Mathematics · Year 2

Active learning ideas

Non-Unit Fractions of a Whole

Active learning helps Year 2 pupils grasp non-unit fractions because they see how multiple equal parts combine to form a whole. By handling shapes, folding paper, and sharing food, children move from abstract symbols to concrete understanding.

• National Curriculum Attainment Targets
• KS1: Mathematics - Fractions

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Outdoor Investigation Session
• 35 min · Pairs

Manipulative Modelling: Fraction Shapes

Provide interlocking cubes or fraction tiles divided into thirds and quarters. Pupils build rectangles showing 2/3 or 3/4 shaded or assembled. Partners compare models and explain compositions using unit fractions. Record findings on mini-whiteboards.

Explain how a non-unit fraction is different from a unit fraction.

Facilitation Tip

During Fraction Shapes, circulate to ensure children use the same-size whole for accurate comparisons when stacking transparencies.

What to look for

Present students with pre-drawn shapes divided into equal parts. Ask them to shade a specific non-unit fraction, for example, 'Shade 2/3 of the circle.' Observe if they correctly identify and shade the required number of parts.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 02

• Outdoor Investigation Session
• 25 min · Small Groups

Paper Folding: Fraction Rectangles

Give A4 paper rectangles. Instruct pupils to fold into three or four equal parts, shade 2/3 or 3/4, then unfold to count units. Groups swap and critique each other's folds for equal parts. Discuss differences from unit fractions.

Construct a model to show 2/3 of a rectangle.

Facilitation Tip

For Fraction Rectangles, model the first fold step-by-step to prevent uneven partitions that distort fraction sizes.

What to look for

Show a picture of a shape divided into 4 equal parts with 3 shaded. Ask: 'How many equal parts is the whole shape divided into? How many parts are shaded? What non-unit fraction does this picture show?' Listen for correct use of numerator and denominator.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 03

• Outdoor Investigation Session
• 40 min · Whole Class

Sharing Circle: Food Fractions

Use paper plates as circles divided into 3 or 4. Pupils colour or cut 2/3 or 3/4 to represent fruit sharing. Whole class shares models, answering how many 1/4 make 3/4. Photograph for display.

Analyze how many unit fractions are needed to make a given non-unit fraction.

Facilitation Tip

In Food Fractions, use real food items to reinforce the idea that fractions represent parts of a whole that can be shared fairly.

What to look for

Give each student a card with a non-unit fraction, such as 3/4. Ask them to draw a representation of this fraction using a rectangle and label the parts. Collect these to check their ability to model non-unit fractions.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 04

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Fraction Builds

Set stations with geoboards, playdough, drawings, and counters. At each, create 2/3 or 3/4 of a shape. Rotate every 7 minutes, noting methods in journals. Debrief comparisons.

Explain how a non-unit fraction is different from a unit fraction.

What to look for

Present students with pre-drawn shapes divided into equal parts. Ask them to shade a specific non-unit fraction, for example, 'Shade 2/3 of the circle.' Observe if they correctly identify and shade the required number of parts.

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

A few notes on teaching this unit

Start with concrete manipulatives to build visual understanding before moving to pictorial representations. Avoid rushing to abstract symbols without solid grounding in equal partitioning. Research shows that hands-on partitioning followed by verbal explanations deepens comprehension more than isolated shading tasks.

Children will correctly identify, represent, and explain non-unit fractions using models and drawings. They will articulate how multiple unit fractions combine to form a non-unit fraction and justify their reasoning to peers.

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Watch Out for These Misconceptions

• During Fraction Shapes, watch for pupils who assume a fraction with a larger numerator is always bigger, such as thinking 3/4 is smaller than 2/3 because 3 is greater than 2.

  Have children overlay same-size transparencies of both fractions and compare the shaded areas directly. Ask them to explain which fraction covers more of the whole and why the denominator matters.

• During Paper Folding: Fraction Rectangles, watch for pupils who treat non-unit fractions as single pieces rather than combinations of unit fractions.

  Guide students to unfold their rectangles and count the unit fractions, such as two 1/3 pieces making 2/3. Ask them to rebuild the fraction while explaining how the parts combine.

• During Sharing Circle: Food Fractions, watch for pupils who shade disconnected or uneven parts instead of continuous regions.

  Provide rulers for drawing equal divisions and prompt students to explain why the shaded area must be connected. Peer checks ensure continuous shading reflects the fraction’s value.

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Methods used in this brief

• Outdoor Investigation Session
• Stations Rotation