Mathematics · Year 4 · Parts of the Whole: Fractions and Decimals · Spring Term

Understanding Unit and Non-Unit Fractions

Students will identify and represent unit and non-unit fractions, including fractions greater than one.

• National Curriculum Attainment Targets
• NC.MA.4.F.1

About This Topic

Equivalent Fractions is a cornerstone of Year 4 mathematics, where students learn that different fractions can represent the same proportion of a whole. The UK National Curriculum requires students to recognise and show, using diagrams, families of common equivalent fractions. This concept is vital because it allows students to simplify fractions and eventually compare or add fractions with different denominators.

Understanding equivalence is about seeing the relationship between the numerator and the denominator. If both are multiplied or divided by the same number, the value remains unchanged. This topic comes alive when students can physically fold paper, cut 'pizzas', or use fraction walls to see these relationships. Students grasp this concept faster through structured discussion and peer explanation, where they can 'prove' equivalence to one another.

Key Questions

1. Differentiate between a unit fraction and a non-unit fraction with examples.
2. Construct a visual representation for 3/5 and explain its meaning.
3. Explain how a fraction like 7/4 can be greater than one whole.

Learning Objectives

• Identify and represent unit fractions and non-unit fractions using pictorial representations.
• Compare and contrast unit fractions and non-unit fractions, providing examples of each.
• Construct visual models for fractions greater than one and explain their meaning.
• Classify fractions as proper, improper, or mixed numbers based on their value relative to one whole.

Before You Start

Introduction to Fractions

Why: Students need to have a basic understanding of what a fraction represents (part of a whole) and the meaning of numerator and denominator.

Dividing Shapes into Equal Parts

Why: The ability to divide shapes into equal parts is fundamental to representing and understanding fractions accurately.

Key Vocabulary

Unit Fraction	A fraction where the numerator is 1, representing one equal part of a whole. Examples include 1/2, 1/4, 1/8.
Non-Unit Fraction	A fraction where the numerator is greater than 1, representing multiple equal parts of a whole. Examples include 2/3, 3/5, 5/4.
Numerator	The top number in a fraction, which indicates how many parts of the whole are being considered.
Denominator	The bottom number in a fraction, which indicates the total number of equal parts the whole is divided into.
Improper Fraction	A fraction where the numerator is greater than or equal to the denominator, meaning the value is one whole or more than one whole.

Watch Out for These Misconceptions

Common Misconception

Thinking that a larger denominator means a larger fraction.

What to Teach Instead

Students often think 1/8 is bigger than 1/4 because 8 is bigger than 4. Use physical fraction strips to show that as the denominator increases, the 'slices' get smaller, which is best reinforced through hands-on comparison.

Common Misconception

Adding the same number to the top and bottom to find an equivalent (e.g., 1/2 = 2/3).

What to Teach Instead

Equivalence is a multiplicative relationship, not an additive one. Use 'scaling' diagrams to show that you must multiply both by the same factor, which is more easily understood through visual modeling.

Active Learning Ideas

Inquiry Circle: The Fraction Wall Challenge

Give groups a blank fraction wall. They must use strips of paper to find as many ways as possible to 'match' the length of 1/2 or 1/3. They then record their findings (e.g., 1/2 = 2/4 = 4/8) and look for a mathematical pattern in the numbers.

30 min·Small Groups

Think-Pair-Share: Is it Equal?

Show pairs two different shaded shapes (e.g., a circle with 2/4 shaded and a square with 4/8 shaded). Students must discuss whether they represent the same amount and how they could 'prove' it to someone who doesn't believe them.

15 min·Pairs

Gallery Walk: Fraction Art

Students create 'Equivalent Art' by shading different fractions of identical grids. They display their work, and others must walk around with sticky notes, writing the equivalent fractions they see in their classmates' designs.

30 min·Whole Class

Real-World Connections

• Bakers often measure ingredients using fractions. A recipe might call for 3/4 cup of flour or 1/2 teaspoon of salt, requiring an understanding of non-unit fractions.
• When sharing food, like a pizza or a cake, children naturally encounter fractions. Dividing a pizza into 8 slices and taking 3 means they have 3/8 of the pizza, a non-unit fraction.
• Construction workers use fractions to measure lengths and materials. For example, a measurement might be 7/8 of an inch, or a project might require 5/4 yards of fabric, demonstrating fractions greater than one.

Assessment Ideas

Exit Ticket

Provide students with a worksheet containing several fractions (e.g., 1/3, 5/6, 7/4, 2/2). Ask them to circle the unit fractions, put a square around the non-unit fractions, and write 'greater than one' next to any improper fractions that represent more than one whole.

Quick Check

Draw a rectangle on the board and divide it into 5 equal parts. Shade 3 parts. Ask students to write the fraction represented and explain in one sentence whether it is a unit or non-unit fraction and why.

Discussion Prompt

Present the fraction 7/4. Ask students: 'How can this fraction be greater than one whole? Can you draw a picture to show what 7/4 looks like? What is the difference between 7/4 and 1/4?'

Frequently Asked Questions

What are the best hands-on strategies for teaching equivalent fractions?

Paper folding is incredibly effective; folding a half into quarters and then eighths provides a tactile 'aha!' moment. Fraction walls and Cuisenaire rods are also excellent for showing how different units fit into the same space. Active learning, like 'Fraction Bingo' or matching games, helps students recognise equivalent pairs quickly and builds confidence.

How do you explain equivalent fractions to a child?

Use the 'pizza' analogy. If you cut a pizza into 2 pieces and eat 1, you've eaten half. If you cut it into 4 pieces and eat 2, you've still eaten the same amount of pizza. The 'slices' are smaller, but you have more of them.

Why do we need to simplify fractions?

Simplifying makes fractions easier to work with and understand. It's much easier to visualise '1/2' than '50/100'. It is also a key skill for more advanced math where answers are expected in their simplest form.

What is the 'rule' for finding equivalent fractions?

Whatever you do to the top (numerator), you must do to the bottom (denominator). If you multiply the top by 3, you must multiply the bottom by 3. This keeps the 'balance' of the fraction the same.