#### Innovative lessons for key K-8 math concepts and skills

Arizona’s math standards provide a clear understanding of what students are expected to learn so they graduate high school ready for college and career. The standards focus on the following mathematical areas: Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations (Base Ten and Fractions), Expressions and Equations, the Number System, Measurement and Data, and Geometry. DreamBox makes it easy to track progress toward Arizona Math standards and create personalized assignments aligned with specific Arizona standards from the Insight Dashboard.

#### Lessons by Standards

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

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 ñhow many moreî and ñhow many lessî 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 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 |

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 = _ 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 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 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 1 100 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 ñAdd 3î and the starting number 0, and given the rule ñAdd 6î 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 |