Mathematics · Year 2 · Parts of the Whole · Spring Term

Non-Unit Fractions of a Whole

Identifying and representing non-unit fractions (2/3, 3/4) of a whole object.

• National Curriculum Attainment Targets
• KS1: Mathematics - Fractions

About This Topic

Year 2 pupils explore non-unit fractions, such as 2/3 and 3/4, by identifying and representing them within a whole object like a rectangle or circle. Unlike unit fractions, which show one equal part out of several (1/3 or 1/4), non-unit fractions combine multiple parts. Children practise shading regions, constructing models with paper or manipulatives, and explaining how three 1/3 pieces make 3/3, or two 1/3 make 2/3. These skills address National Curriculum standards for recognising fractions with numerators greater than one.

This topic strengthens partitioning wholes into equal shares and develops part-whole reasoning, key for later work on equivalence and finding fractions of amounts. Pupils analyse how many unit fractions compose a non-unit one, fostering comparison of fractions with different denominators through visual models. Regular practice builds confidence in describing fractions accurately.

Active learning benefits this topic greatly. Hands-on tasks with everyday objects or fraction tiles allow pupils to physically manipulate parts, making abstract ideas concrete. Collaborative building and sharing models spark discussions that reveal thinking errors, while immediate feedback from peers and teachers solidifies correct representations.

Key Questions

1. Explain how a non-unit fraction is different from a unit fraction.
2. Construct a model to show 2/3 of a rectangle.
3. Analyze how many unit fractions are needed to make a given non-unit fraction.

Learning Objectives

• Identify the numerator and denominator in given non-unit fractions.
• Represent non-unit fractions, such as 2/3 and 3/4, using pictorial models.
• Compare unit fractions to non-unit fractions, explaining the difference in terms of the number of parts.
• Construct a whole object divided into equal parts, then shade a specified non-unit fraction of it.
• Analyze how many unit fractions are combined to form a given non-unit fraction.

Before You Start

Identifying Unit Fractions

Why: Students need to understand the concept of a unit fraction (1/n) before they can grasp how multiple unit fractions form a non-unit fraction.

Partitioning Shapes into Equal Parts

Why: The ability to divide a whole object into a specific number of equal parts is fundamental to representing any fraction accurately.

Key Vocabulary

fraction	A number that represents a part of a whole or part of a set. It has a numerator and a denominator.
numerator	The top number in a fraction, showing how many equal parts are being considered.
denominator	The bottom number in a fraction, showing the total number of equal parts the whole is divided into.
non-unit fraction	A fraction where the numerator is greater than one, meaning more than one equal part of the whole is represented.
unit fraction	A fraction where the numerator is one, representing a single equal part of the whole.

Watch Out for These Misconceptions

Common Misconception

A larger numerator always means a bigger fraction.

What to Teach Instead

Pupils may think 3/4 is smaller than 2/3 since 3>2, ignoring denominators. Active approaches help by having children overlay same-size wholes on transparencies or use fraction strips to align and compare visually. Peer explanations during group builds clarify that equal partitioning determines size.

Common Misconception

Non-unit fractions cannot be broken into unit fractions.

What to Teach Instead

Children believe 2/3 exists as one piece, not two 1/3. Manipulatives like splitting chocolate bars or folding paper demonstrate decomposition. Hands-on partitioning in pairs encourages talk about rebuilding, correcting the idea through tangible evidence.

Common Misconception

Fractions only show separate pieces, not continuous areas.

What to Teach Instead

Some shade disconnected parts instead of whole regions. Drawing and shading activities with rulers for equal parts, followed by partner checks, build accurate representations. Collaborative critiques help pupils see continuous shading matches the fraction value.

Active Learning Ideas

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.

35 min·Pairs

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.

25 min·Small Groups

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.

40 min·Whole Class

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.

45 min·Small Groups

Real-World Connections

• Bakers often divide cakes or pizzas into equal slices. To describe a portion, they might use fractions like 2/8 of a pizza or 3/4 of a cake, indicating how many slices are taken.
• When sharing toys or sweets, children naturally divide them into equal groups. A child might say they have 2 out of 3 sweets, representing the non-unit fraction 2/3.

Assessment Ideas

Quick Check

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.

Discussion Prompt

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.

Exit Ticket

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.

Frequently Asked Questions

What are non-unit fractions in Year 2 maths?

Non-unit fractions have numerators greater than one, like 2/3 or 3/4, showing multiple equal parts of a whole. Year 2 pupils identify them by shading, drawing, or modelling shapes such as rectangles divided into three or four parts. This builds on unit fractions (1/3, 1/4) and supports the National Curriculum goal of fraction recognition within wholes.

How to explain unit vs non-unit fractions to Year 2 children?

Use visuals: a pizza cut into four equals one whole. One slice is 1/4 (unit); three slices are 3/4 (non-unit). Ask: 'How many 1/4 make 3/4?' Models like this show non-unit as combined units. Practice with everyday objects reinforces the distinction clearly.

How can active learning help students understand non-unit fractions?

Active learning engages pupils through manipulatives, folding, and building, turning abstract fractions into physical experiences. For example, assembling fraction tiles for 2/3 lets children see and feel compositions from 1/3 units. Group discussions during tasks uncover errors, promote peer teaching, and make comparisons memorable, leading to deeper retention and flexible thinking.

What activities teach representing 2/3 of a rectangle?

Try paper folding: fold rectangle into three equal parts, shade two. Or use geoboards to stretch bands forming thirds, covering 2/3. Follow with partner explanations of unit breakdown. These 20-30 minute tasks align with curriculum standards, building visual and verbal skills for fraction work.