Mathematics · Grade 3 · Review and Consolidation · Term 4

Operations Review: Multiplication and Division

Students consolidate understanding of multiplication and division strategies and their relationship.

• Ontario Curriculum Expectations
• 3.OA.A.1
• 3.OA.A.2
• 3.OA.B.5

About This Topic

Grade 3 students consolidate multiplication and division strategies in this Term 4 review, focusing on their inverse relationship. They revisit facts to 10x10 through arrays, equal groups, repeated addition or subtraction, and skip counting. Mental math draws on properties such as commutative (3x4=4x3) and associative ((2x3)x4=2x(3x4)). Students design strategies for multi-step problems, like finding how many packs of 6 cookies serve 24 people, then justify using drawings or equations.

This unit builds fluency and reasoning, linking operations to real contexts like sharing items or grouping plants. Key questions guide analysis of multiplication-division pairs and property use, aligning with standards 3.OA.A.1, 3.OA.A.2, and 3.OA.B.5. Fact families reinforce that division undoes multiplication, preparing students for algebraic thinking.

Active learning benefits this topic greatly. Manipulatives and games make abstract relationships visible and engaging. Collaborative problem-solving prompts peers to question and justify strategies, deepening understanding and retention during review.

Key Questions

1. Analyze the relationship between multiplication and division.
2. Design a strategy to solve a multi-step multiplication or division problem.
3. Justify the use of specific properties of operations in mental math.

Learning Objectives

• Analyze the relationship between multiplication and division using fact families.
• Design a strategy to solve a multi-step word problem involving multiplication or division.
• Justify the use of the commutative and associative properties in mental math calculations.
• Calculate the product or quotient for a given multiplication or division fact.
• Compare and contrast different strategies for solving multiplication and division problems.

Before You Start

Introduction to Multiplication

Why: Students need a foundational understanding of what multiplication represents (equal groups, repeated addition) before reviewing strategies and properties.

Introduction to Division

Why: Students must first grasp the concept of division (sharing equally, making equal groups) to understand its relationship with multiplication.

Arrays and Equal Groups

Why: Visual representations like arrays and equal groups help students conceptualize multiplication and division, which is essential for reviewing these operations.

Key Vocabulary

Multiplication	An operation that combines equal groups to find a total amount. It can be thought of as repeated addition.
Division	An operation that separates a total amount into equal groups or finds how many equal groups can be made.
Fact Family	A set of related multiplication and division facts that use the same three numbers, showing the inverse relationship between the operations.
Commutative Property	A property of multiplication that states the order of the factors does not change the product (e.g., 3 x 4 = 4 x 3).
Associative Property	A property of multiplication that states the way factors are grouped does not change the product (e.g., (2 x 3) x 4 = 2 x (3 x 4)).

Watch Out for These Misconceptions

Common Misconception

Multiplication always means repeated addition; division always means repeated subtraction.

What to Teach Instead

Show both operations with arrays: 3x4 as 3 rows of 4, and 12/3 as 12 divided into 3 groups of 4. Active array-building in pairs helps students see the shared structure and inverse nature.

Common Misconception

Order of numbers does not matter in division like it does in multiplication.

What to Teach Instead

Use counters to model 12/3 vs. 3/12, revealing non-commutative property. Group discussions during relay games clarify why dividend-divisor order affects quotients, building precise language.

Common Misconception

All multi-step problems need long division or calculator.

What to Teach Instead

Break problems into steps with drawings or partial products. Collaborative stations let students test and justify mental strategies, proving properties suffice for Grade 3 levels.

Active Learning Ideas

Stations Rotation: Fact Family Cards

Prepare cards with multiplication facts, products, and related divisions. At stations, pairs match sets into fact families (e.g., 3x4, 12, 4x3, 12/3), draw arrays, and write equations. Rotate every 10 minutes, then share one family with the class.

45 min·Pairs

Simulation Game: Multiplication-Division Relay

Divide class into teams. First student solves a multiplication problem on a board, tags next for the inverse division, and so on. Use word problems for multi-step relay legs. Winning team explains one strategy.

30 min·Small Groups

Individual: Strategy Design Challenge

Provide multi-step word problems on sheets. Students choose tools like base-10 blocks or drawings to solve, then write justification using properties. Circulate to conference and extend thinking.

25 min·Individual

Whole Class: Properties Charades

Students act out properties: one mimes commutative by swapping factors, group guesses and solves related division. Builds to mental math showdown with volunteer problems.

20 min·Whole Class

Real-World Connections

• Bakers use multiplication and division to determine ingredient quantities for recipes. For example, if a recipe for 12 cookies needs 2 cups of flour, they use division to figure out how much flour is needed for 24 cookies.
• Event planners use division to arrange seating for guests at tables. If 48 guests are attending and each table seats 6 people, they use division to calculate that 8 tables are needed.
• Retail workers use multiplication to calculate the total cost of multiple items. If a toy costs $5 and a customer buys 3, they use multiplication to find the total cost of $15.

Assessment Ideas

Exit Ticket

Provide students with a card showing a fact family, for example, 4, 5, 20. Ask them to write two multiplication sentences and two division sentences using these numbers. Then, ask them to explain in one sentence how the division sentences relate to the multiplication sentences.

Quick Check

Present a word problem: 'Sarah has 3 boxes of crayons, with 8 crayons in each box. She wants to share them equally among her 4 friends. How many crayons does each friend get?' Observe students' strategies and ask them to write the equation(s) they used to solve it.

Discussion Prompt

Pose the question: 'Is it easier to solve 7 x 8 by thinking of 8 x 7? Why or why not?' Encourage students to explain their reasoning using the commutative property and to share any other mental math strategies they use for multiplication facts.

Frequently Asked Questions

How to teach the relationship between multiplication and division in Grade 3?

Emphasize fact families: present 4x5=20, then ask what undoes it (20/5=4 or 20/4=5). Use arrays and counters to model pairs visually. Regular practice with mixed problems reinforces the inverse link, helping students switch fluently between operations in word problems.

What strategies help with multi-step multiplication and division problems?

Teach breaking problems into single steps: identify operations, draw models, use properties for mental math. For example, 24 cookies in packs of 6: first 24/6=4, then multiply packs by price. Justification sheets prompt students to explain choices, building confidence.

How can active learning help students review multiplication and division?

Games like relays and stations turn review into play, revealing patterns through movement and peers. Manipulatives make strategies tangible; sharing justifications in groups corrects errors collaboratively. This approach boosts engagement, retention, and skill transfer over rote drills.

How to use properties of operations in Grade 3 mental math?

Practice commutative by flipping factors, associative by grouping (2x(4x3)=(2x4)x3). Division uses compatible pairs like 15/5=3, then 3x4=12. Daily mental math routines with peer explanations solidify these, reducing reliance on counting.