Mathematics · Year 3

Active learning ideas

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.

• ACARA Content Descriptions
• AC9M3N05

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Plan-Do-Review
• 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.

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.

What to look for

Present students with 3 word problems. Ask them to circle the operation (multiplication or division) needed for each and write 'R' if a remainder is possible. For example: 'Sarah baked 24 cookies and wants to put them into bags of 4. How many bags can she make?'

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 02

• Plan-Do-Review
• 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.

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.

What to look for

Give students a problem like: '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.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 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.

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.

What to look for

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 different division scenarios and the meaning of remainders.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• 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.

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

What to look for

Present students with 3 word problems. Ask them to circle the operation (multiplication or division) needed for each and write 'R' if a remainder is possible. For example: 'Sarah baked 24 cookies and wants to put them into bags of 4. How many bags can she make?'

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

• 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.

  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.

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

  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.

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

  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?'

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Methods used in this brief

• Plan-Do-Review
• Gallery Walk