Mathematics · Primary 4

Active learning ideas

Problem-Solving Strategies

Active learning works well for problem-solving strategies because students need to try, fail, and adjust their approaches in real time. When children manipulate tools like bar models or work backward step-by-step, abstract concepts become concrete and mistakes become learning opportunities.

• MOE Syllabus Outcomes
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Mathematical Processes: Use appropriate heuristics, e.g. draw a diagram, make a systematic list, look for patterns, work backwards, to solve problems.
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Mathematical Processes: Apply mathematical reasoning, communication and connections to solve problems.
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Whole Numbers: Solve up to 3-step word problems involving the four operations.

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 30 min · Pairs

Pair Challenge: Strategy Swap

Assign pairs a multi-step graph problem. One partner draws a bar model while the other makes a list; they swap methods after 5 minutes and solve together. Partners present their final solution and preferred strategy to the class.

What are some strategies you can use when you are not sure how to start a maths problem?

Facilitation Tip

During Pair Challenge: Strategy Swap, model how to rotate roles so each partner gets to explain and listen.

What to look for

Present students with a word problem. Ask them to first write down which strategy they think would be best to use and why. Then, have them draw a diagram or start making a list to show their initial steps.

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

Activity 02

• Problem-Based Learning
• 40 min · Small Groups

Small Group: Problem Relay

Divide class into small groups with a multi-step problem broken into steps. First student solves step 1 using a strategy and passes the paper; continue until complete. Groups compare solutions and vote on the most efficient strategy.

How does drawing a diagram or bar model help you understand what a problem is asking?

Facilitation Tip

For Small Group: Problem Relay, set a visible timer to keep groups focused on one strategy at a time.

What to look for

Give each student a problem that can be solved by working backward. Ask them to show their steps, starting from the given end result and reversing the operations. They should also write one sentence explaining why this strategy was effective for this problem.

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

Activity 03

• Problem-Based Learning
• 45 min · Pairs

Whole Class: Think-Aloud Gallery

Display 4 problems around the room. Students rotate in pairs, solving one with a chosen strategy and noting their thinking on sticky notes. Regroup to read and discuss effective strategies from all stations.

Can you use the 'guess and check' or 'make a list' strategy to solve a challenging problem?

Facilitation Tip

In Whole Class: Think-Aloud Gallery, provide sticky notes so students can jot questions or comments on peers' work without interrupting.

What to look for

In pairs, students solve a problem using a chosen strategy. They then explain their solution process to their partner. The partner's task is to identify one strength of the explanation and suggest one way the problem-solving steps could have been clearer.

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

Activity 04

• Problem-Based Learning
• 25 min · Individual

Individual: Strategy Journal

Students solve 3 problems individually, recording the strategy used and why. Pair up to share journals, then revise one solution with a peer-suggested strategy. Collect for feedback.

What are some strategies you can use when you are not sure how to start a maths problem?

Facilitation Tip

For Individual: Strategy Journal, require students to date entries so you can track progress over time.

What to look for

Present students with a word problem. Ask them to first write down which strategy they think would be best to use and why. Then, have them draw a diagram or start making a list to show their initial steps.

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

A few notes on teaching this unit

Teach strategies one at a time, but link them through common problems so students see how different tools solve similar challenges. Avoid rushing to the 'right answer'; instead, emphasize the process of testing, revising, and justifying. Research shows that students improve most when they articulate their thinking aloud, so create routines for sharing partial steps before final solutions.

Successful learning looks like students confidently choosing a strategy, explaining their reasoning, and adjusting when needed. You should hear them discuss why one method fits better than another and see them revise diagrams or lists based on peer feedback.

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Watch Out for These Misconceptions

• During Pair Challenge: Strategy Swap, watch for students who insist their chosen strategy is the only way to solve a problem.

  Prompt them to try their partner’s method with the same problem and compare results. Ask guiding questions like, ‘Which steps felt easier or harder? Why?’ to highlight that multiple valid approaches exist.

• During Pair Challenge: Strategy Swap, watch for students who draw bar models only for simple addition or subtraction.

  Provide graph-style problems where bars represent categories or comparisons. Have them adjust models as they realize quantities overlap or change, reinforcing how models clarify complex data.

• During Whole Class: Think-Aloud Gallery, watch for students who describe guess-and-check as random guessing.

  Model how to create a table with columns for guesses, results, and adjustments. During the gallery walk, ask students to point out where peers narrowed options logically rather than haphazardly.

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Methods used in this brief

• Problem-Based Learning