Arizona's College and Career Ready Standards
AZ.7.NS. The Number System (NS)
7.NS.A. Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers except division by zero.
7.NS.A.1. Add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.A.1.b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world context.
7.NS.A.1.c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world context.
7.NS.A.1.d. Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.A.2. Multiply and divide integers and other rational numbers.
7.NS.A.2.a. 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 context.
7.NS.A.2.c. Apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.A.3. Solve mathematical problems and problems in real-world context involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions where a/b ÷ c/d when a,b,c,and d are all integers and b,c, and d ≠ 0.
AZ.7.EE. Expressions and Equations (EE)
7.EE.B. Solve mathematical problems and problems in real-world context using numerical and algebraic expressions and equations.
7.EE.B.3. Solve multi-step mathematical problems and problems in real-world context posed with positive and negative rational numbers in any form. Convert between forms as appropriate and assess the reasonableness of answers. For example, If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50 per hour.
7.EE.B.4. Use variables to represent quantities in mathematical problems and problems in real-world context, and construct simple equations and inequalities to solve problems.
7.EE.B.4.a. 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.