Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Operations with Fractions: Addition & Subtraction

Active learning works well for operations with fractions because students often rely on memorized steps without understanding why procedures change for unlike denominators or mixed numbers. Hands-on tasks make abstract rules visible and build confidence through repeated, guided practice with manipulatives and visual models.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.4

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 35 min · Pairs

Manipulative Matching: Fraction Addition Pairs

Provide fraction strips or tiles for like and unlike denominators. Pairs match equivalent fractions first, then add by combining strips and recording sums. Extend to mixed numbers by separating wholes. Groups share one strategy on chart paper.

Explain the necessity of a common denominator for adding or subtracting fractions.

Facilitation Tip

During Manipulative Matching, circulate and ask pairs to verbalize why their fraction circles or bars represent the correct sum before recording equations.

What to look for

Present students with two fraction addition problems: one with like denominators (e.g., 1/5 + 3/5) and one with unlike denominators (e.g., 1/3 + 1/6). Ask students to solve both and write one sentence explaining the key difference in their approach for each problem.

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

Activity 02

• Collaborative Problem-Solving
• 30 min · Small Groups

Number Line Relay: Subtraction Races

Draw number lines on floor with tape, marking fractions and mixed numbers. Small groups race to subtract by jumping back, using mini whiteboards to note common denominators and results. Debrief efficient paths.

Construct a step-by-step process for adding mixed numbers.

Facilitation Tip

For Number Line Relay, provide sticky notes for students to label each jump with the fraction being subtracted, reinforcing the connection between visual steps and numerical moves.

What to look for

Give students a mixed number subtraction problem, such as 3 1/2 - 1 1/4. Ask them to write down the steps they took to solve it, focusing on how they handled the fractional parts and the whole numbers.

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

Activity 03

• Collaborative Problem-Solving
• 45 min · Whole Class

Recipe Share-Out: Real-World Fractions

Whole class divides recipe ingredients into fractions with unlike denominators. Students find common denominators to add portions, subtract for adjustments, including mixed numbers. Present scaled recipes to class.

Evaluate the most efficient strategy for finding a common denominator.

Facilitation Tip

In Recipe Share-Out, require students to double or halve recipes and present the fraction operations they used to justify their adjustments.

What to look for

Pose the question: 'If you need to add 2/3 and 1/4, what are two different ways you could find a common denominator? Which way do you think is faster and why?' Facilitate a brief class discussion comparing strategies.

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

Activity 04

• Collaborative Problem-Solving
• 25 min · Individual

Strategy Sort: Common Denominator Cards

Individual students sort cards showing fraction pairs by best strategy: like denominators, LCM, or listing multiples. Discuss sorts in small groups, justifying choices for addition or subtraction.

Explain the necessity of a common denominator for adding or subtracting fractions.

Facilitation Tip

During Strategy Sort, have students explain their chosen common denominator method to peers, then time how long it takes to solve two problems using their method.

What to look for

Present students with two fraction addition problems: one with like denominators (e.g., 1/5 + 3/5) and one with unlike denominators (e.g., 1/3 + 1/6). Ask students to solve both and write one sentence explaining the key difference in their approach for each problem.

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

A few notes on teaching this unit

Teachers should avoid rushing students into symbolic procedures before they can model operations with physical or pictorial representations. Use mixed numbers sparingly at first, focusing on whole numbers and unit fractions so students see the separation of parts clearly. Research shows that students who practice converting between mixed numbers and improper fractions early develop stronger number sense for later topics like multiplication and division.

Students will demonstrate procedural fluency by accurately adding and subtracting fractions with like and unlike denominators, including mixed numbers. They will also explain their steps using visual or written evidence, showing conceptual transfer from concrete models to symbolic operations.

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Watch Out for These Misconceptions

• During Manipulative Matching, watch for students who add numerators and denominators separately for unlike fractions by combining 1/2 and 1/3 as 2/5.

  Prompt students to build each fraction with circles or bars, then ask them to describe how the combined model would look if it were 2/5. Challenge them to redraw the sum to match 5/6 and explain the missing pieces.

• During Number Line Relay, watch for students who subtract whole numbers first in mixed number subtraction without adjusting the fractional part.

  Have the student re-walk the number line with sticky notes showing the regrouped whole as an improper fraction (e.g., 2 1/4 becomes 1 + 5/4) before completing the subtraction.

• During Recipe Share-Out, watch for students who convert mixed numbers to improper fractions immediately after each operation, regardless of whether the result is a mixed number.

  Ask the group to keep the final answer as a mixed number if the context allows (e.g., 2 3/4 cups) and explain why converting to an improper fraction isn’t necessary for the recipe task.

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Methods used in this brief

• Collaborative Problem-Solving