Problem Solving with Multiplication & Division

Active learning works well here because Year 3 students need concrete experiences to link abstract multiplication and division to real contexts. Handling real objects and collaboratively solving problems helps them move from rote calculations to flexible thinking about operations and remainders.

• Year 3
• Mathematics
• 4 activities
• 30 min–45 min

Learning Objectives

1. Analyze word problems to identify whether multiplication or division is the appropriate operation for solving.
2. Construct a multi-step word problem requiring both multiplication and addition, and then solve it.
3. Evaluate at least two different strategies (e.g., arrays, repeated addition) for solving a given multiplication or division word problem.
4. Calculate the solution to multiplication and division word problems, including those with remainders, and interpret the remainder in context.

Problem-Based Learning

⏱ 35 min·Small Groups

Manipulative Sharing Stations

Set up stations with scenarios like dividing 28 counters into 5 groups. Students model with counters or drawings, record the quotient and remainder, then discuss real-life meanings like extra items. Rotate stations every 10 minutes.

Prepare & details

Analyze a word problem to determine whether multiplication or division is required.

Facilitation Tip: During Manipulative Sharing Stations, rotate among groups to listen for students explaining how equal sharing relates to division and why multiplication builds groups.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

Problem-Based Learning

⏱ 40 min·Pairs

Multi-Step Problem Chains

Provide problem chains where answers feed into the next step, such as multiplying 4 packs of 6 pencils then dividing among 3 classes. Pairs solve step-by-step using number lines or arrays, then explain their path.

Prepare & details

Construct a multi-step word problem that involves both multiplication and addition.

Facilitation Tip: When running Multi-Step Problem Chains, provide calculators only after students have set up the problem structure to encourage number sense first.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

Problem-Based Learning

⏱ 30 min·Whole Class

Strategy Swap Circle

Students solve a problem individually with their preferred strategy, then pass to a partner for evaluation and alternative method suggestion. Regroup to share best approaches with the class.

Prepare & details

Evaluate different strategies for solving a given multiplication or division word problem.

Facilitation Tip: In the Strategy Swap Circle, limit turns to 30 seconds each so quieter students get a chance to share and more dominant students practice concise explanations.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

Gallery Walk

⏱ 45 min·Pairs

Problem Creation Gallery Walk

In pairs, create multi-step word problems using classroom objects like blocks. Display on walls for gallery walk where groups solve others' problems and leave feedback notes.

Prepare & details

Analyze a word problem to determine whether multiplication or division is required.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Teaching This Topic

Teachers should start with manipulatives to build meaning before moving to symbols. Avoid rushing to abstract methods; instead, connect each step back to the concrete. Research shows that students who explain their thinking aloud while solving problems develop deeper understanding than those who work silently. Model mistakes openly so students see that errors are part of learning.

What to Expect

Successful learning looks like students confidently selecting the correct operation for word problems, explaining their choices, and interpreting remainders in context. They should use manipulatives or drawings to model problems and discuss strategies with peers.

Watch Out for These Misconceptions

Common Misconception

During Manipulative Sharing Stations, watch for students who always multiply when they see 'groups of' without considering whether the problem is asking to build groups or split them up.

What to Teach Instead

Guide students to first act out the scenario with counters or blocks, then ask them to describe whether they are making groups larger (multiplication) or smaller (division) before writing any symbols.

Common Misconception

During Multi-Step Problem Chains, students may ignore remainders or treat them as errors when combining operations.

What to Teach Instead

Have students pause after each step to ask, 'Does this answer make sense in the story?' Remind them to circle remainders and discuss what they could mean in context before moving on.

Common Misconception

During Problem Creation Gallery Walk, students might write problems that only fit one operation, missing opportunities to mix multiplication and division.

What to Teach Instead

Prompt students to swap problems and try solving a peer's creation, then give feedback using sentence starters like, 'I think this needs multiplication because...' or 'Could this also involve dividing?'

Assessment Ideas

Quick Check

After Manipulative Sharing Stations, present students with 3 word problems. Ask them to circle the operation needed for each and write 'R' if a remainder is possible.

Exit Ticket

During Strategy Swap Circle, give students the problem: 'A class of 28 students is going on a field trip. Each bus can hold 10 students. How many buses are needed?' Ask them to write the calculation, the answer, and one sentence explaining what the remainder means in this situation.

Discussion Prompt

After Multi-Step Problem Chains, pose the problem: 'A group of friends collected 45 seashells. They want to share them equally. What are two different ways they could share the seashells? What happens if they can't share them equally?' Encourage students to discuss how remainders change based on the sharing method.

Extensions & Scaffolding

• Challenge early finishers to create a two-step problem using both multiplication and division with a remainder that has a real-world purpose.
• Scaffolding: Provide visual templates with labeled sections for writing the operation, drawing, and writing the answer for students who need structured support.
• Deeper exploration: Ask students to research how division with remainders is used in everyday life (e.g., baking, packaging) and present one example to the class.

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 splits a total amount into equal groups or determines how many equal groups can be made.
Remainder	The amount left over after a division problem is completed, when the total cannot be divided equally into the specified number of groups.
Word Problem	A mathematical problem presented in a story format that requires students to apply operations to find a solution.