Mathematics · Primary 5

Active learning ideas

Comparing and Ordering Fractions

Active learning works well for comparing and ordering fractions because it transforms abstract numerical comparisons into visual, kinesthetic, and collaborative experiences. Students need repeated hands-on practice with concrete tools to internalize the relative size of fractions and mixed numbers before moving to symbolic reasoning.

• MOE Syllabus Outcomes
• MOE: Fractions - P5

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Gallery Walk
• 35 min · Small Groups

Fraction Strip Match-Up: Visual Ordering

Provide pre-cut fraction strips for a set of fractions and mixed numbers. Students arrange them on a shared number line, physically overlapping to compare sizes. Groups justify their order by discussing equivalent representations.

Analyze different strategies for comparing fractions with unlike denominators.

Facilitation Tip

During Fraction Strip Match-Up, have students physically place strips side by side on a grid to see gaps or overlaps that reveal fraction sizes.

What to look for

Present students with three fractions, e.g., 1/2, 3/4, 2/5. Ask them to write down the steps they would take to order these fractions from least to greatest and then perform the ordering. Collect responses to gauge understanding of strategy application.

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

Activity 02

• Gallery Walk
• 25 min · Pairs

Strategy Speedway: Pairs Race

Pairs draw cards with fraction pairs, race to compare using assigned strategies (e.g., common denominator, benchmarks), and record justifications. Switch strategies midway and debrief as a class on efficiency.

Predict the order of a set of fractions before converting them to a common denominator.

Facilitation Tip

In Strategy Speedway, circulate with a timer and listen for students naming their chosen strategy before converting fractions.

What to look for

Pose the question: 'When would it be easier to compare 2/3 and 4/7 by finding a common numerator instead of a common denominator?' Facilitate a class discussion where students share their reasoning and justify their choices, highlighting flexibility in strategy.

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

Activity 03

• Gallery Walk
• 40 min · Pairs

Fraction War Tournament: Competitive Comparison

Students draw fraction cards like in War, compare tops using any strategy, and explain to opponents. Winners collect cards; rotate partners after rounds to share strategies.

Justify why converting to a common numerator can sometimes be more efficient than a common denominator for comparison.

Facilitation Tip

For Fraction War Tournament, model how to record comparisons on whiteboards before declaring a winner to reinforce justification.

What to look for

Give each student a card with two mixed numbers, e.g., 2 1/3 and 2 2/5. Ask them to determine which is larger and write one sentence explaining their comparison method. This checks their ability to handle mixed numbers and articulate their process.

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

Activity 04

• Gallery Walk
• 30 min · Whole Class

Mixed Number Line-Up: Whole Class Parade

Assign each student a mixed number card. They position themselves on a floor number line, negotiate spots based on comparisons, and vote on the final order with evidence.

Analyze different strategies for comparing fractions with unlike denominators.

Facilitation Tip

In Mixed Number Line-Up, provide masking tape for the number line so students can step onto it to mark mixed numbers and adjust positions as needed.

What to look for

Present students with three fractions, e.g., 1/2, 3/4, 2/5. Ask them to write down the steps they would take to order these fractions from least to greatest and then perform the ordering. Collect responses to gauge understanding of strategy application.

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

A few notes on teaching this unit

Teach this topic by starting with visual models, then gradually layering symbolic strategies. Avoid rushing to algorithms; instead, let students discover when each method is efficient. Research shows that students who practice estimating first—placing fractions on a number line—build stronger number sense than those who only convert to decimals or common denominators. Encourage frequent partner talk to solidify language like 'greater than,' 'less than,' and 'closest to one.'

Successful learning is evident when students confidently select and apply multiple strategies to compare fractions, explain their reasoning clearly, and catch their own mistakes through visual or peer checks. They move flexibly between methods like common denominators, benchmarks, and decimal conversions without over-relying on one approach.

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Watch Out for These Misconceptions

• During Fraction Strip Match-Up, watch for students assuming 3/10 is smaller than 1/4 because 10 is larger than 4.

  Have them lay 1/4 and 3/10 strips side by side on a grid to see that 3/10 covers more space, prompting a discussion about why the denominator alone doesn't determine size.

• During Strategy Speedway, watch for students comparing 3/8 and 2/5 by only looking at the numerators 3 and 2.

  Ask them to convert both to decimals using strips or grids, then compare the decimal values to shift their focus to overall fraction size rather than separate parts.

• During Mixed Number Line-Up, watch for students ignoring the whole number part when comparing 1 4/5 and 2 1/10.

  Direct them to step onto the number line, marking the wholes first, then adjust for the fractions to reinforce that the whole number determines the starting position on the line.

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Methods used in this brief

• Gallery Walk