Mathematics · Year 6

Active learning ideas

Exploring Problem Solving Strategies

Active learning turns abstract strategies into visible thinking. When students physically swap methods, hunt for patterns in teams, or explain their diagrams to peers, they move from hearing about problem-solving to experiencing how strategies shape solutions. This hands-on work makes strategy selection concrete rather than theoretical.

• ACARA Content Descriptions
• AC9M6N07
• AC9M6A03

• 25–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 30 min · Pairs

Pairs Challenge: Strategy Swap

Pairs solve the same multi-step word problem using different strategies, such as one drawing a diagram and the other working backwards. They swap papers after 10 minutes, explain the approach used, and evaluate its strengths. Discuss as a class which worked best and why.

Compare the effectiveness of different problem-solving strategies for a given problem.

Facilitation Tip

During the Pairs Challenge, provide a one-minute timer after each swap so students focus on articulating the method’s strengths, not just solving.

What to look for

Present students with two different word problems. Ask them to write down which strategy (working backwards, drawing diagrams, looking for patterns) they would use for each problem and briefly explain why.

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

Activity 02

• Collaborative Problem-Solving
• 45 min · Small Groups

Small Groups: Pattern Hunt Relay

Divide a sheet of pattern-based problems among group members. Each solves one using a chosen strategy, passes to the next for verification and pattern extension. Groups race to complete and justify their full solutions.

Design a step-by-step approach to solve a multi-step word problem.

Facilitation Tip

For the Pattern Hunt Relay, give each group a different colored marker to track their steps, making progress visible for quick checks.

What to look for

Give students a multi-step word problem. On their exit ticket, they should show their chosen strategy, the steps they took, and write one sentence explaining why their strategy was a good choice for this problem.

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

Activity 03

• Collaborative Problem-Solving
• 50 min · Whole Class

Whole Class: Diagram Gallery Walk

Students create posters showing diagrams for various problems. Display around the room. Class walks, notes strategies, and votes on most effective visuals. Debrief on when diagrams outperform other methods.

Justify the choice of a particular strategy for a specific mathematical challenge.

Facilitation Tip

In the Diagram Gallery Walk, ask students to carry a sticky note to jot down one question or observation per diagram to spark discussion.

What to look for

Pose a complex word problem to the class. Ask: 'What are two different strategies we could use to solve this? How would the steps differ for each strategy? Which strategy do you think is more efficient and why?'

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

Activity 04

• Collaborative Problem-Solving
• 25 min · Individual

Individual: Strategy Journal

Students tackle three problems solo, recording strategies tried, successes, and adjustments. Share one entry with a partner for feedback. Compile class insights on versatile strategies.

Compare the effectiveness of different problem-solving strategies for a given problem.

Facilitation Tip

During Strategy Journal time, model how to write a clear justification by thinking aloud with a sample problem first.

What to look for

Present students with two different word problems. Ask them to write down which strategy (working backwards, drawing diagrams, looking for patterns) they would use for each problem and briefly explain why.

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

A few notes on teaching this unit

Teach strategies in short, focused bursts followed by immediate application. Avoid overwhelming students with too many methods at once; introduce one per lesson with guided practice. Emphasize that no single strategy is superior—context determines fit. Use anchor charts with visual examples to reinforce when to use each method. Research shows that students benefit from comparing strategies side-by-side, which builds metacognition and flexible thinking.

Students will confidently choose appropriate strategies, justify their choices, and compare effectiveness across problems. They will recognize when a diagram clarifies relationships, patterns reveal sequences, or working backwards untangles unknowns. Clear reasoning and flexibility in method use signal successful learning.

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Watch Out for These Misconceptions

• During Pairs Challenge: Strategy Swap, watch for students who treat the activity as a race to finish rather than a chance to compare method efficiency.

  Structure the one-minute swaps with a focus question: 'What made this strategy work well for this problem?' Collect responses and discuss as a class after each round.

• During Small Groups: Pattern Hunt Relay, watch for students who search randomly without recording steps, assuming patterns will reveal themselves.

  Provide a template with columns for observations, predicted next steps, and justification. Require groups to fill one row before moving to the next station.

• During Whole Class: Diagram Gallery Walk, watch for students who assume diagrams only belong in geometry or spatial tasks.

  Label each station with a word problem context (e.g., sharing items, scheduling tasks). After viewing, ask students to redraw one diagram for a new context to reinforce versatility.

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Methods used in this brief

• Collaborative Problem-Solving