Mathematics · Grade 5

Active learning ideas

Adding and Subtracting Mixed Numbers

Active learning works for adding and subtracting mixed numbers because handling concrete materials and visual tools helps students see why common denominators and regrouping matter. When students move fraction bars, mark number lines, or scale recipes, they connect abstract rules to tangible experiences that build lasting understanding.

• Ontario Curriculum Expectations
• 5.NF.A.1

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 45 min · Small Groups

Fraction Bar Stations: Add and Subtract

Set up three stations with fraction bars: one for addition, one for subtraction, one for strategy comparison. Small groups model five mixed number problems per station, recording steps and drawings. Rotate every 12 minutes, then share one regrouping example class-wide.

Compare different strategies for adding mixed numbers, such as converting to improper fractions versus adding whole numbers and fractions separately.

Facilitation Tip

During Fraction Bar Stations, circulate to ask groups: 'How did you decide which fraction bar to use first? What does the total look like now?'

What to look for

Provide students with the problem: 'Sarah needs 3 1/2 cups of sugar for cookies and 1 1/4 cups for frosting. How much sugar does she need in total?' Ask students to solve the problem and write one sentence explaining their strategy.

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

Activity 02

• Problem-Based Learning
• 30 min · Pairs

Number Line Pairs: Mixed Operations

Create floor number lines marked in fourths and sixths. Pairs jump to plot mixed numbers, add or subtract by moving markers, and note common denominators used. Switch roles and verify solutions together.

Explain how to regroup when subtracting mixed numbers with unlike denominators.

Facilitation Tip

For Number Line Pairs, remind pairs to label each jump with both the fraction and the whole number to avoid skipping steps.

What to look for

Write the problem '5 1/3 - 2 1/2' on the board. Ask students to show their work on mini-whiteboards. Observe their methods for finding common denominators and regrouping, providing immediate feedback.

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

Activity 03

• Problem-Based Learning
• 40 min · Pairs

Recipe Scale-Up Challenge

Hand out recipes using mixed numbers, like 2 3/4 cups flour. Pairs add or subtract to adjust for more servings, convert as needed, and present adjusted recipes. Class votes on most creative applications.

Construct a real-world problem that requires adding or subtracting mixed numbers.

Facilitation Tip

In Recipe Scale-Up Challenge, provide measuring cups with markings to connect the scaled fractions to real quantities.

What to look for

Pose the question: 'When is it easier to convert mixed numbers to improper fractions before adding or subtracting, and when is it better to add/subtract the whole numbers and fractions separately?' Facilitate a class discussion where students share their reasoning and examples.

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

Activity 04

• Problem-Based Learning
• 35 min · Small Groups

Strategy Relay Race

Divide class into teams. Each member solves one step of a mixed number problem on a whiteboard using a different strategy, then tags the next. Teams race for accuracy and speed, debriefing methods after.

Compare different strategies for adding mixed numbers, such as converting to improper fractions versus adding whole numbers and fractions separately.

Facilitation Tip

During Strategy Relay Race, assign roles so every student contributes: one finds common denominators, one handles whole numbers, and one records the final answer.

What to look for

Provide students with the problem: 'Sarah needs 3 1/2 cups of sugar for cookies and 1 1/4 cups for frosting. How much sugar does she need in total?' Ask students to solve the problem and write one sentence explaining their strategy.

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

A few notes on teaching this unit

Teachers should first let students explore mixed numbers with visual tools before introducing algorithms, as this builds number sense and reduces rote errors. Avoid rushing to rules; instead, ask students to compare their methods and justify why they work. Research shows that students who explain their own strategies alongside peers retain concepts longer than those who only follow procedures.

Successful learning looks like students explaining their steps with clear reasoning, choosing strategies based on the problem rather than habit, and correcting their own mistakes after comparing results with peers. Students should also describe when regrouping is needed and why common denominators are essential.

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Watch Out for These Misconceptions

• During Fraction Bar Stations, watch for students who subtract fractions without regrouping when the numerator is smaller. Redirect them by asking: 'What whole part can you break to make the top fraction larger? Show me with the bars.'

  During Fraction Bar Stations, if students try to subtract fractions directly without regrouping, have them physically break one whole bar into smaller parts to see why regrouping is necessary. Ask them to explain how this is similar to subtracting whole numbers when the top digit is smaller.

• During Number Line Pairs, watch for students who add whole numbers and fractions separately without finding common denominators. Redirect by asking them to mark both jumps on the same number line to see misalignment.

  During Number Line Pairs, if students add whole numbers and fractions separately without common denominators, ask them to plot each fraction on the same line to observe gaps. Have them adjust the number line to show equal parts before combining.

• During Recipe Scale-Up Challenge, watch for students who assume mixed numbers and improper fractions are different amounts. Redirect by asking them to compare side-by-side circle models of the same total.

  During Recipe Scale-Up Challenge, if students treat mixed numbers and improper fractions as different, have them build both forms using fraction circles and compare the total area. Then ask them to convert the mixed number to an improper fraction and verify the amounts match.

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Methods used in this brief

• Problem-Based Learning