Foundations of Mathematical Thinking · 1st Year

Active learning ideas

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.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Algebra

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Provide students with a simple word problem (e.g., 'Sarah has 5 apples and John gives her 3 more. How many apples does Sarah have now?'). Ask them to draw a picture to represent the problem and write the answer. Collect these to check their ability to visualize and solve.

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

Activity 02

• 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.

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.

What to look for

Present two different word problems, one suited for drawing a picture and another for making a list. Ask students to choose one problem, explain which strategy they will use and why, and then solve it. Observe their choices and reasoning.

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

Activity 03

• 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.

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.

What to look for

Pose a problem and ask students to share their solutions and the strategies they used. Facilitate a discussion by asking: 'Who solved this problem differently? Which strategy do you think was most helpful for this particular problem, and why?'

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

Activity 04

• 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.

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.

What to look for

Provide students with a simple word problem (e.g., 'Sarah has 5 apples and John gives her 3 more. How many apples does Sarah have now?'). Ask them to draw a picture to represent the problem and write the answer. Collect these to check their ability to visualize and solve.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Problem-Based Learning