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.

• Year 3
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the sum of two or more fractions with the same denominator, representing the result as a single fraction.
2. Calculate the difference between two fractions with the same denominator, representing the result as a single fraction.
3. Explain why the denominator remains constant when adding or subtracting fractions with like denominators.
4. Identify and represent fractions equivalent to one whole (e.g., 3/3, 5/5) resulting from addition or subtraction.
5. Analyze and represent fraction addition and subtraction problems using bar models.

Collaborative Problem-Solving

⏱ 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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Collaborative Problem-Solving

⏱ 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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Collaborative Problem-Solving

⏱ 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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Collaborative Problem-Solving

⏱ 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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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?'

Assessment Ideas

Exit Ticket

After Bar Model Relay, provide an exit ticket with two problems: 3/8 + 4/8 and 7/10 - 2/10. Ask students to write one sentence explaining why the denominator did not change in their calculations.

Quick Check

During Fraction Strip Matching, 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.

Discussion Prompt

After Sharing Circle, 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.

Extensions & Scaffolding

• Challenge: After Bar Model Relay, ask students to create their own fraction addition problems using the same denominator, then swap with a partner to solve.
• Scaffolding: During Fraction Strip Matching, provide pre-labeled strips for students to arrange before writing subtraction equations.
• Deeper exploration: After Sharing Circle, invite students to invent a real-world scenario involving fractions greater than one whole and model it with strips.

Key Vocabulary

Numerator	The top number in a fraction, representing the number of parts being considered.
Denominator	The bottom number in a fraction, representing the total number of equal parts the whole is divided into.
Fraction	A number that represents a part of a whole, written with a numerator and a denominator.
Whole	The complete unit or amount, represented by a fraction where the numerator and denominator are the same.