Mathematics · Year 5

Active learning ideas

Multiplication Strategies (2-digit by 2-digit)

Active learning helps Year 5 students grasp multiplication strategies because manipulating models and comparing methods turns abstract numbers into concrete understanding. When students build, debate, and teach these strategies, they move beyond memorization to true fluency and flexibility with 2-digit multiplication.

• ACARA Content Descriptions
• AC9M5N06

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

Activity 01

• Problem-Based Learning
• 30 min · Pairs

Pairs: Area Model Builder

Partners use grid paper to draw and shade area models for problems like 23 x 45. They calculate partial products within rectangles, add them, and explain the distributive property to each other. Switch problems and compare results.

Explain how breaking a number into its factors can simplify complex multiplication.

Facilitation Tip

During Area Model Builder, circulate with base-10 blocks to prompt students to align their models with place value labels.

What to look for

Present students with the problem 34 x 56. Ask them to solve it using the area model and then again using the standard algorithm. Collect both solutions to check for accuracy in each method.

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

Activity 02

• Problem-Based Learning
• 45 min · Small Groups

Small Groups: Strategy Showdown

Each group solves three problems using a different strategy: area model, partial products, standard algorithm. They time each and discuss efficiency. Present findings to the class with examples on chart paper.

Compare the efficiency of different multiplication strategies for specific problems.

Facilitation Tip

In Strategy Showdown, assign roles like 'Algorithm Advocate' and 'Partial Products Proponent' to structure the debate.

What to look for

Pose the question: 'When would you choose to use partial products instead of the standard algorithm for a problem like 72 x 19? Explain your reasoning.' Listen for students to articulate efficiency based on number properties or ease of mental calculation.

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

Activity 03

• Problem-Based Learning
• 35 min · Individual

Individual: Peer Guide Creator

Students design a visual step-by-step guide for a given problem, including their chosen strategy and rationale. They swap guides with a partner, follow it to verify the answer, and provide feedback.

Design a step-by-step guide for a peer to solve a 2-digit by 2-digit multiplication problem.

Facilitation Tip

For Peer Guide Creator, provide sentence stems to scaffold clear written explanations of each step.

What to look for

Students work in pairs to solve a multiplication problem. One student solves it using one strategy, and the other uses a different strategy. They then exchange work and use a checklist to assess their partner's steps, accuracy, and clarity of explanation.

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

Activity 04

• Problem-Based Learning
• 40 min · Whole Class

Whole Class: Multiplication Relay

Divide class into teams. First student starts partial products for a problem on board, tags next for next step, and so on until complete. Correct teams first advance; discuss errors as a class.

Explain how breaking a number into its factors can simplify complex multiplication.

Facilitation Tip

During Multiplication Relay, call out 'pause points' where teams must verbalize their next partial product before writing it.

What to look for

Present students with the problem 34 x 56. Ask them to solve it using the area model and then again using the standard algorithm. Collect both solutions to check for accuracy in each method.

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

A few notes on teaching this unit

Effective teaching balances visual, verbal, and written representations to build deep understanding. Avoid rushing to the standard algorithm before students can explain why it works. Research shows that students who explain multiple strategies transfer their understanding to new problems more successfully. Use peer teaching to reinforce clarity and precision in mathematical language.

Students will confidently select and apply multiplication strategies, explain their reasoning clearly, and recognize when one method suits a problem better than another. They will also use peer feedback to refine their explanations and calculations.

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Watch Out for These Misconceptions

• During Area Model Builder, watch for students multiplying digits without considering place value, such as treating 23 x 45 as just 2x4, 2x5, 3x4, 3x5.

  Prompt students to label each section with its actual value (e.g., 20x40 = 800) and use base-10 blocks to verify. Circulate and ask, 'What does this part of your model represent in the problem?'

• During Strategy Showdown, watch for students dismissing partial products as 'too slow' without testing it on friendly numbers.

  Assign each group a problem where partial products simplify the calculation (e.g., 72 x 19) and require them to time their methods. Debate must include evidence from actual calculations.

• During Peer Guide Creator, watch for students forgetting to add partial products or misaligning them when writing explanations.

  Provide a checklist that includes 'list all partial products' and 'show addition steps clearly.' Require peer reviewers to circle any missing or misaligned numbers before approving the guide.

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Methods used in this brief

• Problem-Based Learning