Operations Review: Multiplication and Division

Active learning helps students solidify their understanding of multiplication and division by connecting abstract symbols to concrete representations. When students move, discuss, and manipulate materials in stations or games, they build flexible mental models that go beyond memorization to true comprehension of inverse operations and properties.

• Grade 3
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

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

Stations Rotation

⏱ 45 min·Pairs

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.

Prepare & details

Analyze the relationship between multiplication and division.

Facilitation Tip: During Station Rotation: Fact Family Cards, circulate to ask each pair which equation they will write first and why, prompting them to verbalize their strategy choice.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Simulation Game

⏱ 30 min·Small Groups

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.

Prepare & details

Design a strategy to solve a multi-step multiplication or division problem.

Facilitation Tip: In Multiplication-Division Relay, assign roles so every student participates as a writer, runner, or checker to keep the game moving and accountable.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Collaborative Problem-Solving

⏱ 25 min·Individual

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.

Prepare & details

Justify the use of specific properties of operations in mental math.

Facilitation Tip: For Strategy Design Challenge, provide grid paper and colored pencils to support students in drawing clear models that match their equations.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 20 min·Whole Class

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.

Prepare & details

Analyze the relationship between multiplication and division.

Facilitation Tip: During Properties Charades, model how to use hand signals or props to represent properties before students create their own, ensuring clarity in abstract concepts.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Teaching This Topic

Start with hands-on experiences before abstract symbols to avoid rote memorization. Use arrays and equal groups to build visual fluency, then connect these models to written equations. Research shows that when students explain their thinking aloud, their understanding deepens and misconceptions surface early. Avoid rushing to algorithms; instead, let students discover patterns and justify their own methods to strengthen retention.

What to Expect

Successful learning looks like students confidently using multiple strategies to solve problems, explaining their reasoning with precise mathematical language, and recognizing the relationships between multiplication and division. Students should justify their work with drawings, equations, or verbal explanations, demonstrating both procedural fluency and conceptual understanding.

Watch Out for These Misconceptions

Common Misconception

During Station Rotation: Fact Family Cards, watch for students who treat multiplication and division as separate unrelated operations.

What to Teach Instead

Have students physically build arrays for each equation in the fact family, pointing to rows and groups as they write the corresponding equations, reinforcing the shared structure.

Common Misconception

During Multiplication-Division Relay, watch for students who reverse dividend and divisor without recognizing the impact.

What to Teach Instead

After modeling 12 ÷ 3 vs. 3 ÷ 12 with counters, ask students to explain in one sentence why the groups look different, reinforcing the importance of order in division.

Common Misconception

During Strategy Design Challenge, watch for students who default to long division or calculators for multi-step problems.

What to Teach Instead

Require students to draw a picture or write a partial product equation first, then justify why their mental method works before using any written algorithm.

Assessment Ideas

Exit Ticket

After Station Rotation: Fact Family Cards, provide students with an incomplete fact family (e.g., 7, __ , 21) and ask them to write all four equations and explain how the division sentences relate to the multiplication sentences.

Quick Check

During Multiplication-Division Relay, present the crayon problem word problem and ask students to solve it on scrap paper using any strategy, then share their equations with a partner before moving on.

Discussion Prompt

After Properties Charades, pose the question 'Is it easier to solve 6 x 9 by thinking of 9 x 6? Why or why not?' and have students discuss their answers using the commutative property and any other strategies they know.

Extensions & Scaffolding

• Challenge: Create a two-step problem using a fact family of your choice, then solve it using two different strategies and explain which was more efficient.
• Scaffolding: Provide equation strips with missing numbers (e.g., 6 x __ = 30) and counters to model the relationship before writing full equations.
• Deeper: Explore the distributive property by having students break down 7 x 8 as (5 x 8) + (2 x 8) using arrays, then compare with classmates' methods.

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)).