7.NOS.A: Use structure and representations to reason with rational numbers.

Use structure and representations to reason with rational numbers.

7.NOS.A.1Add and subtract rational numbers using multiple strategies and representations. a. Describe situations in which opposite quantities combine to make 0. b. Model the addition of rational numbers as movement along a number line, where the direction and distance depend on the sign and magnitude of the addend. Show that a number and its opposite have a sum of 0 (are additive inverses). c. Rewrite subtraction as addition using the additive inverse p – q = p + (–q). Use strategies such as number lines and applying absolute value of the difference to determine the distance between two rational numbers and solve problems in context. d. Model and solve multistep contextual problems involving addition and subtraction of rational numbers, using efficient and flexible strategies.7.NOS.A.2Multiply and divide rational numbers using multiple strategies and representations. a. Model multiplication of rational numbers using number lines, arrays, or area models to show how properties of operations (e.g., the distributive property) lead to rules for signed number multiplication, including (–1) × (–1) = 1. b. Interpret quotients of rational numbers in context and represent division of signed numbers in different forms, such as –p/q = (–p)/q = p/(–q) when the divisor is not zero. c. Use properties of operations to multiply and divide rational numbers flexibly and efficiently. d. Analyze the decimal representation of a quotient resulting from dividing rational numbers to determine whether it terminates or repeats and use this pattern to explain why all rational numbers have decimal forms that either terminate or repeat. e. Model and solve multistep contextual problems involving multiplication and division of rational numbers, using efficient and flexible strategies.7.NOS.A.3Solve multistep problems involving positive and negative rational numbers in any form (i.e., fractions, decimals, percents) using all four operations. a. Apply properties of operations to efficiently compute with rational numbers and convert between forms when appropriate to support problem solving. b. Evaluate the reasonableness of solutions using estimation, mental math, and understanding of the context.

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