Mathematics · Primary 2

Active learning ideas

Thirds and Other Unit Fractions

Active learning helps students grasp fractions by making abstract ideas concrete. Folding paper, sharing candy, and building walls let them see, touch, and discuss equal parts in ways that static worksheets cannot. These hands-on tasks turn the confusing idea of parts of a whole into something they can manipulate and understand deeply.

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

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Plan-Do-Review
• 20 min · Pairs

Pairs: Paper Folding for Thirds

Each pair gets coloured paper and scissors. Fold paper into three equal parts, crease firmly, then unfold and label each as 1/3. Compare folds with partner and shade one-third. Extend by folding into fourths.

How do we divide a shape into exactly three equal parts?

Facilitation Tip

During Paper Folding for Thirds, circulate to ensure students fold carefully along the edges and unfold to check for equal sections before marking lines.

What to look for

Provide students with pre-drawn shapes (circles, rectangles) and ask them to partition each into three equal parts. Then, have them shade one part and write the corresponding unit fraction next to it.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 02

• Plan-Do-Review
• 30 min · Small Groups

Small Groups: Candy Sharing Sets

Provide 12 candies per group. Divide into three equal sets of four, take one set as 1/3. Record with drawings and notation. Try with 15 items for 1/3 of 15 equals five.

What does the denominator of a fraction tell us?

Facilitation Tip

In Candy Sharing Sets, model how to create equal groups by physically separating counters one by one, then step back to let students struggle and adjust their groupings.

What to look for

Present students with a set of 9 counters. Ask them to draw a representation of one-third of the set and write the numerical answer. Include a question: 'What does the number 3 in 1/3 tell you?'

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 25 min · Whole Class

Whole Class: Fraction Wall Build

Display a fraction wall template. Class chorally counts as teacher cuts strips into thirds, fourths, fifths. Students replicate on paper, compare lengths to see unit fractions differ by whole size.

How does knowing the whole help us find a unit fraction of a set?

Facilitation Tip

For the Fraction Wall Build, provide sticky notes in three colors so groups can label each third clearly and compare their walls to spot inconsistencies.

What to look for

Show students two shapes, one divided into three equal parts and another into three unequal parts. Ask: 'Which shape shows thirds? How do you know?' Then, display a shape divided into four equal parts and ask: 'If I shade one part, what fraction is that? How is it different from thirds?'

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• Plan-Do-Review
• 15 min · Individual

Individual: Shape Partition Draw

Students draw circles, rectangles, then divide each into three equal parts with straight lines. Label 1/3, shade one part. Repeat for four parts, noting denominator change.

How do we divide a shape into exactly three equal parts?

Facilitation Tip

During Shape Partition Draw, remind students to use rulers for straight lines and to count grid spaces to confirm equal areas before shading.

What to look for

Provide students with pre-drawn shapes (circles, rectangles) and ask them to partition each into three equal parts. Then, have them shade one part and write the corresponding unit fraction next to it.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

A few notes on teaching this unit

Start with paper folding because it builds spatial understanding without distractions. Then move to sets of objects to connect fractions to counting and grouping. Avoid rushing to symbols until students have a firm grasp of what one-third or one-fourth means in real contexts. Research shows that students who physically partition shapes internalize fraction concepts better than those who only see drawn examples.

By the end of these activities, students should partition shapes and sets precisely, name unit fractions using correct notation, and explain that the denominator shows equal shares while the numerator shows how many shares they have. Success looks like confident sharing of materials, clear explanations of their work, and correct answers on recording sheets.

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Watch Out for These Misconceptions

• During Paper Folding for Thirds, watch for students who assume all thirds look identical in shape or orientation, even when folded from different starting points.

  After they fold, have partners compare their shapes side by side and discuss why equal area matters more than equal appearance. Ask them to adjust folds until the three sections cover the same space.

• During Candy Sharing Sets, listen for students who say 'one-third means one piece' regardless of the total number of candies.

  Have them physically group the candies into three piles and count how many are in each pile. Then ask, 'Does the number of candies change the size of one-third?' to highlight that one-third is always one group out of three equal groups.

• During Fraction Wall Build, notice if students treat the denominator as a count of total items rather than a count of equal shares.

  Have them build the wall one third at a time, labeling each section as 'one of three equal parts' before moving to the next. Ask, 'What does the 3 in 1/3 tell you about the wall?' to reinforce the meaning of the denominator.

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Methods used in this brief

• Plan-Do-Review