Rewriting Expressions Using Properties of Real Numbers

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8th Grade level IIIBTC Style / Thinking ClassroomsUse the structure of an expression to write it in multiple ways.50 min

Learning Objective

Students will apply the Commutative, Associative, Distributive, Identity, and Inverse properties of real numbers to rewrite and simplify algebraic expressions in multiple equivalent forms.

Lesson Overview

Students progress from identifying and naming properties to strategically applying Commutative, Associative, Distributive, and Identity/Inverse properties to simplify increasingly complex algebraic expressions. Each task changes exactly one variable — number type, operation, number of terms, or structure — building toward multi-step simplification with like terms and nested grouping.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Pencils and scratch paper

Scaffolded Task Progression

1Task 1

State whether each equation is true or false. If true, name the property it illustrates.
a)

3 + 9 = 9 + 3

4 \cdot 7 = 7 \cdot 4

12 + 0 = 12

5 \cdot 1 = 5

2Task 2

State whether each equation is true or false. If true, name the property it illustrates.
a)

(2 + 5) + 8 = 2 + (5 + 8)

(3 \cdot 4) \cdot 5 = 3 \cdot (4 \cdot 5)

7 + (- 7) = 0

\frac{3}{4} \cdot \frac{4}{3} = 1

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