Mathematics · Year 3

Active learning ideas

Understanding Unit Fractions

Active learning helps Year 3 pupils grasp unit fractions because it transforms abstract symbols into tangible experiences. When students manipulate objects, draw, and move, they build mental images that connect the meaning of numerators and denominators to real shares.

• National Curriculum Attainment Targets
• KS2: Mathematics - Fractions

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

Activity 01

• Inside-Outside Circle
• 25 min · Pairs

Pairs: Fraction Strip Comparisons

Pupils cut strips of paper into unit fractions like 1/2, 1/4, 1/8. They lay strips side by side to compare lengths and discuss why more parts mean smaller slices. Pairs justify findings using the key question on denominators.

Justify why one tenth is smaller than one half even though ten is larger than two.

Facilitation Tip

During Fraction Strip Comparisons, circulate and ask pairs to explain which strip is shorter and why the denominator matters, not the numeral size.

What to look for

Display several shapes divided into different numbers of equal parts, with one part shaded. Ask students to write the unit fraction for the shaded part of each shape. For example, 'Write the fraction for the shaded part of this circle divided into 5 equal parts.'

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 02

• Inside-Outside Circle
• 30 min · Small Groups

Small Groups: Share the Snacks

Provide drawings of snacks like biscuits or grapes. Groups divide each into equal parts for denominators 2 to 10, shading one part. They compare shaded sections across snacks and explain relative sizes.

Explain how we know when a shape has been divided into equal parts.

Facilitation Tip

For Share the Snacks, ensure every group has enough counters so pupils must divide fairly and label each share with the correct unit fraction.

What to look for

Show students two shapes: one divided into 3 equal parts with one shaded (1/3), and another divided into 6 equal parts with one shaded (1/6). Ask: 'Which fraction is larger, 1/3 or 1/6? Explain your reasoning using the terms denominator and equal parts.'

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 03

• Inside-Outside Circle
• 20 min · Whole Class

Whole Class: Human Number Line

Mark a floor number line from 0 to 2. Select pupils to stand at positions like 1/2, 1/3, 1/4. Class observes and discusses order, justifying why 1/10 falls closer to zero.

Analyze what the denominator tells us about the size of the slice.

Facilitation Tip

Build the Human Number Line by first having pupils place whole numbers, then guiding them to position 1/2, 1/4, and 1/10 between 0 and 1.

What to look for

Give each student a blank number line from 0 to 1. Ask them to mark and label where 1/4 would be. Then, ask them to write one sentence explaining why 1/4 is smaller than 1/2.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 04

• Inside-Outside Circle
• 15 min · Individual

Individual: Shape Partition Challenge

Pupils draw circles or rectangles and divide into 3, 4, or 6 equal parts, shading one. They check equality by folding or overlaying, then label and compare to a partner's work.

Justify why one tenth is smaller than one half even though ten is larger than two.

Facilitation Tip

In Shape Partition Challenge, ask students to fold or cut paper shapes to confirm equal parts before shading and labeling.

What to look for

Display several shapes divided into different numbers of equal parts, with one part shaded. Ask students to write the unit fraction for the shaded part of each shape. For example, 'Write the fraction for the shaded part of this circle divided into 5 equal parts.'

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teachers should avoid rushing to rules; instead, let pupils discover the inverse relationship between denominator and slice size. Use consistent language: ‘the denominator names the equal parts’ and ‘the numerator counts how many of those parts we have (always one here)’. Research shows that physical folding and cutting create stronger memory traces than drawing alone.

Successful learning is visible when pupils can name unit fractions correctly, justify their size using denominators, and spot unequal parts without prompting. They explain why 1/10 is smaller than 1/2 and transfer the idea from shapes to sets.

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Watch Out for These Misconceptions

• During Fraction Strip Comparisons, watch for pupils claiming 1/10 is larger because 10 is a bigger number.

  Hand each pair two strips, one labeled 1/2 and one labeled 1/10. Ask them to lay them side by side and explain which strip is shorter and why the number of parts affects the size of each slice.

• During Share the Snacks, watch for pupils assuming equal-looking piles are equal without checking counts.

  Give counters of two colors and ask groups to divide 12 red and 12 blue into equal piles. Have them compare the size of each pile and write the unit fraction for each color.

• During Shape Partition Challenge, watch for pupils labeling unequal regions as equal parts.

  Provide scissors and grid paper. Pupils must cut shapes into equal parts, reassemble to verify, and only then label with the correct unit fraction.

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Methods used in this brief

• Inside-Outside Circle