Problem Solving Strategies

Active learning helps students connect abstract numbers to real situations, which builds both number sense and confidence. When they move, draw, and discuss, they turn word problems into concrete experiences, making strategies like visualizing or listing feel natural rather than forced.

• 1st Year
• Foundations of Mathematical Thinking
• 4 activities
• 20 min–35 min

Learning Objectives

1. Analyze how visual representations, such as drawings or diagrams, clarify the relationships between quantities in a word problem.
2. Design a step-by-step plan to solve a given word problem, identifying necessary operations and information.
3. Evaluate the effectiveness of different problem-solving strategies, such as drawing a picture or making a list, for specific types of addition and subtraction problems.
4. Calculate the solution to simple word problems by applying a chosen problem-solving strategy.

Problem-Based Learning

⏱ 25 min·Pairs

Pairs Practice: Picture Power

Give pairs a set of five word problems on cards. They draw pictures to model and solve each one, labeling parts with numbers. Pairs then compare drawings with a neighboring pair and explain how visuals helped.

Prepare & details

Analyze how drawing a picture can help solve a math problem.

Facilitation Tip: During Pairs Practice: Picture Power, circulate and ask guiding questions like 'What do you see happening in the problem?' to push students to explain their drawings beyond just counting.

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

⏱ 35 min·Small Groups

Small Groups: Strategy Stations

Set up four stations, each with a different strategy: draw, list, act out, table. Groups solve two problems per station, recording their method and answer. Rotate every 7 minutes and reflect on strategy strengths.

Prepare & details

Design a plan to solve a given word problem.

Facilitation Tip: In Strategy Stations, assign roles (e.g., recorder, counter, speaker) so every student contributes and stays engaged with the material.

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

⏱ 30 min·Whole Class

Whole Class: Strategy Showdown

Present one word problem to the class. Students work individually first with their preferred strategy, then share in a class discussion. Vote on the clearest method and solve a second problem as a group using it.

Prepare & details

Evaluate which problem-solving strategy works best for different types of problems.

Facilitation Tip: For Strategy Showdown, time the explanations strictly to keep the energy high and prevent over-explaining by dominant students.

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

⏱ 20 min·Individual

Individual: Strategy Journal

Students choose three problems from a worksheet and note the strategy used, steps taken, and why it worked. Follow with a quick share-out where two volunteers present their journals.

Prepare & details

Analyze how drawing a picture can help solve a math problem.

Facilitation Tip: During Strategy Journal, provide sentence stems like 'I drew this because...' to scaffold reflections for students who struggle with metacognition.

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, modeling each with a think-aloud before students practice. Avoid rushing to combine strategies too soon; mastery of individual methods builds the foundation for flexibility. Research shows that students benefit from seeing peers use different approaches, so rotate strategies across activities to normalize variety. Keep problems grounded in everyday contexts students recognize to strengthen relevance.

What to Expect

Students will confidently select and apply a strategy to solve simple word problems, explaining their reasoning to peers. They will recognize that different problems may require different approaches and feel comfortable trying multiple methods.

Watch Out for These Misconceptions

Common Misconception

During Pairs Practice: Picture Power, watch for students who rush to write numbers without first sketching the scenario.

What to Teach Instead

Pause the pairs and ask them to explain their drawings aloud before calculating; circulate with a clipboard to gently redirect those who skip the visual step.

Common Misconception

During Strategy Stations, watch for students who default to their preferred strategy regardless of the problem type.

What to Teach Instead

Place a sign at each station with a problem example and the strategy name, then ask students to justify their choice aloud to their group before starting.

Common Misconception

During Strategy Journal, watch for students who believe drawing only works for 'easy' problems and avoid it for harder ones.

What to Teach Instead

Include a 'challenge problem' in their journals and require them to draw a picture even if they solve it another way, then compare strategies in a class discussion.

Assessment Ideas

Exit Ticket

After Pairs Practice: Picture Power, collect students' drawings and answers to the exit-ticket problem to check if they connected the visual to the numbers before computing.

Quick Check

During Strategy Stations, listen as groups explain their chosen strategy and why it fits the problem; note students who struggle to articulate their reasoning.

Discussion Prompt

After Strategy Showdown, facilitate a discussion by asking students to share which strategy worked best for each problem and why, noting their ability to evaluate strategy effectiveness.

Extensions & Scaffolding

• Challenge: Provide multi-step problems (e.g., 'There are 12 apples to share among 4 friends. Each friend eats 1 apple and gives half of the rest to a neighbor. How many apples does the neighbor get?') and ask students to choose two strategies to solve it.
• Scaffolding: Offer partially completed tables or starter drawings with labeled quantities to reduce cognitive load.
• Deeper exploration: Ask students to create their own word problems that require a specific strategy (e.g., 'Make a problem that works best with a list') and exchange with peers to solve.

Key Vocabulary

Word Problem	A mathematical problem presented in a narrative format that requires students to identify the question and the relevant information to find a solution.
Strategy	A specific method or approach used to solve a mathematical problem, such as drawing a picture, making a list, or acting it out.
Visualize	To create a mental image or a drawing of the information presented in a problem to better understand the relationships and quantities involved.
Plan	A sequence of steps or actions to be taken to solve a problem, including deciding which operations to use and what information is needed.