The Number System
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. [7-NS1]
Apply properties of operations as strategies to add and subtract rational numbers. [7-NS1d]
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. [7-NS2]
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. [7-NS2a]
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers, then –(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. [7-NS2b]
Apply properties of operations as strategies to multiply and divide rational numbers. [7-NS2c]
Expressions and Equations
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7-EE4]
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. [7-EE4a]