Mathematics · Year 6

Active learning ideas

Comparing and Ordering Fractional Equivalencies

Active learning works because comparing and ordering fractions with unrelated denominators requires students to physically manipulate and visualize size relationships. When students move, sort, and prove equivalencies with their hands, they build mental models that replace rote procedures with deep understanding.

• ACARA Content Descriptions
• AC9M6N04
• AC9M6N05

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

Activity 01

• Gallery Walk
• 35 min · Small Groups

Manipulative: Fraction Strip Matching

Provide pre-cut fraction strips for halves, thirds, quarters, sixths. Students match equivalents by length, then order sets from least to greatest. Discuss common multiples found during matching.

Why is it necessary to have a common denominator when adding or subtracting fractions?

Facilitation Tip

During Fraction Strip Matching, circulate and ask students to explain why two strips of different lengths represent the same fraction, reinforcing the connection between visuals and values.

What to look for

Present students with a list of fractions, such as 2/3, 5/6, and 3/4. Ask them to find a common denominator for all three fractions and then order them from least to greatest. Observe their strategy for finding the LCM and ordering.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Simulation Game
• 25 min · Small Groups

Simulation Game: Fraction Sorting Relay

Write 12 fractions on cards with unrelated denominators. Teams line up, first student places one on a class number line, next adds without repeating, until all ordered. Correct as a class.

How can we prove that two fractions are equivalent using visual models?

Facilitation Tip

For Fraction Sorting Relay, set a timer and have teams rotate roles so every student actively participates in ordering and peer-checking fractions.

What to look for

Give each student two fractions with unrelated denominators, e.g., 3/5 and 5/8. Ask them to write one sentence explaining how they would determine which fraction is larger and then show their calculation. Collect and review their explanations and calculations.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 03

• Gallery Walk
• 40 min · Pairs

Pairs: Recipe Fraction Challenge

Give recipes needing fraction adjustments, like doubling thirds into sixths. Pairs convert using models, compare totals, and order ingredient amounts. Share efficient decimal conversions.

When is it more efficient to use a decimal instead of a fraction?

Facilitation Tip

In Recipe Fraction Challenge, provide measuring cups so students can physically pour and compare fractional amounts to see real-world applications of equivalency.

What to look for

Pose the question: 'Why is it impossible to directly compare 1/3 and 1/4 without changing them first?' Facilitate a class discussion where students explain the concept of a common denominator and its role in comparing fractions, referencing visual aids if helpful.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 20 min · Individual

Individual: Visual Proof Sheets

Students draw area models or number lines to prove two fractions equivalent, then order a list of four. Circulate to prompt common multiple strategies.

Why is it necessary to have a common denominator when adding or subtracting fractions?

Facilitation Tip

With Visual Proof Sheets, insist students label each drawing with both the fraction and its equivalent form to build clear connections between models.

What to look for

Present students with a list of fractions, such as 2/3, 5/6, and 3/4. Ask them to find a common denominator for all three fractions and then order them from least to greatest. Observe their strategy for finding the LCM and ordering.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Teachers should start with concrete models before moving to symbols, as research shows this builds proportional reasoning. Avoid rushing to the algorithm; instead, let students discover why common denominators matter through guided discovery. Model think-alouds to show how you decide when to convert to decimals or find equivalents, making the process transparent for students.

Successful learning looks like students moving beyond rules to explain their reasoning with visual evidence and common denominators. They should confidently justify fraction sizes using models, decimals, or equivalent forms during discussions and written work.

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Watch Out for These Misconceptions

• During Fraction Strip Matching, watch for students who assume longer strips always mean larger fractions.

  Have them align strips side-by-side to the same whole and physically compare the shaded portions, then ask them to explain why 3/6 covers the same space as 1/2.

• During Fraction Sorting Relay, watch for students who compare fractions by only looking at numerators or denominators.

  Pause the relay and ask teams to use fraction strips or number lines to verify their order, requiring them to explain how the whole unit affects the size.

• During Recipe Fraction Challenge, watch for students who believe equivalent fractions must look identical in every model.

  Have them draw two different visual models (circle and rectangle) for the same fraction and explain how both represent the same value despite different shapes.

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Methods used in this brief

• Gallery Walk
• Simulation Game