 | Students can: Rewrite simple rational expressions in different forms; write ùëé(ùë•)/ùëè(ùë•) in the form ùëû(ùë•) + ùëü(ùë•)/ùëè(ùë•), where ùëé(ùë•), ùëè(ùë•), ùëû(ùë•), and ùëü(ùë•) are polynomials with the degree of ùëü(ùë•) less than the degree of ùëè(ùë•), using inspection, long division, or, for the more complicated examples, a computer algebra system. | High School | |

Colorado | HS.A-APR.D.7 | Students can: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expressions; add, subtract, multiply, and divide rational expressions. | High School | |

Colorado | HS.A-CED.A.1 | Students can: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. | High School | |

Colorado | HS.A-CED.A.2 | Students can: Create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales. | High School | |

Colorado | HS.A-CED.A.3 | Students can: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. | High School | |

Colorado | HS.A-CED.A.4 | Students can: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | High School | |

Colorado | HS.A-REI.A.1 | Students can: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. | High School | |

Colorado | HS.A-REI.A.2 | Students can: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | High School | |

Colorado | HS.A-REI.B.3 | Students can: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School | |

Colorado | HS.A-REI.B.4 | Students can: Solve quadratic equations in one variable. | High School | |

Colorado | HS.A-REI.C.5 | Students can: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | High School | |

Colorado | HS.A-REI.C.6 | Students can: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | High School | |

Colorado | HS.A-REI.C.7 | Students can: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | High School | |

Colorado | HS.A-REI.C.8 | Students can: Represent a system of linear equations as a single matrix equation in a vector variable. | High School | |

Colorado | HS.A-REI.C.9 | Students can: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 √ó 3 or greater). | High School | |

Colorado | HS.A-REI.D.10 | Students can: Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). | High School | |

Colorado | HS.A-REI.D.11 | Students can: Explain why the ùë•-coordinates of the points where the graphs of the equations ùë¶ =ùëì(ùë•) and ùë¶ = ùëî(ùë•) intersect are the solutions of the equation ùëì(ùë•) = ùëî(ùë•); find the solutions approximately e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ùëì(ùë•) and/or ùëî(ùë•) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. | High School | |

Colorado | HS.A-REI.D.12 | Students can: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | High School | |

Colorado | HS.F-IF.A.1 | Students can: Explain that a function is a correspondence from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. If ùëì is a function and ùë• is an element of its domain, then ùëì(ùë•) denotes the output of ùëì corresponding to the input ùë•. The graph of ùëì is the graph of the equation ùë¶ = ùëì(ùë•). | High School | |

Colorado | HS.F-IF.A.2 | Students can: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School | |

Colorado | HS.F-IF.A.3 | Students can: Demonstrate that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | High School | |

Colorado | HS.F-IF.B.4 | Students can: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | High School | |

Colorado | HS.F-IF.B.5 | Students can: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. | High School | |

Colorado | HS.F-IF.B.6 | Students can: Calculate and interpret the average rate of change presented symbolically or as a table, of a function over a specified interval. Estimate the rate of change from a graph. | High School | |

Colorado | HS.F-IF.C.7 | Students can: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School | |

Colorado | HS.F-IF.C.8 | Students can: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | High School | |

Colorado | HS.F-IF.C.9 | Students can: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | High School | |

Colorado | HS.F-BF.A.1 | Students can: Write a function that describes a relationship between two quantities. | High School | |

Colorado | HS.F-BF.A.2 | Students can: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | High School | |

Colorado | HS.F-BF.B.3 | Students can: Identify the effect on the graph of replacing ùëì(ùë•) by ùëì(ùë•) + ùëò, ùëòùëì(ùë•), ùëì(ùëòx), and ùëì(ùë• + ùëò) for specific values of ùëò both positive and negative; find the value of ùëò given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. | High School | |

Colorado | HS.F-BF.B.4 | Students can: Find inverse functions. | High School | |

Colorado | HS.F-BF.B.5 | Students can: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. | High School | |

Colorado | HS.F-LE.A.1 | Students can: Distinguish between situations that can be modeled with linear functions and with exponential functions. | High School | |

Colorado | HS.F-LE.A.2 | Students can: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | High School | |

Colorado | HS.F-LE.A.3 | Students can: Use graphs and tables to describe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | High School | |

Colorado | HS.F-LE.A.4 | Students can: For exponential models, express as a logarithm the solution to ùëéùëè·∂ú·µó = ùëë where ùëé, ùëê, and ùëë are numbers and the base ùëè is 2, 10, or ùëí; evaluate the logarithm using technology. | High School | |

Colorado | HS.F-LE.B.5 | Students can: Interpret the parameters in a linear or exponential function in terms of a context. | High School | |

Colorado | HS.F-TF.A.1 | Students can: Use radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | High School | |

Colorado | HS.F-TF.A.2 | Students can: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | High School | |

Colorado | HS.F-TF.A.3 | Students can: Use special triangles to determine geometrically the values to sine, cosine, tangent for ùúã/3, ùúã/4, and ùúã/6 and use the unit circle to express the values sine, cosine, and tangent for ùë•, ùúã + ùë•, and 2ùúã - ùë• and in terms of their values for ùë• where ùë• is any real number. | High School | |

Colorado | HS.F-TF.A.4 | Students can: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. | High School | |

Colorado | HS.F-TF.B.5 | Students can: Model periodic phenomena with trigonometric functions with specified amplitude, frequency, and midline. | High School | |

Colorado | HS.F-TF.B.6 | Students can: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. | High School | |

Colorado | HS.F-TF.B.7 | Students can: Use inverse function to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. | High School | |

Colorado | HS.F-TF.C.8 | Students can: Prove the Pythagorean identity sin¬≤ (ùúÉ) + cos¬≤ (ùúÉ) = 1 and use it to find sin(ùúÉ), cos(ùúÉ), or tan(ùúÉ) given sin(ùúÉ), cos(ùúÉ), or tan(ùúÉ) and the quadrant of the angle. | High School | |

Colorado | HS.F-TF.C.9 | Students can: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. | High School | |

Colorado | HS.S-ID.A.1 | Students can: Model data in context with plots on the real number line (dot plots, histograms, and box plots). | High School | |

Colorado | HS.S-ID.A.2 | Students can: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | High School | |

Colorado | HS.S-ID.A.3 | Students can: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | High School | |

Colorado | HS.S-ID.A.4 | Students can: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages and identify data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | High School | |

Colorado | HS.S-ID.B.5 | Students can: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | High School | |

Colorado | HS.S-ID.B.6 | Students can: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School | |

Colorado | HS.S-ID.B.7 | Students can: Distinguish between correlation and causation. | High School | |

Colorado | HS.S-ID.C.7 | Students can: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | High School | |

Colorado | HS.S-ID.C.8 | Students can: Using technology, compute and interpret the correlation coefficient of a linear fit. | High School | |

Colorado | HS.S-IC.A.1 | Students can: Describe statistics as a process for making inferences about population parameters based on a random sample from that population. | High School | |

Colorado | HS.S-IC.A.2 | Students can: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. | High School | |

Colorado | HS.S-IC.B.3 | Students can: Identify the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | High School | |

Colorado | HS.S-IC.B.4 | Students can: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | High School | |

Colorado | HS.S-IC.B.5 | Students can: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | High School | |

Colorado | HS.S-IC.B.6 | Students can: Evaluate reports based on data. Define and explain the meaning of significance, both statistical (using p-values) and practical (using effect size). | High School | |

Colorado | HS.S-CP.A.1 | Students can: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (‚Äúor,‚Äù ‚Äúand,‚Äù ‚Äúnot‚Äù). | High School | |

Colorado | HS.S-CP.A.2 | Students can: Explain that two events ùê¥ and ùêµ are independent if the probability of ùê¥ and ùêµ occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | High School | |

Colorado | HS.S-CP.A.3 | Students can: Using the conditional probability of ùê¥ given ùêµ as ùëÉ(ùê¥ and ùêµ)/ùëÉ(ùêµ), interpret the independence of ùê¥ and ùêµ as saying that the conditional probability of ùê¥ given ùêµ is the same as the probability of ùê¥, and the conditional probability of ùêµ given ùê¥ is the same as the probability of ùêµ. | High School | |

Colorado | HS.S-CP.A.4 | Students can: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | High School | |

Colorado | HS.S-CP.A.5 | Students can: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | High School | |

Colorado | HS.S-CP.B.6 | Students can: Find the conditional probability of ùê¥ given ùêµ as the fraction of ùêµ‚Äôs outcomes that also belong to ùê¥, and interpret the answer in terms of the model. | High School | |

Colorado | HS.S-CP.B.7 | Students can: Apply the Addition Rule, ùëÉ(ùê¥ or ùêµ) = ùëÉ(ùê¥) + ùëÉ(ùêµ) ‚Äì ùëÉ (ùê¥ and ùêµ), and interpret the answer in terms of the model. | High School | |

Colorado | HS.S-CP.B.8 | Students can: Apply the general Multiplication Rule in a uniform probability model, ùëÉ(ùê¥ and ùêµ) = ùëÉ(ùê¥) ùëÉ(ùêµ ‚à£ ùê¥) = ùëÉ(ùêµ) ùëÉ(ùê¥ ‚à£ ùêµ), and interpret the answer in terms of the model. | High School | |

Colorado | HS.S-CP.B.9 | Students can: Use permutations and combinations to compute probabilities of compound events and solve problems. | High School | |

Colorado | HS.S-MD.A.1 | Students can: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. | High School | |

Colorado | HS.S-MD.A.2 | Students can: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. | High School | |

Colorado | HS.S-MD.A.3 | Students can: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. | High School | |

Colorado | HS.S-MD.A.4 | Students can: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. | High School | |

Colorado | HS.S-MD.B.5 | Students can: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. | High School | |

Colorado | HS.S-MD.B.6 | Students can: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | High School | |

Colorado | HS.S-MD.B.7 | Students can: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | High School | |

Colorado | HS.G-CO.A.1 | Students can: State precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | High School | |

Colorado | HS.G-CO.A.2 | Students can: Represent transformations in the plane using e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). | High School | |

Colorado | HS.G-CO.A.3 | Students can: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | High School | |

Colorado | HS.G-CO.A.4 | Students can: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | High School | |

Colorado | HS.G-CO.A.5 | Students can: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using appropriate tools (e.g., graph paper, tracing paper, or geometry software). Specify a sequence of transformations that will carry a given figure onto another. | High School | |

Colorado | HS.G-CO.B.6 | Students can: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. | High School | |

Colorado | HS.G-CO.B.7 | Students can: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. | High School | |

Colorado | HS.G-CO.B.8 | Students can: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | High School | |

Colorado | HS.G-CO.C.9 | Students can: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment‚Äôs endpoints. | High School | |

Colorado | HS.G-CO.C.10 | Students can: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180¬∞; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. | High School | |

Colorado | HS.G-CO.C.11 | Students can: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. | High School | |

Colorado | HS.G-CO.D.12 | Students can: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. | High School | |

Colorado | HS.G-CO.D.13 | Students can: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | High School | |

Colorado | HS.G-SRT.A.1 | Students can: Verify experimentally the properties of dilations given by a center and a scale factor. | High School | |

Colorado | HS.G-SRT.A.2 | Students can: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. | High School | |

Colorado | HS.G-SRT.A.3 | Students can: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. | High School | |

Colorado | HS.G-SRT.B.4 | Students can: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. | High School | |

Colorado | HS.G-SRT.B.5 | Students can: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | High School | |

Colorado | HS.G-SRT.C.6 | Students can: Explain that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. | High School | |

Colorado | HS.G-SRT.C.7 | Students can: Explain and use the relationship between the sine and cosine of complementary angles. | High School | |

Colorado | HS.G-SRT.C.8 | Students can: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | High School | |

Colorado | HS.G-SRT.D.9 | Students can: Derive the formula ùê¥ = ¬Ω ùëéùëè sin(ùê∂) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. | High School | |

Colorado | HS.G-SRT.D.10 | Students can: Prove the Laws of Sines and Cosines and use them to solve problems. | High School | |

Colorado | HS.G-SRT.D.11 | Students can: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). | High School | |

Colorado | HS.G-C.A.1 | Students can: Prove that all circles are similar. | High School | |

Colorado | HS.G-C.A.2 | Students can: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. | High School | |

Colorado | HS.G-C.A.3 | Students can: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | High School | |

Colorado | HS.G-C.A.4 | Students can: Construct a tangent line from a point outside a given circle to the circle. | High School | |

Colorado | HS.G-C.B.5 | Students can: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. | High School | |

Colorado | HS.G-GPE.A.1 | Students can: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. | High School | |

Colorado | HS.G-GPE.A.2 | Students can: Derive the equation of a parabola given a focus and directrix. | High School | |

Colorado | HS.G-GPE.A.3 | Students can: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. | High School | |

Colorado | HS.G-GPE.B.4 | Students can: Use coordinates to prove simple geometric theorems algebraically. | High School | |

Colorado | HS.G-GPE.B.5 | Students can: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | High School | |

Colorado | HS.G-GPE.B.6 | Students can: Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | High School | |

Colorado | HS.G-GPE.B.7 | Students can: Use coordinates and the distance formula to compute perimeters of polygons and areas of triangles and rectangles. | High School | |

Colorado | HS.G-GMD.A.1 | Students can: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri‚Äôs principle, and informal limit arguments. | High School | |

Colorado | HS.G-GMD.A.2 | Students can: Give an informal argument using Cavalieri‚Äôs principle for the formulas for the volume of a sphere and other solid figures. | High School | |

Colorado | HS.G-GMD.A.3 | Students can: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | High School | |

Colorado | HS.G-GMD.B.4 | Students can: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | High School | |

Colorado | HS.G-MG.A.1 | Students can: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | High School | |

Colorado | HS.G-MG.A.2 | Students can: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). | High School | |

Colorado | HS.G-MG.A.3 | Students can: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). | High School | |

Colorado | HS.N-RN.A.1 | Students can: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | High School | |

Colorado | HS.N-RN.A.2 | Students can: Rewrite expressions involving radicals and rational exponents using the properties of exponents. | High School | |

Colorado | HS.N-RN.B.3 | Students can: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | High School | |

Colorado | HS.N-Q.A.1 | Students can: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | High School | |

Colorado | HS.N-Q.A.2 | Students can: Define appropriate quantities for the purpose of descriptive modeling. | High School | |

Colorado | HS.N-Q.A.3 | Students can: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | High School | |

Colorado | HS.N-CN.A.1 | Students can: Define complex number ùëñ such that ùëñ¬≤ = ‚Äì1, and show that every complex number has the form ùëé + ùëèùëñ where ùëé and ùëè are real numbers. | High School | |

Colorado | HS.N-CN.A.2 | Students can: Use the relation ùëñ¬≤ = ‚Äì1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | High School | |

Colorado | HS.N-CN.A.3 | Students can: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. | High School | |

Colorado | HS.N-CN.B.4 | Students can: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. | High School | |

Colorado | HS.N-CN.B.5 | Students can: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. | High School | |

Colorado | HS.N-CN.B.6 | Students can: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. | High School | |

Colorado | HS.N-CN.C.7 | Students can: Solve quadratic equations with real coefficients that have complex solutions. | High School | |

Colorado | HS.N-CN.C.8 | Students can: Extend polynomial identities to the complex numbers. | High School | |

Colorado | HS.N-CN.C.9 | Students can: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | High School | |

Colorado | HS.N-VM.A.1 | Students can: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., ùíó, |ùíó|, ||ùíó||, ùë£). | High School | |

Colorado | HS.N-VM.A.2 | Students can: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. | High School | |

Colorado | HS.N-VM.A.3 | Students can: Solve problems involving velocity and other quantities that can be represented by vectors. | High School | |

Colorado | HS.N-VM.B.4 | Students can: Add and subtract vectors. | High School | |

Colorado | HS.N-VM.B.5 | Students can: Multiply a vector by a scalar. | High School | |

Colorado | HS.N-VM.C.6 | Students can: Use matrices to represent and manipulate data, e.g., as when all of the payoffs or incidence relationships in a network. | High School | |

Colorado | HS.N-VM.C.7 | Students can: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. | High School | |

Colorado | HS.N-VM.C.8 | Students can: Add, subtract, and multiply matrices of appropriate dimensions. | High School | |

Colorado | HS.N-VM.C.9 | Students can: Understand that, unlike the multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. | High School | |

Colorado | HS.N-VM.C.10 | Students can: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. | High School | |

Colorado | HS.N-VM.C.11 | Students can: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimension to produce another vector. Work with matrices as transformations of vectors. | High School | |

Colorado | HS.N-VM.C.12 | Students can: Work with 2 √ó 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area. | High School | |

Connecticut | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten | |

Connecticut | K.CC.A.2 | Kindergarten | ||

Connecticut | K.CC.A.3 | Kindergarten | ||

Connecticut | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten | |

Connecticut | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten | |

Connecticut | K.CC.C.6 | Kindergarten | ||

Connecticut | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten | |

Connecticut | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten | |

Connecticut | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten | |

Connecticut | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten | |

Connecticut | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten | |

Connecticut | K.G.B.5 | Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. | Kindergarten | |

Connecticut | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten | |

Connecticut | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten | |

Connecticut | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten | |

Connecticut | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten | |

Connecticut | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten | |

Connecticut | K.OA.A.1 | Kindergarten | ||

Connecticut | K.OA.A.2 | Kindergarten | ||

Connecticut | K.OA.A.3 | Kindergarten | ||

Connecticut | K.OA.A.4 | Kindergarten | ||

Connecticut | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten | |

Connecticut | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 | |

Connecticut | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 | |

Connecticut | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 | |

Connecticut | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 | |

Connecticut | 1.MD.A.2 | Grade 1 | ||

Connecticut | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 | |

Connecticut | 1.MD.C.4 | Grade 1 | ||

Connecticut | 1.NBT.A.1 | Grade 1 | ||

Connecticut | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 | |

Connecticut | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 | |

Connecticut | 1.NBT.C.4 | Grade 1 | ||

Connecticut | 1.NBT.C.5 | Grade 1 |