South Carolina State Standards for Mathematics: Grade 6

SC.6-1 Mathematical Processes: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

6-1.1 Generate and solve complex abstract problems that involve modeling physical, social, and/or mathematical phenomena.

6-1.2 Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.

6-1.3 Use inductive and deductive reasoning to formulate mathematical arguments.

6-1.4 Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship.

6-1.5 Generalize mathematical statements based on inductive and deductive reasoning.

6-1.6 Use correct and clearly written or spoken words, variables, and notations to communicate about significant mathematical tasks.

6-1.7 Generalize connections among a variety of representational forms and real-world situations.

6-1.8 Use standard and nonstandard representations to convey and support mathematical relationships.

SC.6-2 Number and Operations: The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable methods of multiplying and dividing fractions and decimals; and the use of exponential notation to represent whole numbers.

6-2.1 Understand whole-number percentages through 100.

6-2.2 Understand integers.

6-2.3 Compare rational numbers and whole-number percentages through 100 by using the symbols less than or equal to, greater than or equal to, <, >, and =.

6-2.4 Apply an algorithm to add and subtract fractions.

6-2.5 Generate strategies to multiply and divide fractions and decimals.

6-2.6 Understand the relationship between ratio/rate and multiplication/division.

6-2.7 Apply strategies and procedures to determine values of powers of 10, up to 10to the 6th.

6-2.8 Represent the prime factorization of numbers by using exponents.

6-2.9 Represent whole numbers in exponential form.

SC.6-3 Algebra: The student will demonstrate through the mathematical processes an understanding of writing, interpreting, and using mathematical expressions, equations, and inequalities.

6-3.1 Analyze numeric and algebraic patterns and pattern relationships.

6-3.2 Apply order of operations to simplify whole-number expressions.

6-3.3 Represent algebraic relationships with variables in expressions, simple equations, and simple inequalities.

6-3.4 Use the commutative, associative, and distributive properties to show that two expressions are equivalent.

6-3.5 Use inverse operations to solve one-step equations that have whole-number solutions and variables with whole-number coefficients.

SC.6-4 Geometry: The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary angles; and the relationship between line and rotational symmetry.

6-4.1 Represent with ordered pairs of integers the location of points in a coordinate grid.

6-4.2 Apply strategies and procedures to find the coordinates of the missing vertex of a square, rectangle, or right triangle when given the coordinates of the polygon's other vertices.

6-4.3 Generalize the relationship between line symmetry and rotational symmetry for two-dimensional shapes.

6-4.4 Construct two-dimensional shapes with line or rotational symmetry.

6-4.5 Identify the transformation(s) used to move a polygon from one location to another in the coordinate plane.

6-4.6 Explain how transformations affect the location of the original polygon in the coordinate plane.

6-4.7 Compare the angles, side lengths, and perimeters of similar shapes.

6-4.8 Classify shapes as similar.

6-4.9 Classify pairs of angles as either complementary or supplementary.

SC.6-5 Measurement: The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine unit rates; and the use of scale to determine distance.

6-5.1 Explain the relationships among the circumference, diameter, and radius of a circle.

6-5.2 Apply strategies and formulas with an approximation of pi (3.14, or 22/7) to find the circumference and area of a circle.

6-5.3 Generate strategies to determine the surface area of a rectangular prism and a cylinder.

6-5.4 Apply strategies and procedures to estimate the perimeters and areas of irregular shapes.

6-5.5 Apply strategies and procedures of combining and subdividing to find the perimeters and areas of irregular shapes.

6-5.6 Use proportions to determine unit rates.

6-5.7 Use a scale to determine distance.

SC.6-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the relationships within one population or sample.

6-6.1 Predict the characteristics of one population based on the analysis of sample data.

6-6.2 Organize data in frequency tables, histograms, or stem-and-leaf plots as appropriate.

6-6.3 Analyze which measure of central tendency (mean, median, or mode) is the most appropriate for a given purpose.

6-6.4 Use theoretical probability to determine the sample space and probability for one- and two-stage events such as tree diagrams, models, lists, charts, and pictures.

6-6.5 Apply procedures to calculate the probability of complementary events.