Multiplication Shortcuts: Properties of Multiplication

About This Resource

A complete Grade 3 math lesson pack on the properties of multiplication: the commutative property (turn-around facts), the associative property (grouping), the distributive property (break apart), the identity property of one and the zero property, with arrays, missing-number practice and strategy word problems. Includes a lesson plan, worksheet, quiz, homework, A5 flashcards, a rubric, detailed slides with speaker notes, Word files and answer keys.

Overview

Students learn five properties that make multiplication easier. Turning an array shows that 3 × 5 = 5 × 3 (commutative), grouping factors differently gives the same product (associative), breaking a hard fact into easier parts helps solve 7 × 8 as 7 × 5 + 7 × 3 (distributive), any number times 1 stays the same (identity) and any number times 0 is 0 (zero). Students use arrays, fill in missing numbers, name the property used and solve word problems with smart strategies.

Resource Details

Subject: Math
Topic: Properties of Multiplication
Category: Multiplication & Division
File Type: PDF
File Size: 320.6 KB
Published: 01 Nov 2026
Downloads: 0

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Grade 3 (ages 8–9) 55 minutes Multiplication arrays mental math reasoning problem solving

Learning Objectives

Use the commutative, associative and distributive properties to multiply.
Apply the identity property of one and the zero property.
Choose and explain a property that makes a multiplication problem easier.

How to Use This Resource

Show an array of 3 rows of 5 counters, then turn it, to introduce turn-around facts with the slides.
Use the flashcards for property names and examples, then complete the worksheet.
Use the quiz to check learning and send the homework home; answers are in the answer keys.

Classroom Activity Ideas

Array turn: students build an array with counters on a card and turn the card to see the turn-around fact.
Break it apart: draw a 6 × 7 array on grid paper and cut it into 6 × 5 and 6 × 2 to find the total.
Property match: students match number sentences to property cards and explain their choice.

Differentiation

Support: use arrays and counters for every question and focus on the commutative, identity and zero properties. Challenge: use the distributive property to multiply two-digit numbers by one-digit numbers, such as 6 × 14.

Assessment

The worksheet and quiz check using and naming the properties (answer keys included). Use the rubric for explanations and word problems.

Teacher Tips

Use friendly names first: turn-around (commutative), grouping (associative), break apart (distributive). Add the math names once students understand the ideas.

What's Included

10-page printable PDF lesson pack: teacher lesson plan with timings, materials and differentiation
Key vocabulary list (8 words with meanings and examples)
Student worksheet (5 activities)
Quiz / assessment (3 parts)
Homework practice page
Printable flashcards: 8 A5 picture cards (separate PDF)
Assessment rubric (4 levels)
Lesson slides (editable PowerPoint)
Editable Word version of all student pages
Complete answer key (also as a separate PDF)