Mathematics · Primary 2

Active learning ideas

Comparing and Ordering Unit Fractions

Active learning works for comparing unit fractions because students need physical and visual evidence to grasp abstract concepts. When children fold strips or shade pizzas, they create mental images that counter misconceptions. These hands-on actions turn invisible rules (like 'more pieces means smaller shares') into visible truths.

• MOE Syllabus Outcomes
• MOE: Numbers and Algebra - P2
• MOE: Fractions - P2

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Pairs: Fraction Strip Overlays

Each pair gets paper strips and scissors. They fold one into halves, another into thirds, and a third into quarters, marking unit fractions. Partners overlay strips on a whole rectangle to compare sizes and order from least to greatest. Conclude with sharing one comparison.

If the whole is the same, why does a larger denominator give a smaller fraction?

Facilitation Tip

During Fraction Strip Overlays, circulate to ensure pairs align strips at the left edge for accurate comparison.

What to look for

Provide students with pre-cut fraction strips for ½, ⅓, and ¼. Ask them to lay the strips side-by-side and record which fraction is the largest and which is the smallest. Ask: 'How do you know?'

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

Activity 02

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

Small Groups: Ordering Fraction Cards

Prepare cards showing ½, ⅓, ¼ with visuals. Groups draw cards, discuss sizes using 'more parts mean smaller shares,' and arrange in order on a mat. Rotate roles: one explains, others agree or challenge. Class shares final orders.

How can fraction strips help us compare unit fractions?

Facilitation Tip

For Ordering Fraction Cards, remind groups to compare all three fractions at once, not one pair at a time.

What to look for

Give each student a card with three unit fractions (e.g., ¼, ½, ⅓). Ask them to write the fractions in order from smallest to largest. Then, ask them to draw a picture to show why ½ is larger than ⅓.

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

Activity 03

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

Whole Class: Pizza Fraction Model

Draw a large circle pizza on chart paper. Divide into 2, 3, 4 parts sequentially, shading unit fractions. Students vote and justify which shaded part is largest using arms to mimic strip lengths. Record orders on board.

Which is greater: one half or one third? How do you know?

Facilitation Tip

When using the Pizza Fraction Model, ask students to trace the shaded part to connect visuals to written fractions.

What to look for

Pose the question: 'If you have a chocolate bar and share it equally with one friend (making halves), and then another day you share the same size chocolate bar equally with three friends (making thirds), which piece is bigger?' Facilitate a discussion using fraction strips or drawings to support their reasoning.

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

Activity 04

• Think-Pair-Share
• 20 min · Individual

Individual: Fraction Line Plot

Students draw a number line from 0 to 1. Mark positions for ½, ⅓, ¼ using string or rulers divided equally. Label and order them, noting spaces between marks show comparisons. Share personal lines in pairs.

If the whole is the same, why does a larger denominator give a smaller fraction?

Facilitation Tip

For the Fraction Line Plot, prompt students to mark fractions in order while explaining their choices aloud.

What to look for

Provide students with pre-cut fraction strips for ½, ⅓, and ¼. Ask them to lay the strips side-by-side and record which fraction is the largest and which is the smallest. Ask: 'How do you know?'

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

A few notes on teaching this unit

Start with fraction strips to build concrete understanding before moving to symbols. Avoid rushing to abstract rules; let students discover patterns through guided play. Research shows that children need repeated exposure to denominators’ meaning before they internalize that a larger denominator means a smaller share. Use discussion to bridge their actions to vocabulary like 'unit fraction' and 'denominator.'

Successful learning shows when students use fraction strips or models to explain why ½ > ⅓ without relying on rules alone. They should justify comparisons using words like 'more parts' and 'smaller pieces.' Discussions should include evidence from their visuals rather than guessing.

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Watch Out for These Misconceptions

• During Fraction Strip Overlays, watch for students who assume ¼ > ½ because 4 is greater than 2. Redirect them by asking, 'Which strip has larger pieces? How does the size change when we divide the whole into more parts?'

  Have students physically measure the strips side-by-side and mark the longer strip with a pencil to confirm ½ is larger.

• During Ordering Fraction Cards, watch for students who treat all unit fractions as equal. Redirect them by asking, 'Would you rather have one large slice or three small slices from the same pizza?'

  Ask peers to demonstrate with strips, then have the student reorder the cards with guidance.

• During Pizza Fraction Model, watch for students who ignore denominators when comparing fractions. Redirect them by asking, 'Which pizza shows bigger slices when shared with more friends?'

  Have students shade the pizzas and count the pieces aloud to connect symbols to visuals.

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Methods used in this brief

• Think-Pair-Share