Mathematics · 3rd Year

Active learning ideas

Problem Solving with Addition & Subtraction

Active learning helps students move from abstract symbols to concrete understanding in problem solving. By translating stories into visual models and kinesthetic actions, learners connect language patterns to mathematical operations. This hands-on approach reduces reliance on keyword guessing and builds confidence in choosing the right operation.

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

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Bar Model Stations

Prepare four stations with story cards: one for addition unknowns, one for subtraction differences, one for mixed, and one for self-created problems. Groups draw bar models, solve, and justify answers on mini-whiteboards. Rotate every 10 minutes, then share one insight per group.

Differentiate which words in a story indicate that we need to find the difference.

Facilitation Tip

For Model Match-Up, include both correct and incorrect bar models so students practice identifying valid representations.

What to look for

Present students with a word problem like: 'Sarah had 15 stickers. She gave 7 to her friend. How many stickers does Sarah have left?' Ask students to write the number sentence and the answer, then draw a bar model to represent the problem.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Outdoor Investigation Session
• 25 min · Pairs

Pairs: Story Swap Challenge

Pairs write a short addition or subtraction story with an unknown. Swap papers, draw bar models to solve, and check back with the author. Discuss what made the problem clear or tricky.

Explain how drawing a bar model can help us visualize a missing part of a whole.

What to look for

Present two word problems. One is straightforward (e.g., 'Tom has 5 apples, Jane has 3. How many altogether?'). The other is more complex (e.g., 'There are 20 birds on a tree. 8 fly away. How many are left? Then 5 more birds land. How many now?'). Ask students: 'Which problem was easier to solve and why? What made the other problem more challenging?'

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 03

• Outdoor Investigation Session
• 30 min · Whole Class

Whole Class: Problem Charades

One student acts out a word problem silently while the class draws bar models and solves collaboratively on shared charts. Reveal the story, compare models, and vote on the best strategy.

Critique what makes a word problem difficult to solve and propose strategies.

What to look for

Give each student a card with a scenario. For example: 'A baker made 30 cookies. He sold 12 in the morning and 8 in the afternoon. How many cookies are left?' Ask students to write one sentence explaining what operation they used and why, and to state the final answer.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 04

• Outdoor Investigation Session
• 20 min · Individual

Individual: Model Match-Up

Provide cut-out bar model pieces and matching stories. Students assemble models to solve, then explain their reasoning to a partner for feedback.

Differentiate which words in a story indicate that we need to find the difference.

What to look for

Present students with a word problem like: 'Sarah had 15 stickers. She gave 7 to her friend. How many stickers does Sarah have left?' Ask students to write the number sentence and the answer, then draw a bar model to represent the problem.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

A few notes on teaching this unit

Teach operations as actions first, not as rules. Use real objects or drawings to model 'adding on' or 'taking away' before introducing symbols. Avoid teaching isolated keywords, as context often overrides common associations. Research shows bar models work best when students build them themselves rather than copy teacher-drawn versions.

Successful learning looks like students fluently translating narratives into number sentences and bar models without hesitation. Students should justify their choices by explaining the story behind each operation they use. Accuracy in both calculation and representation shows they see part-whole relationships clearly.

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Watch Out for These Misconceptions

• During Problem Charades, watch for students assuming 'difference' always signals subtraction between a larger and smaller number.

  Remind students to act out the scenario exactly as written, then ask their partner to propose both addition and subtraction expressions before choosing the best fit.

• During Bar Model Stations, watch for students only using bars for addition problems with totals.

  Have students rebuild the bar for a subtraction problem by covering parts with paper to physically see the subtraction as removal of a segment.

• During Story Swap Challenge, watch for students treating every word problem as requiring one operation only.

  Prompt pairs to read each story aloud twice, once to identify the first operation and again to check for additional steps needed before sharing their final number sentence.

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Methods used in this brief

• Stations Rotation
• Outdoor Investigation Session