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

The SCCR content standards and the process standards work together to enable all students to develop the world-class knowledge, skills, and life and career characteristics identified in the Profile of the South Carolina Graduate. Because manipulatives and technology are integral to the development of mathematical understanding in all grade levels and courses, SCCR recommends that the curriculum should support, and instructional approaches should include, the use of a variety of concrete materials and technological tools in order to help students explore connections, make conjectures, formulate generalizations, draw conclusions, and discover new mathematical ideas. DreamBox provides rigorous lessons and easy-to-use reporting that supports the SCCR, teachers, and students. You can track progress with Insight Reports that surface student performance by each standard and even create personalized assignments aligned with specific South Carolina standards.

#### Lessons by Standards

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

South Carolina | AAPR.3 | Graph polynomials identifying zeros when suitable factorizations are available and indicating end behavior. Write a polynomial function of least degree corresponding to a given graph. | Algebra |

South Carolina | ACE.2 | Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. | Algebra |

South Carolina | ASE.2 | Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions. | Algebra |

South Carolina | ASE.3.a | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression (Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain the connection between the zeros of the function, its linear factors, the x-intercepts of its graph, and the solutions to the corresponding quadratic equation) | Algebra |

South Carolina | ASE.3.b | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression (Determine the maximum or minimum value of a quadratic function by completing the square) | Algebra |

South Carolina | ASE.3.c | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression (Use the properties of exponents to transform expressions for exponential functions) | Algebra |

South Carolina | FBF.1.a | Write a function that describes a relationship between two quantities (Write a function that models a relationship between two quantities using both explicit expressions and a recursive process and by combining standard forms using addition, subtraction, multiplication and division to build new functions) | Algebra |

South Carolina | FBF.1.b | Write a function that describes a relationship between two quantities (Combine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations) | Algebra |

South Carolina | FIF.2 | Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation. | Algebra |

South Carolina | FIF.4 | Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. | Algebra |

South Carolina | FIF.7.a | Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases (Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior) | Algebra |

South Carolina | FIF.7.c | Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases (Graph exponential and logarithmic functions, showing intercepts and end behavior) | Algebra |

South Carolina | FIF.7.d | Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases (Graph trigonometric functions, showing period, midline, and amplitude) | Algebra |

South Carolina | SPID.6 | Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data. | Algebra |

South Carolina | SPID.7 | Create a linear function to graphically model data from a real-world problem and interpret the meaning of the slope and intercept(s) in the context of the given problem. | Algebra |

South Carolina | 1.ATO.3 | Apply Commutative and Associative Properties of Addition to find the sum (through 20) of two or three addends. | Grade 1 |

South Carolina | 1.ATO.4 | Understand subtraction as an unknown addend problem. | Grade 1 |

South Carolina | 1.ATO.5 | Recognize how counting relates to addition and subtraction. | Grade 1 |

South Carolina | 1.ATO.6.a | Demonstrate: (addition and subtraction through 20) | Grade 1 |

South Carolina | 1.ATO.6.b | Demonstrate: (fluency with addition and related subtraction facts through 10) | Grade 1 |

South Carolina | 1.ATO.7 | Understand the meaning of the equal sign as a relationship between two quantities (sameness) and determine if equations involving addition and subtraction are true. | Grade 1 |

South Carolina | 1.ATO.8 | Determine the missing number in addition and subtraction equations within 20. | Grade 1 |

South Carolina | 1.MDA.3 | Use analog and digital clocks to tell and record time to the hour and half hour. | Grade 1 |

South Carolina | 1.MDA.4 | Collect, organize, and represent data with up to 3 categories using object graphs, picture graphs, t-charts and tallies. | Grade 1 |

South Carolina | 1.NSBT.1.a | Extend the number sequence to: (count forward by ones to 120 starting at any number) | Grade 1 |

South Carolina | 1.NSBT.2.a | Understand place value through 99 by demonstrating that: (ten ones can be thought of as a bundle (group) called a 'ten') | Grade 1 |

South Carolina | 1.NSBT.3 | Compare two two-digit numbers based on the meanings of the tens and ones digits, using the words greater than, equal to, or less than. | Grade 1 |

South Carolina | 1.NSBT.4.a | Add through 99 using concrete models, drawings, and strategies based on place value to: (add a two-digit number and a one-digit number, understanding that sometimes it is necessary to compose a ten (regroup)) | Grade 1 |

South Carolina | 1.NSBT.4.b | Add through 99 using concrete models, drawings, and strategies based on place value to: (add a two-digit number and a multiple of 10) | Grade 1 |

South Carolina | 1.NSBT.5 | Determine the number that is 10 more or 10 less than a given number through 99 and explain the reasoning verbally and with multiple representations, including concrete models. | Grade 1 |

South Carolina | 1.NSBT.6 | Subtract a multiple of 10 from a larger multiple of 10, both in the range 10 to 90, using concrete models, drawings, and strategies based on place value. | Grade 1 |

South Carolina | 2.ATO.1 | Solve one- and two-step real-world/story problems using addition (as a joining action and as a part-part-whole action) and subtraction (as a separation action, finding parts of the whole, and as a comparison) through 99 with unknowns in all positions. | Grade 2 |

South Carolina | 2.ATO.2 | Demonstrate fluency with addition and related subtraction facts through 20. | Grade 2 |

South Carolina | 2.G.1 | Identify triangles, quadrilaterals, hexagons, and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. | Grade 2 |

South Carolina | 2.MDA.6 | Use analog and digital clocks to tell and record time to the nearest five-minute interval using a.m. and p.m. | Grade 2 |

South Carolina | 2.MDA.8 | Generate data by measuring objects in whole unit lengths and organize the data in a line plot using a horizontal scale marked in whole number units. | Grade 2 |

South Carolina | 2.MDA.9 | Collect, organize, and represent data with up to four categories using picture graphs and bar graphs with a single-unit scale. | Grade 2 |

South Carolina | 2.NSBT.1.a | Understand place value through 999 by demonstrating that: (100 can be thought of as a bundle (group) of 10 tens called a 'hundred') | Grade 2 |

South Carolina | 2.NSBT.2 | Count by tens and hundreds to 1,000 starting with any number. | Grade 2 |

South Carolina | 2.NSBT.3 | Read, write and represent numbers through 999 using concrete models, standard form, and equations in expanded form. | Grade 2 |

South Carolina | 2.NSBT.4 | Compare two numbers with up to three digits using words and symbols (i.e., >, =, or <). | Grade 2 |

South Carolina | 2.NSBT.5 | Add and subtract fluently through 99 using knowledge of place value and properties of operations. | Grade 2 |

South Carolina | 2.NSBT.6 | Add up to four two-digit numbers using strategies based on knowledge of place value and properties of operations. | Grade 2 |

South Carolina | 2.NSBT.7 | Add and subtract through 999 using concrete models, drawings, and symbols which convey strategies connected to place value understanding. | Grade 2 |

South Carolina | 2.NSBT.8 | Determine the number that is 10 or 100 more or less than a given number through 1,000 and explain the reasoning verbally and in writing. | Grade 2 |

South Carolina | 3.ATO.1 | Use concrete objects, drawings and symbols to represent multiplication facts of two single-digit whole numbers and explain the relationship between the factors (i.e., 0 - 10) and the product. | Grade 3 |

South Carolina | 3.ATO.2 | Use concrete objects, drawings and symbols to represent division without remainders and explain the relationship among the whole number quotient (i.e., 0 - 10), divisor (i.e., 0 - 10), and dividend. | Grade 3 |

South Carolina | 3.ATO.3 | Solve real-world problems involving equal groups, area/array, and number line models using basic multiplication and related division facts. Represent the problem situation using an equation with a symbol for the unknown. | Grade 3 |

South Carolina | 3.ATO.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient. | Grade 3 |

South Carolina | 3.ATO.5 | Apply properties of operations (i.e., Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property) as strategies to multiply and divide and explain the reasoning. | Grade 3 |

South Carolina | 3.ATO.6 | Understand division as a missing factor problem. | Grade 3 |

South Carolina | 3.ATO.7 | Demonstrate fluency with basic multiplication and related division facts of products and dividends through 100. | Grade 3 |

South Carolina | 3.G.1 | Understand that shapes in different categories (e.g., rhombus, rectangle, square, and other 4-sided shapes) may share attributes (e.g., 4-sided figures) and the shared attributes can define a larger category (e.g., quadrilateral). 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 |

South Carolina | 3.MDA.1 | Use analog and digital clocks to determine and record time to the nearest minute, using a.m. and p.m.; measure time intervals in minutes; and solve problems involving addition and subtraction of time intervals within 60 minutes. | Grade 3 |

South Carolina | 3.MDA.3 | Collect, organize, classify, and interpret data with multiple categories and draw a scaled picture graph and a scaled bar graph to represent the data. | Grade 3 |

South Carolina | 3.MDA.4 | Generate data by measuring length to the nearest inch, half-inch and quarter-inch and organize the data in a line plot using a horizontal scale marked off in appropriate units. | Grade 3 |

South Carolina | 3.MDA.5.a | Understand the concept of area measurement (Recognize area as an attribute of plane figures) | Grade 3 |

South Carolina | 3.MDA.5.b | Understand the concept of area measurement (Measure area by building arrays and counting standard unit squares) | Grade 3 |

South Carolina | 3.MDA.5.c | Understand the concept of area measurement (Determine the area of a rectilinear polygon and relate to multiplication and addition) | Grade 3 |

South Carolina | 3.NSBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |

South Carolina | 3.NSBT.2 | Add and subtract whole numbers fluently to 1,000 using knowledge of place value and properties of operations. | Grade 3 |

South Carolina | 3.NSBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10 - 90, using knowledge of place value and properties of operations. | Grade 3 |

South Carolina | 3.NSF.1.a | Develop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers (A fraction 1/b (called a unit fraction) is the quantity formed by one part when a whole is partitioned into b equal parts) | Grade 3 |

South Carolina | 3.NSF.1.b | Develop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers (A fraction a/b is the quantity formed by ?? parts of size 1/b) | Grade 3 |

South Carolina | 3.NSF.1.c | Develop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers (A fraction is a number that can be represented on a number line based on counts of a unit fraction) | Grade 3 |

South Carolina | 3.NSF.2.a | Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: (two fractions are equal if they are the same size, based on the same whole, or at the same point on a number line) | Grade 3 |

South Carolina | 3.NSF.2.b | Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: (fraction equivalence can be represented using set, area, and linear models) | Grade 3 |

South Carolina | 3.NSF.2.c | Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: (whole numbers can be written as fractions (e.g., 4 = 4/1 and 1 = 4/4)) | Grade 3 |

South Carolina | 3.NSF.2.d | Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: (fractions with the same numerator or same denominator can be compared by reasoning about their size based on the same whole) | Grade 3 |

South Carolina | 4.ATO.1 | Interpret a multiplication equation as a comparison (e.g. interpret 35 = 5x7 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 |

South Carolina | 4.ATO.2 | Solve real-world problems using multiplication (product unknown) and division (group size unknown, number of groups unknown). | Grade 4 |

South Carolina | 4.ATO.4 | Recognize that a whole number is a multiple of each of its factors. Find all factors for a whole number in the range 1 - 100 and determine whether the whole number is prime or composite. | Grade 4 |

South Carolina | 4.ATO.5 | Generate a number or shape pattern that follows a given rule and determine a term that appears later in the sequence. | Grade 4 |

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

South Carolina | 4.G.2 | Classify quadrilaterals based on the presence or absence of parallel or perpendicular lines. | Grade 4 |

South Carolina | 4.MDA.1 | Convert measurements within a single system of measurement, customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric (i.e., cm, m, km, g, kg, mL, L) from a larger to a smaller unit. | Grade 4 |

South Carolina | 4.MDA.2 | Solve real-world problems involving distance/length, intervals of time within 12 hours, liquid volume, mass, and money using the four operations. | Grade 4 |

South Carolina | 4.MDA.4 | Create a line plot to display a data set (i.e., generated by measuring length to the nearest quarter-inch and eighth-inch) and interpret the line plot. | Grade 4 |

South Carolina | 4.MDA.5 | Understand the relationship of an angle measurement to a circle. | Grade 4 |

South Carolina | 4.MDA.6 | Measure and draw angles in whole number degrees using a protractor. | Grade 4 |

South Carolina | 4.MDA.7 | Solve addition and subtraction problems to find unknown angles in real-world and mathematical problems. | Grade 4 |

South Carolina | 4.NSBT.1 | Understand that, in a multi-digit whole number, a digit represents ten times what the same digit represents in the place to its right. | Grade 4 |

South Carolina | 4.NSBT.3 | Use rounding as one form of estimation and round whole numbers to any given place value. | Grade 4 |

South Carolina | 4.NSBT.4 | Fluently add and subtract multi-digit whole numbers using strategies to include a standard algorithm. | Grade 4 |

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

South Carolina | 4.NSBT.6 | Divide up to a four-digit dividend by a one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. | Grade 4 |

South Carolina | 4.NSF.1 | Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100), 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 |

South Carolina | 4.NSF.2 | Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2 and represent the comparison using the symbols >, =, or <. | Grade 4 |

South Carolina | 4.NSF.3 | Develop an understanding of addition and subtraction of fractions based on unit fractions. | Grade 4 |

South Carolina | 4.NSF.4 | Apply and extend an understanding of multiplication by multiplying a whole number and a fraction. | Grade 4 |

South Carolina | 4.NSF.5 | Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators of 10 and 100. | Grade 4 |

South Carolina | 4.NSF.6 | Write a fraction with a denominator of 10 or 100 using decimal notation, and read and write a decimal number as a fraction. | Grade 4 |

South Carolina | 4.NSF.7 | Compare and order decimal numbers to hundredths, and justify using concrete and visual models. | Grade 4 |

South Carolina | 5.ATO.1 | Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces). | Grade 5 |

South Carolina | 5.ATO.3.a | Investigate the relationship between two numerical patterns (Generate two numerical patterns given two rules and organize in tables) | Grade 5 |

South Carolina | 5.ATO.3.b | Investigate the relationship between two numerical patterns (Translate the two numerical patterns into two sets of ordered pairs) | Grade 5 |

South Carolina | 5.ATO.3.c | Investigate the relationship between two numerical patterns (Graph the two sets of ordered pairs on the same coordinate plane) | Grade 5 |

South Carolina | 5.ATO.3.d | Investigate the relationship between two numerical patterns (Identify the relationship between the two numerical patterns) | Grade 5 |

South Carolina | 5.G.1.a | Define a coordinate system (The x- and y- axes are perpendicular number lines that intersect at 0 (the origin)) | Grade 5 |

South Carolina | 5.G.1.b | Define a coordinate system (Any point on the coordinate plane can be represented by its coordinates) | Grade 5 |

South Carolina | 5.G.1.c | Define a coordinate system (The first number in an ordered pair is the x-coordinate and represents the horizontal distance from the origin) | Grade 5 |

South Carolina | 5.G.1.d | Define a coordinate system (The second number in an ordered pair is the y-coordinate and represents the vertical distance from the origin) | Grade 5 |

South Carolina | 5.G.2 | Plot and interpret points in the first quadrant of the coordinate plane to represent real-world and mathematical situations. | Grade 5 |

South Carolina | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |

South Carolina | 5.MDA.2 | Create a line plot consisting of unit fractions and use operations on fractions to solve problems related to the line plot. | Grade 5 |

South Carolina | 5.NSBT.1 | Understand that, in a multi-digit whole number, a digit in one place represents 10 times what the same digit represents in the place to its right, and represents 1/10 times what the same digit represents in the place to its left. | Grade 5 |

South Carolina | 5.NSBT.2.a | Use whole number exponents to explain: (patterns in the number of zeroes of the product when multiplying a number by powers of 10) | Grade 5 |

South Carolina | 5.NSBT.2.b | Use whole number exponents to explain: (patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10) | Grade 5 |

South Carolina | 5.NSBT.3 | Read and write decimals in standard and expanded form. Compare two decimal numbers to the thousandths using the symbols >, =, or <. | Grade 5 |

South Carolina | 5.NSBT.4 | Round decimals to any given place value within thousandths. | Grade 5 |

South Carolina | 5.NSBT.5 | Fluently multiply multi-digit whole numbers using strategies to include a standard algorithm. | Grade 5 |

South Carolina | 5.NSBT.6 | Divide up to a four-digit dividend by a two-digit divisor, using strategies based on place value, the properties of operations, and the relationship between multiplication and division. | Grade 5 |

South Carolina | 5.NSBT.7 | Add, subtract, multiply, and divide decimal numbers to hundredths using concrete area models and drawings. | Grade 5 |

South Carolina | 5.NSF.3 | Understand the relationship between fractions and division of whole numbers by interpreting a fraction as the numerator divided by the denominator (i.e., a/b = a divided by b). | Grade 5 |

South Carolina | 5.NSF.4.a | Extend the concept of multiplication to multiply a fraction or whole number by a fraction (Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths) | Grade 5 |

South Carolina | 5.NSF.4.b | Extend the concept of multiplication to multiply a fraction or whole number by a fraction (Interpret multiplication of a fraction by a whole number and a whole number by a fraction and compute the product) | Grade 5 |

South Carolina | 5.NSF.5.a | Justify the reasonableness of a product when multiplying with fractions (Estimate the size of the product based on the size of the two factors) | Grade 5 |

South Carolina | 5.NSF.5.b | Justify the reasonableness of a product when multiplying with fractions (Explain why multiplying a given number by a number greater than 1 (e.g., improper fractions, mixed numbers, whole numbers) results in a product larger than the given number) | Grade 5 |

South Carolina | 5.NSF.5.c | Justify the reasonableness of a product when multiplying with fractions (Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number) | Grade 5 |

South Carolina | 5.NSF.5.d | Justify the reasonableness of a product when multiplying with fractions (Explain why multiplying the numerator and denominator by the same number has the same effect as multiplying the fraction by 1) | Grade 5 |

South Carolina | 5.NSF.6 | Solve real-world problems involving multiplication of a fraction by a fraction, improper fraction and a mixed number. | Grade 5 |

South Carolina | 5.NSF.7.a | Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations (Interpret division of a unit fraction by a non-zero whole number and compute the quotient) | Grade 5 |

South Carolina | 5.NSF.7.b | Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations (Interpret division of a whole number by a unit fraction and compute the quotient) | Grade 5 |

South Carolina | 5.NSF.8 | Solve real-world problems involving division of unit fractions and whole numbers, using visual fraction models and equations. | Grade 5 |

South Carolina | 6.EEI.1 | Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the Order of Operations. | Grade 6 |

South Carolina | 6.EEI.2.a | Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers (Translate between algebraic expressions and verbal phrases that include variables) | Grade 6 |

South Carolina | 6.EEI.2.b | Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers (Investigate and identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and factor) | Grade 6 |

South Carolina | 6.EEI.2.c | Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers (Evaluate real-world and algebraic expressions for specific values using the Order of Operations. Grouping symbols should be limited to parentheses, braces, and brackets. Exponents should be limited to whole-numbers) | Grade 6 |

South Carolina | 6.EEI.3 | Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions. | Grade 6 |

South Carolina | 6.EEI.5 | Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. | Grade 6 |

South Carolina | 6.EEI.7 | Write and solve one-step linear equations in one variable involving nonnegative rational numbers for real-world and mathematical situations. | Grade 6 |

South Carolina | 6.EEI.8.a | Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations (Write an inequality of the form x > c or x < c and graph the solution set on a number line) | Grade 6 |

South Carolina | 6.EEI.8.b | Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations (Recognize that inequalities have infinitely many solutions) | Grade 6 |

South Carolina | 6.GM.3.a | Apply the concepts of polygons and the coordinate plane to real-world and mathematical situations (Given coordinates of the vertices, draw a polygon in the coordinate plane) | Grade 6 |

South Carolina | 6.GM.3.b | Apply the concepts of polygons and the coordinate plane to real-world and mathematical situations (Find the length of an edge if the vertices have the same x-coordinates or same y-coordinates) | Grade 6 |

South Carolina | 6.NS.1 | Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real-world situations). | Grade 6 |

South Carolina | 6.NS.2 | Fluently divide multi-digit whole numbers using a standard algorithmic approach. | Grade 6 |

South Carolina | 6.NS.3 | Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard algorithmic approach. | Grade 6 |

South Carolina | 6.NS.5 | Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation. | Grade 6 |

South Carolina | 6.NS.6.a | Extend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane (Understand the concept of opposite numbers, including zero, and their relative locations on the number line) | Grade 6 |

South Carolina | 6.NS.6.b | Extend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane (Understand that the signs of the coordinates in ordered pairs indicate their location on an axis or in a quadrant on the coordinate plane) | Grade 6 |

South Carolina | 6.NS.7.b | Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers (Interpret statements using less than (), and equal to (=) as relative locations on the number line) | Grade 6 |

South Carolina | 6.NS.7.c | Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers (Use concepts of equality and inequality to write and to explain real-world and mathematical situations) | Grade 6 |

South Carolina | 6.NS.7.d | Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers (Understand that absolute value represents a number's distance from zero on the number line and use the absolute value of a rational number to represent real-world situations) | Grade 6 |

South Carolina | 6.NS.7.e | Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers (Recognize the difference between comparing absolute values and ordering rational numbers. For negative rational numbers, understand that as the absolute value increases, the value of the negative number decreases) | Grade 6 |

South Carolina | 6.NS.8.a | Extend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers (Plot points in all four quadrants to represent the problem) | Grade 6 |

South Carolina | 6.NS.8.b | Extend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers (Find the distance between two points when ordered pairs have the same x-coordinates or same y-coordinates) | Grade 6 |

South Carolina | 6.RP.1 | Interpret the concept of a ratio as the relationship between two quantities, including part to part and part to whole. | Grade 6 |

South Carolina | 6.RP.2.b | Investigate relationships between ratios and rates (Recognize that a rate is a type of ratio involving two different units) | Grade 6 |

South Carolina | 6.RP.3.a | Apply the concepts of ratios and rates to solve real-world and mathematical problems (Create a table consisting of equivalent ratios and plot the results on the coordinate plane) | Grade 6 |

South Carolina | 6.RP.3.c | Apply the concepts of ratios and rates to solve real-world and mathematical problems (Use two tables to compare related ratios) | Grade 6 |

South Carolina | 6.RP.3.d | Apply the concepts of ratios and rates to solve real-world and mathematical problems (Apply concepts of unit rate to solve problems, including unit pricing and constant speed) | Grade 6 |

South Carolina | 6.RP.3.e | Apply the concepts of ratios and rates to solve real-world and mathematical problems (Understand that a percentage is a rate per 100 and use this to solve problems involving wholes, parts, and percentages) | Grade 6 |

South Carolina | 7.EEI.1 | Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic expressions with rational coefficients. | Grade 7 |

South Carolina | 7.EEI.3 | Extend previous understanding of Order of Operations to solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol. | Grade 7 |

South Carolina | 7.GM.1 | Determine the scale factor and translate between scale models and actual measurements (e.g., lengths, area) of real-world objects and geometric figures using proportional reasoning. | Grade 7 |

South Carolina | 7.GM.2.a | Construct triangles and special quadrilaterals using a variety of tools (e.g., freehand, ruler and protractor, technology) (Construct triangles given all measurements of either angles or sides) | Grade 7 |

South Carolina | 7.GM.2.b | Construct triangles and special quadrilaterals using a variety of tools (e.g., freehand, ruler and protractor, technology) (Decide if the measurements determine a unique triangle, more than one triangle, or no triangle) | Grade 7 |

South Carolina | 7.GM.5 | Write equations to solve problems involving the relationships between angles formed by two intersecting lines, including supplementary, complementary, vertical, and adjacent. | Grade 7 |

South Carolina | 7.NS.1.a | Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Understand that the additive inverse of a number is its opposite and their sum is equal to zero) | Grade 7 |

South Carolina | 7.NS.1.b | Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Understand that the sum of two rational numbers (p + q) represents a distance from p on the number line equal to |q| where the direction is indicated by the sign of q) | Grade 7 |

South Carolina | 7.NS.1.c | Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Translate between the subtraction of rational numbers and addition using the additive inverse, p ? q = p + (?q)) | Grade 7 |

South Carolina | 7.NS.1.d | Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference) | Grade 7 |

South Carolina | 7.NS.1.e | Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line (Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers) | Grade 7 |

South Carolina | 7.NS.2.b | Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers (Understand sign rules for multiplying rational numbers) | Grade 7 |

South Carolina | 7.NS.2.c | Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers (Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number) | Grade 7 |

South Carolina | 7.NS.2.d | Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers (Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide rational numbers) | Grade 7 |

South Carolina | 7.NS.2.e | Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers (Understand that some rational numbers can be written as integers and all rational numbers can be written as fractions or decimal numbers that terminate or repeat) | Grade 7 |

South Carolina | 7.NS.3 | Apply the concepts of all four operations with rational numbers to solve real-world and mathematical problems. | Grade 7 |

South Carolina | 7.RP.1 | Compute unit rates, including those involving complex fractions, with like or different units. | Grade 7 |

South Carolina | 7.RP.2.a | Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Determine when two quantities are in a proportional relationship) | Grade 7 |

South Carolina | 7.RP.2.b | Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Recognize or compute the constant of proportionality) | Grade 7 |

South Carolina | 7.RP.2.c | Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Understand that the constant of proportionality is the unit rate) | Grade 7 |

South Carolina | 7.RP.2.d | Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Use equations to model proportional relationships) | Grade 7 |

South Carolina | 7.RP.2.e | Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations (Investigate the graph of a proportional relationship and explain the meaning of specific points (e.g., origin, unit rate) in the context of the situation) | Grade 7 |

South Carolina | 7.RP.3 | Solve real-world and mathematical problems involving ratios and percentages using proportional reasoning (e.g., multi-step dimensional analysis, percent increase/decrease, tax). | Grade 7 |

South Carolina | 8.DSP.1.a | Investigate bivariate data (Collect bivariate data) | Grade 8 |

South Carolina | 8.DSP.1.b | Investigate bivariate data (Graph the bivariate data on a scatter plot) | Grade 8 |

South Carolina | 8.DSP.1.c | Investigate bivariate data (Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear)) | Grade 8 |

South Carolina | 8.DSP.2 | Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line to the data points. | Grade 8 |

South Carolina | 8.EEI.3.a | Explore the relationship between quantities in decimal and scientific notation (Express very large and very small quantities in scientific notation in the form a x 10 to the b power = p where 1 ? a < 10 and b is an integer) | Grade 8 |

South Carolina | 8.EEI.4.a | Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems (Multiply and divide numbers expressed in both decimal and scientific notation) | Grade 8 |

South Carolina | 8.EEI.4.b | Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems (Select appropriate units of measure when representing answers in scientific notation) | Grade 8 |

South Carolina | 8.EEI.5.a | Apply concepts of proportional relationships to real-world and mathematical situations (Graph proportional relationships) | Grade 8 |

South Carolina | 8.EEI.5.b | Apply concepts of proportional relationships to real-world and mathematical situations (Interpret unit rate as the slope of the graph) | Grade 8 |

South Carolina | 8.EEI.5.c | Apply concepts of proportional relationships to real-world and mathematical situations (Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions) | Grade 8 |

South Carolina | 8.EEI.6.a | Apply concepts of slope and y - intercept to graphs, equations, and proportional relationships (Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles) | Grade 8 |

South Carolina | 8.EEI.6.b | Apply concepts of slope and y - intercept to graphs, equations, and proportional relationships (Derive the slope-intercept form (y = mx + b) for a non-vertical line) | Grade 8 |

South Carolina | 8.EEI.7.a | Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations (Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides) | Grade 8 |

South Carolina | 8.EEI.7.b | Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations (Recognize the three types of solutions to linear equations: one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b)) | Grade 8 |

South Carolina | 8.EEI.7.c | Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations (Generate linear equations with the three types of solutions) | Grade 8 |

South Carolina | 8.EEI.7.d | Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations (Justify why linear equations have a specific type of solution) | Grade 8 |

South Carolina | 8.EEI.8.a | Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions (Graph systems of linear equations and estimate their point of intersection) | Grade 8 |

South Carolina | 8.EEI.8.b | Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions (Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines) | Grade 8 |

South Carolina | 8.EEI.8.c | Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions (Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection) | Grade 8 |

South Carolina | 8.F.1.a | Explore the concept of functions (Understand that a function assigns to each input exactly one output) | Grade 8 |

South Carolina | 8.F.2 | Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions. | Grade 8 |

South Carolina | 8.F.3.a | Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions) (Define an equation in slope-intercept form (y = mx + b) as being a linear function) | Grade 8 |

South Carolina | 8.F.3.c | Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions) (Provide examples of nonlinear functions) | Grade 8 |

South Carolina | 8.F.4.b | Apply the concepts of linear functions to real-world and mathematical situations (Determine the slope and the ??-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions) | Grade 8 |

South Carolina | 8.F.4.c | Apply the concepts of linear functions to real-world and mathematical situations (Construct a function in slope-intercept form that models a linear relationship between two quantities) | Grade 8 |

South Carolina | 8.F.4.d | Apply the concepts of linear functions to real-world and mathematical situations (Interpret the meaning of the slope and the y - intercept of a linear function in the context of the situation) | Grade 8 |

South Carolina | 8.F.5.a | Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations (Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous)) | Grade 8 |

South Carolina | 8.F.5.b | Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations (Sketch the graph of a function from a verbal description) | Grade 8 |

South Carolina | 8.GM.1.a | Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology) (Verify that lines are mapped to lines, including parallel lines) | Grade 8 |

South Carolina | 8.GM.1.b | Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology) (Verify that corresponding angles are congruent) | Grade 8 |

South Carolina | 8.GM.1.c | Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology) (Verify that corresponding line segments are congruent) | Grade 8 |

South Carolina | 8.GM.2.d | Apply the properties of rigid transformations (rotations, reflections, translations) (Recognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image) | Grade 8 |

South Carolina | 8.GM.2.e | Apply the properties of rigid transformations (rotations, reflections, translations) (Given two congruent figures, describe the series of rigid transformations that justifies this congruence) | Grade 8 |

South Carolina | 8.GM.4.b | Apply the properties of transformations (rotations, reflections, translations, dilations) (Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image) | Grade 8 |

South Carolina | 8.GM.4.c | Apply the properties of transformations (rotations, reflections, translations, dilations) (Given two similar figures, describe the series of transformations that justifies this similarity) | Grade 8 |

South Carolina | 8.GM.7 | Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles. | Grade 8 |

South Carolina | 8.GM.8 | Find the distance between any two points in the coordinate plane using the Pythagorean Theorem. | Grade 8 |

South Carolina | K.ATO.1 | Model situations that involve addition and subtraction within 10 using objects, fingers, mental images, drawings, acting out situations, verbal explanations, expressions, and equations. | Kindergarten |

South Carolina | K.ATO.2 | Solve real-world/story problems using objects and drawings to find sums up to 10 and differences within 10. | Kindergarten |

South Carolina | K.ATO.3 | Compose and decompose numbers up to 10 using objects, drawings, and equations. | Kindergarten |

South Carolina | K.ATO.4 | Create a sum of 10 using objects and drawings when given one of two addends 1 - 9. | Kindergarten |

South Carolina | K.ATO.5 | Add and subtract fluently within 5. | Kindergarten |

South Carolina | K.NS.1 | Count forward by ones and tens to 100. | Kindergarten |

South Carolina | K.NS.2 | Count forward by ones beginning from any number less than 100. | Kindergarten |

South Carolina | K.NS.3 | Read numbers from 0 - 20 and represent a number of objects 0 - 20 with a written numeral. | Kindergarten |

South Carolina | K.NS.4.a | Understand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that: (the last number said tells the number of objects in the set (cardinality)) | Kindergarten |

South Carolina | K.NS.4.b | Understand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that: (the number of objects is the same regardless of their arrangement or the order in which they are counted (conservation of number)) | Kindergarten |

South Carolina | K.NS.4.c | Understand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that: (each successive number name refers to a quantity that is one more and each previous number name refers to a quantity that is one less) | Kindergarten |

South Carolina | K.NS.5 | Count a given number of objects from 1 - 20 and connect this sequence in a one-to-one manner. | Kindergarten |

South Carolina | K.NS.7 | Determine whether the number of up to ten objects in one group is more than, less than, or equal to the number of up to ten objects in another group using matching and counting strategies. | Kindergarten |

South Carolina | K.NS.8 | Compare two written numerals up to 10 using more than, less than or equal to. | Kindergarten |

South Carolina | K.NSBT.1 | Compose and decompose numbers from 11 - 19 separating ten ones from the remaining ones using objects and drawings. | Kindergarten |