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.

• Primary 4
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Analyze multi-step word problems by identifying the knowns, unknowns, and the relationships between them.
2. Select and apply appropriate problem-solving strategies, such as drawing diagrams, working backward, or making a list, to solve mathematical problems.
3. Evaluate the reasonableness of a solution by checking if it logically answers the question asked in the problem.
4. Explain the steps taken to solve a problem, using mathematical vocabulary and clear reasoning.
5. Create a visual representation, like a bar model or a systematic list, to model the information presented in a word problem.

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.

Prepare & details

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.

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·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.

Prepare & details

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.

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

⏱ 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.

Prepare & details

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.

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

⏱ 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.

Prepare & details

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.

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Pair Challenge: Strategy Swap, collect the first draft of each student’s diagram or list. Look for clear labels, correct quantities, and notes explaining why they chose that strategy. Note students who skip steps or use vague language for follow-up.

Exit Ticket

After Small Group: Problem Relay, collect each student’s written steps for solving the backward-working problem. Check that they start from the end result and reverse operations accurately, and look for their explanation connecting the strategy to the problem’s structure.

Peer Assessment

During Whole Class: Think-Aloud Gallery, pair students to present their solutions. Listen for partners to identify one clear explanation step and suggest one way to make the process more visual, such as adding arrows to a diagram or numbering list items.

Extensions & Scaffolding

• Challenge: Give early finishers a problem with missing data and ask them to create two different bar models or lists to explore how the gaps affect the solution.
• Scaffolding: Provide partially completed diagrams or tables for students to finish, focusing their attention on the missing relationships.
• Deeper Exploration: Assign a multi-step data problem that requires combining two strategies, such as drawing a bar model and then working backward to find an unknown value.

Key Vocabulary

Bar Model	A visual representation used to solve word problems, showing the relationship between quantities as parts and a whole.
Working Backward	A strategy where you start with the final answer and reverse the operations to find the initial value or unknown.
Make a List	A strategy that involves systematically recording all possible outcomes or combinations to find a solution.
Guess and Check	A strategy where you make an educated guess, check if it works, and adjust your guess based on the result until you find the correct answer.