Mathematics · Grade 5

Active learning ideas

Comparing and Ordering Fractions

Active learning helps students grasp fractions by letting them manipulate physical models and collaborate. When students build, fold, and discuss fractions, they move beyond memorization to truly see how parts relate to each other. This hands-on approach builds the spatial reasoning needed for comparing and ordering fractions with confidence.

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

• 25–55 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 50 min · Small Groups

Stations Rotation: Fraction Construction Site

Students move through stations using different materials (pattern blocks, Cuisenaire rods, and paper folding) to solve addition and subtraction problems. At each station, they must draw a 'blueprint' of their physical model to show how they reached the answer.

Compare two fractions with unlike denominators and explain which is greater.

Facilitation Tip

During Fraction Construction Site, circulate with a checklist to note which students are struggling with finding common denominators and which are ready for the next challenge.

What to look for

Provide students with two fractions, such as 3/4 and 5/6. Ask them to write one sentence explaining which fraction is larger and show one method they used to compare them (e.g., drawing, common denominator, benchmark).

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

Activity 02

• Inquiry Circle
• 55 min · Small Groups

Inquiry Circle: The Recipe Swap

Groups are given a recipe that serves 4 people but need to adjust it for 6 or 2. This involves adding or subtracting fractional amounts of ingredients. They must use fraction circles to prove that their new measurements (e.g., 1 1/2 cups) are correct.

Justify the use of a benchmark fraction to compare two given fractions.

Facilitation Tip

In The Recipe Swap, assign roles so every student participates—one measures, one records, and one explains their group’s reasoning to the class.

What to look for

Display a number line from 0 to 1. Write three fractions on the board (e.g., 1/3, 7/8, 1/2). Ask students to place these fractions on their own drawn number line and label each one, then write one sentence comparing two of the fractions.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Think-Pair-Share
• 25 min · Pairs

Think-Pair-Share: Beyond the Whole

The teacher shows a model of 7/4. Students work in pairs to find as many ways as possible to name that amount (e.g., 1 and 3/4, 4/4 + 3/4, 1.75). They share their 'names' with the class to build a collective understanding of improper fractions.

Predict the order of a set of fractions when placed on a number line.

Facilitation Tip

For Beyond the Whole, provide sentence stems like 'I know ______ is larger because...' to scaffold student discussions about improper fractions.

What to look for

Pose the question: 'Imagine you have two identical chocolate bars. One is cut into 5 equal pieces and you eat 2 (2/5). The other is cut into 8 equal pieces and you eat 3 (3/8). Which bar did you eat more of?' Have students discuss their strategies for comparison.

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

A few notes on teaching this unit

Start with concrete models like fraction circles and paper folding to build visual understanding before moving to abstract methods. Avoid rushing to algorithms—students need time to visualize why 3/4 is greater than 2/3 before practicing subtraction. Research shows that students who struggle benefit from repeated exposure to visual comparisons before symbolic work.

Students will confidently compare and order fractions using visual models, number lines, and common denominators. They will explain their reasoning using precise math language and correct any misconceptions they hold. Peer discussion will deepen their understanding as they justify their thinking to others.

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Watch Out for These Misconceptions

• During Fraction Construction Site, watch for students who add both numerators and denominators when combining fractions. Have them build 1/4 + 1/4 with fraction circles and record that the result is 2/4, not 2/8.

  During Fraction Construction Site, watch for students who think a larger denominator means a larger fraction. Give them two pieces of paper and ask them to fold one into halves and the other into sixths. Then have them shade 1/2 and 1/6 to see which is bigger.

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Methods used in this brief

• Stations Rotation
• Inquiry Circle
• Think-Pair-Share