Mathematics · 3rd Year

Active learning ideas

Problem Solving with Multiplication & Division

Active learning lets students handle multiplication and division by doing rather than listening. When they move, draw, and discuss, they build mental models that stick beyond the lesson. Real objects and visuals turn abstract problems into concrete reasoning.

• NCCA Curriculum Specifications
• NCCA: Primary - Problem Solving
• NCCA: Primary - Operations

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 25 min · Pairs

Pairs Challenge: Operation Sort

Pairs receive cards with word problems. They sort into multiplication or division piles, underline key phrases, draw a quick visual model, and write a one-sentence justification. Pairs then swap piles with neighbors to verify and discuss differences.

Differentiate between a multiplication problem and a division problem in a word scenario.

Facilitation Tip

During the Visual Model Gallery, assign each small group a specific problem type (equal groups, arrays, or comparisons) so the gallery showcases a variety of representations.

What to look for

Provide students with two word problems: one requiring multiplication (e.g., 'Sarah buys 4 packs of stickers with 8 stickers in each pack. How many stickers does she have?') and one requiring division (e.g., 'Tom has 32 marbles and wants to share them equally with 4 friends. How many marbles does each friend get?'). Ask students to write the operation used for each and the answer.

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

Activity 02

• Problem-Based Learning
• 40 min · Small Groups

Small Groups: Real-World Shop Simulation

Groups set up a pretend shop with toy money and items. One student poses problems like buying packs of pencils or sharing costs equally. Others solve using drawings or counters, then rotate roles and explain their operation choice.

Design a visual representation to solve a given multiplication word problem.

What to look for

Present a word problem on the board, such as 'A farmer plants 5 rows of carrots with 7 carrots in each row. How many carrots did the farmer plant in total?'. Ask students to draw a visual representation (array or bar model) to solve the problem and hold up their drawings.

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

Activity 03

• Problem-Based Learning
• 35 min · Whole Class

Whole Class: Visual Model Gallery

Display 8-10 word problems around the room. Students circulate in pairs, select three, create visual models on sticky notes, and post justifications. Conclude with a class vote on strongest models and discussions.

Justify the choice of operation to solve a real-world problem.

What to look for

Pose a scenario: 'You have 20 sweets to share equally among your classmates. How do you know whether to multiply or divide to find out how many sweets each person gets? Explain your reasoning using the terms 'equal groups' or 'sharing'.

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

Activity 04

• Problem-Based Learning
• 30 min · Individual

Individual: Create Your Own

Each student writes two word problems from daily life, one multiplication and one division. They solve with visuals and justifications, then share one with a partner for peer review and revision.

Differentiate between a multiplication problem and a division problem in a word scenario.

What to look for

Provide students with two word problems: one requiring multiplication (e.g., 'Sarah buys 4 packs of stickers with 8 stickers in each pack. How many stickers does she have?') and one requiring division (e.g., 'Tom has 32 marbles and wants to share them equally with 4 friends. How many marbles does each friend get?'). Ask students to write the operation used for each and the answer.

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

A few notes on teaching this unit

Start with concrete objects to anchor the concepts before moving to symbols. Avoid rushing to abstract computation. Use sentence stems like 'This drawing shows...' to scaffold verbal reasoning. Research shows that students who draw first make fewer operation errors later.

Students will confidently choose between multiplication and division in one-step word problems within 100. They will justify choices using equal groups, arrays, or bar models. Missteps will be caught early as peers compare drawings and calculations.

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Watch Out for These Misconceptions

• During Pairs Challenge: Operation Sort, watch for students who place division cards under multiplication because they assume division always results in a smaller number.

  Ask the pair to model the division scenario with counters to test their assumption. Have them record the starting number, the number of groups, and the size of each group on their card.

• During Visual Model Gallery, watch for students who skip drawing and jump straight to writing the equation.

  Prompt them to add color-coded labels to their drawing to match the numbers in their equation. Compare their drawing to a peer’s to highlight missing details.

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Methods used in this brief

• Problem-Based Learning