Mathematics · Year 3

Active learning ideas

Adding and Subtracting Fractions

Active learning works for adding and subtracting fractions because students need to see equal parts stay fixed while numerators combine. Hands-on tools like bar models and fraction strips turn abstract rules into concrete understanding. Movement and collaboration during activities reinforce the concept that denominators do not change during these operations.

• National Curriculum Attainment Targets
• KS2: Mathematics - Fractions

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

Activity 01

• Think-Pair-Share
• 30 min · Small Groups

Bar Model Relay: Fraction Addition

Divide class into teams. Each student draws a bar model for a given fraction addition problem, like 1/4 + 2/4, passes to partner for numerator sum, then next for labelling the whole. Teams race to complete five problems correctly. Review as whole class.

Justify why we only add the numerators and not the denominators when adding fractions.

Facilitation Tip

During Bar Model Relay, circulate to ensure students partition wholes into equal parts before combining fractions.

What to look for

Provide students with two problems: 1. Calculate 3/8 + 4/8. 2. Calculate 7/10 - 2/10. Ask them to write one sentence explaining why the denominator did not change in their calculations.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 25 min · Pairs

Fraction Strip Matching: Subtraction

Provide pre-cut fraction strips with same denominators. Pairs match strips to subtraction equations, such as removing 1/8 from 3/8, then record results on mini-whiteboards. Extend by creating their own problems from strips.

Explain what happens when the numerator becomes equal to the denominator.

Facilitation Tip

For Fraction Strip Matching, ask guiding questions like 'How do you know the parts are equal?' to reinforce the concept.

What to look for

Display a bar model showing 5/6 shaded. Ask students to write a subtraction problem that results in the unshaded portion (1/6). Observe their ability to connect the visual representation to the calculation.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 35 min · Whole Class

Sharing Circle: Real-World Fractions

Use paper pizzas cut into equal slices. Whole class sits in circle; teacher poses problems like add 2/8 + 3/8 slices. Students take turns combining slices physically and explaining to group before recording.

Analyze how we can represent fraction addition using a bar model.

Facilitation Tip

In Sharing Circle, model think-alouds to demonstrate how to explain reasoning step-by-step.

What to look for

Pose the question: 'If you have 5/5 of a chocolate bar and eat 2/5, what do you have left? Explain your answer using the terms numerator and denominator.' Listen for correct use of vocabulary and understanding of the concept of a whole.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Think-Pair-Share
• 20 min · Individual

Individual Bar Model Journals

Students work alone to solve five mixed addition/subtraction problems using bar models in journals. Circulate to prompt justifications. Share one solution per student with class for peer feedback.

Justify why we only add the numerators and not the denominators when adding fractions.

Facilitation Tip

In Individual Bar Model Journals, check that students label both numerators and denominators clearly in their drawings.

What to look for

Provide students with two problems: 1. Calculate 3/8 + 4/8. 2. Calculate 7/10 - 2/10. Ask them to write one sentence explaining why the denominator did not change in their calculations.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teachers should start with visual models before moving to symbolic calculations, as research shows concrete representations build lasting understanding. Avoid rushing to abstract rules; instead, let students articulate why denominators stay the same through guided questions. Model errors intentionally during demonstrations to normalize mistakes and spark discussion about correct processes.

Successful learning looks like students using bar models and fraction strips to combine numerators while keeping denominators unchanged. They justify answers by pointing to equal parts and explain why results like 5/4 represent a whole plus a part. Peer discussions show understanding through correct use of numerator and denominator vocabulary.

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Watch Out for These Misconceptions

• During Bar Model Relay, watch for students who add denominators alongside numerators.

  Pause the relay and ask the group to recount the equal parts in the bar model. Have students point to the fixed denominator while combining fractions to reinforce the visual rule.

• During Fraction Strip Matching, watch for students who reject improper fractions like 5/4.

  Prompt students to lay out five fourths strips and discuss how they cover one whole plus one more part. Ask them to name the mixed number 1 1/4 to build acceptance.

• During Bar Model Relay or Fraction Strip Matching, watch for students trying to add fractions with different denominators directly.

  Have students return to the station with same-denominator tasks only. Use guiding questions to highlight why denominators must match, such as 'What happens if the parts aren’t the same size?'

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Methods used in this brief

• Think-Pair-Share