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.

• 3rd Year
• Mathematical Foundations and Real World Reasoning
• 4 activities
• 20 min–45 min

Learning Objectives

1. Calculate the unknown quantity in a word problem involving addition or subtraction.
2. Explain the relationship between a whole and its parts using a bar model representation.
3. Identify keywords and phrases in narrative scenarios that indicate the need for addition or subtraction.
4. Critique the clarity and solvability of a given word problem, proposing specific modifications.
5. Compare the effectiveness of different mental strategies for solving addition and subtraction problems.

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Problem-Based Learning

⏱ 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.

Prepare & details

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

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: 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.

Prepare & details

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

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: 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.

Prepare & details

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

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 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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Bar Model Stations, present students with a word problem like 'Liam had 24 marbles. He lost 9 playing outside. How many marbles does Liam have now?' Ask students to write the number sentence and answer, then draw a bar model to represent the problem on the same sheet.

Discussion Prompt

After Problem Charades, present two word problems. One is straightforward (e.g., 'A farmer picked 18 apples in the morning and 12 in the afternoon. How many apples were picked altogether?'). The other is more complex (e.g., 'A fish tank had 50 liters of water. 8 liters evaporated. Then 15 liters were added. How many liters are in the tank now?'). Ask students: 'Which problem felt easier to act out and why? What clues helped you decide on the operations for the second problem?' Ask volunteers to share their reasoning.

Exit Ticket

After Story Swap Challenge, give each student a scenario card, for example: 'Maria baked 42 cookies. She gave 15 to her neighbors and 9 to her classmates. How many cookies does Maria have left?' Ask students to write one sentence explaining what operation they used and why, and to state the final answer before leaving the room.

Extensions & Scaffolding

• Challenge early finishers to write their own two-step story problem and trade with a partner to solve.
• Scaffolding for struggling students: provide story stems with blanks for numbers and allow them to use counters or drawings before writing number sentences.
• Deeper exploration: Ask students to create a set of problems that use the same numbers but different contexts to highlight how context changes the operation needed.

Key Vocabulary

Unknown	A quantity in a problem that is not given and needs to be found.
Bar Model	A visual representation of a problem using a bar divided into parts to show the relationship between a whole and its components.
Difference	The result of subtracting one number from another, often indicated by phrases like 'how many more' or 'how many less'.
Part-Part-Whole	A conceptual framework where a whole quantity is composed of two or more distinct parts.