Major Cluster

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.

5 Lessons

13 Activities

Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

3 Lessons

3 Activities

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 contexts.

7 Lessons

8 Activities

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 contexts.

8 Lessons

9 Activities

Apply properties of operations as strategies to add and subtract rational numbers.

3 Lessons

3 Activities

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

2 Lessons

4 Activities

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.

4 Lessons

6 Activities

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero 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.

3 Lessons

4 Activities

Apply properties of operations as strategies to multiply and divide rational numbers.

4 Lessons

4 Activities

Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

5 Lessons

8 Activities

Solve real-world and mathematical problems involving the four operations with rational numbers.^1

14 Lessons

13 Activities