Share It Out: The Distributive Property

About This Resource

A free Grade 6 math lesson and worksheet on the distributive property: breaking numbers apart for mental math, area models, expanding expressions such as 3(x + 4), factoring sums with the greatest common factor and spotting common mistakes. Includes a timed lesson plan, worksheet, editable Word version and answer key.

Overview

Students learn that multiplying a number by a sum is the same as multiplying it by each part and adding: a(b + c) = ab + ac. They use the property for mental math (7 × 38 = 7 × 30 + 7 × 8), see it in area models, expand algebraic expressions such as 3(x + 4) = 3x + 12, factor sums like 24 + 36 = 12(2 + 3) using the greatest common factor and find mistakes such as forgetting to multiply the second term.

Resource Details

Subject: Math
Topic: The Distributive Property
Category: Number Sense
File Type: PDF
File Size: 213.6 KB
Published: 31 Oct 2026
Downloads: 0

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Grade 6 (ages 11–12) 40 minutes Multiplication mental math expressions factoring reasoning

Student Task

Draw an area model for 7 × 38 split into 7 × 30 and 7 × 8.
Teach the property, then do the first questions of activity 1 together.
Students complete activities 2 to 5; answers are in the answer key.

Classroom Use

Mental math challenge: students use the distributive property to solve 6 × 47 and 8 × 52 in their heads.
Area model cards: match area model pictures to expanded expressions.
Party bags: 5 bags each hold 3 candies and 2 stickers; show 5(3 + 2) = 15 + 10.

Differentiation

Support: use area models and whole numbers only. Challenge: expand expressions with subtraction such as 4(2x − 3) and factor expressions with variables.

Answer Key & Assessment

Activity 1 checks using the property with numbers; activities 2 to 5 check expanding, factoring and reasoning (answer key included).

Learning Objectives

Use the distributive property to multiply mentally.
Expand expressions such as 3(x + 4).
Factor a sum using the greatest common factor.

Teacher Tips

Use arrows from the outside number to each term inside the brackets. Drawing both arrows helps students remember to multiply every term.

What's Included

6-page printable PDF lesson pack: teacher lesson plan with timings, materials and differentiation
Key vocabulary list (4 words with meanings and examples)
Student worksheet (5 activities)
Editable Word version of the worksheet
Complete answer key (also as a separate PDF)