Mathematics · Year 5

Active learning ideas

Comparing and Ordering Fractions

Active learning works for comparing and ordering fractions because students need to physically manipulate parts of a whole to see relationships. Moving fraction pieces or plotting on a number line makes abstract rules visible, reducing errors about size and equivalence.

• ACARA Content Descriptions
• AC9M5N04

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

Activity 01

• Collaborative Problem-Solving
• 35 min · Pairs

Manipulative Sort: Fraction Strips

Give pairs sets of fraction strips for denominators 2-12. Students draw two fraction cards, find the least common multiple, create equivalent strips, and compare lengths by aligning. They record the order and explain their reasoning on a worksheet. Extend by ordering three fractions.

Explain why a common denominator is essential for accurately adding or subtracting fractions.

Facilitation Tip

During Fraction Strips, have students physically align strips to the same length to confirm equivalence before comparing.

What to look for

Present students with pairs of fractions like 2/5 and 3/10, and 5/6 and 7/8. Ask them to find a common denominator for each pair, rewrite the fractions, and then circle the larger fraction. Observe their process for finding common denominators.

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

Activity 02

• Collaborative Problem-Solving
• 25 min · Small Groups

Relay Race: Number Line Ordering

Create a large floor number line from 0 to 2 with benchmark marks. Small groups receive fraction cards; one student per turn places a card correctly while explaining the comparison strategy used. Groups compete to order sets fastest with accuracy.

Evaluate the most effective strategy for comparing fractions that are very close in size.

Facilitation Tip

During Number Line Ordering, ensure students mark benchmarks like halves and quarters first to guide placement of close fractions.

What to look for

Pose the question: 'Imagine you have two pieces of cake, one is 3/4 of a whole cake and the other is 5/6 of a whole cake. How can you be absolutely sure which piece is bigger without tasting them? Explain your strategy using the idea of common denominators.' Facilitate a class discussion where students share their reasoning.

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

Activity 03

• Collaborative Problem-Solving
• 40 min · Small Groups

Real-World Divide: Pizza Sharing Challenge

Provide paper pizzas or drawings divided into parts. In small groups, students represent fractions like 3/4 and 5/6, find common multiples to compare portions, and order who gets the largest slice. Discuss strategies and shade models to visualize.

Construct an argument for why comparing fractions with different denominators requires a common reference.

Facilitation Tip

During Pizza Sharing Challenge, prompt students to cut pizzas into equal parts and label slices to reinforce part-whole understanding.

What to look for

Give each student a card with two fractions that are close in value, such as 4/5 and 7/9. Ask them to write down the steps they would take to compare these fractions accurately and determine which is larger. Collect the cards to assess their understanding of the comparison process.

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

Activity 04

• Collaborative Problem-Solving
• 20 min · Individual

Card Match: Equivalent Comparisons

Prepare cards with fractions, equivalents, and visuals. Individuals or pairs match pairs with different denominators, then order matched sets from least to greatest using common multiples. Review as whole class by projecting selections.

Explain why a common denominator is essential for accurately adding or subtracting fractions.

Facilitation Tip

During Card Match: Equivalent Comparisons, circulate to listen for students explaining how they know fractions are equivalent using denominators and numerators.

What to look for

Present students with pairs of fractions like 2/5 and 3/10, and 5/6 and 7/8. Ask them to find a common denominator for each pair, rewrite the fractions, and then circle the larger fraction. Observe their process for finding common denominators.

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

A few notes on teaching this unit

Start with concrete models like fraction strips to build understanding of part-whole relationships. Move to number lines to connect fractions to their relative positions on a continuous scale. Avoid rushing to algorithms; let students discover why common denominators matter through guided exploration and peer discussion.

Students will confidently rewrite fractions with common denominators and order them correctly. They will explain their process using precise language and visual models to justify comparisons.

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Watch Out for These Misconceptions

• During Fraction Strips, watch for students who assume the strip with the larger denominator is bigger because it has more parts.

  Have students line up multiple strips (for example, 1/2 and 1/5) against a whole strip to see which portion is actually larger. Ask them to write the equivalent fractions with a common denominator like 10, then compare 5/10 and 2/10 to confirm their observation.

• During Number Line Ordering, watch for students who compare numerators without considering denominators.

  Ask students to plot 3/4 and 2/5 on the same number line after finding a common denominator like 20. If they place 2/5 to the right of 3/4, have them compare 15/20 and 8/20 to correct the placement together in pairs.

• During Card Match: Equivalent Comparisons, watch for students who think rewriting 2/3 as 8/12 changes its value.

  Have students measure both 2/3 and 8/12 strips against a whole strip to see they cover the same length. Then ask them to order 2/3, 8/12, and 3/4 together to see that equivalence preserves size for comparison.

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Methods used in this brief

• Collaborative Problem-Solving