Mathematics · Grade 4

Active learning ideas

Comparing Fractions Using Models and Benchmarks

Active learning helps students grasp fraction comparison by letting them physically manipulate models, which builds spatial reasoning. When students align fraction strips or plot on number lines, they see how size relates to parts of a whole in a way that symbolic rules alone cannot convey.

• Ontario Curriculum Expectations
• CCSS.MATH.CONTENT.4.NF.A.2

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Pairs Activity: Fraction Strip Alignment

Partners draw or cut fraction strips for two unlike fractions, such as 3/5 and 4/7. They align strips end-to-end or use a common multiple to compare lengths, then label the larger fraction. Pairs share one comparison with the class.

How can fraction strips or a number line help you compare two fractions?

Facilitation Tip

During Fraction Strip Alignment, circulate to ensure pairs align strips precisely at the zero mark to avoid skewed comparisons.

What to look for

Present students with two fractions, such as 2/5 and 3/4. Ask them to draw a visual model (e.g., fraction bars or circles) for each fraction and then write a sentence explaining which fraction is larger and why.

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

Activity 02

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

Small Groups: Benchmark Sorting Relay

Provide fraction cards with denominators up to 12. Groups sort cards into bins: less than 1/2, equal to 1/2, between 1/2 and 1, or greater than 1. One student runs to place a card, then tags the next. Discuss sorts as a class.

What benchmark fractions (0, 1/2, 1) help you decide which fraction is greater?

Facilitation Tip

In Benchmark Sorting Relay, assign benchmarks to small groups so each student has a role in placing fractions correctly.

What to look for

Give each student a card with a number line marked from 0 to 1. Provide two fractions, like 1/3 and 5/6. Ask students to plot both fractions on their number line and circle the larger fraction, then write one sentence using a benchmark fraction (0, 1/2, or 1) to justify their choice.

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

Activity 03

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

Whole Class: Number Line Fraction Walk

Draw a large number line from 0 to 2 on the floor with tape. Call out fractions; students stand at their positions to compare pairs visually. Adjust positions as needed and note benchmark references like 1/2.

Can you show which fraction is larger when both fractions have the same denominator?

Facilitation Tip

For Number Line Fraction Walk, model how to space fractions evenly between 0 and 1 before students begin walking.

What to look for

Pose the question: 'Imagine you have two cookies, one cut into 6 equal pieces and one cut into 8 equal pieces. If you eat 3 pieces from the first cookie and 4 pieces from the second, did you eat more cookie from the first or the second?' Facilitate a discussion where students use models or reasoning to compare 3/6 and 4/8.

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

Activity 04

• Think-Pair-Share
• 20 min · Individual

Individual: Model Matching Challenge

Students get fraction pairs and blank models (strips, circles, lines). They create visuals to compare, using benchmarks, then write explanations. Collect and review for patterns in strategies.

How can fraction strips or a number line help you compare two fractions?

Facilitation Tip

In Model Matching Challenge, remind students to label each model clearly with the fraction it represents.

What to look for

Present students with two fractions, such as 2/5 and 3/4. Ask them to draw a visual model (e.g., fraction bars or circles) for each fraction and then write a sentence explaining which fraction is larger and why.

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

A few notes on teaching this unit

Teach this topic by starting with concrete models before moving to abstract reasoning. Avoid rushing to common denominators; instead, let students discover when they are helpful. Research shows that visual and kinesthetic experiences help students transfer understanding to symbolic comparisons. Encourage students to verbalize their thinking as they work, which clarifies misconceptions in real time.

Students will confidently compare fractions by using visual tools and benchmarks, explaining their reasoning with clear language. They will move beyond memorized rules to flexible strategies that work for any pair of fractions.

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Watch Out for These Misconceptions

• During Fraction Strip Alignment, watch for students who assume 1/6 is larger than 1/2 because the denominator is bigger.

  Guide them to lay both strips side by side from zero to see that 1/2 covers more space than 1/6. Ask them to label each strip and explain which fraction is closer to 1.

• During Fraction Strip Alignment, watch for students comparing numerators alone without considering the denominator.

  Have them adjust the strips to the same length, then compare the shaded portions. Ask, 'Which strip has more of its length shaded?' to redirect their focus to the whole.

• During Benchmark Sorting Relay, watch for students who insist fractions must have common denominators to be compared.

  Prompt them to use benchmarks instead, such as placing 3/4 near 1 and 2/5 near 0. Discuss how benchmarks offer a quick way to judge size without rewriting fractions.

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Methods used in this brief

• Think-Pair-Share