Mathematics · 3rd Class · Fractions · Summer Term

Comparing and Ordering Fractions

Use fraction walls and diagrams to figure out which fractions are bigger or smaller. We will learn to order simple fractions from smallest to largest.

TL;DR:Let's get hands-on with fractions! This topic moves beyond simply naming parts to figuring out which slice of the cake is actually bigger.

• NCCA Curriculum Specifications
• PSMC: Number - Fractions (3rd/4th Class)

About This Topic

This topic, 'Comparing and Ordering Fractions', is a crucial step for Third Class pupils within the Number strand of the Irish Primary School Mathematics Curriculum (PSMC). It builds upon their initial understanding of fractions as parts of a whole, moving towards relational understanding. The focus here is not on abstract rules or procedures, like finding common denominators, but on developing a strong conceptual foundation through the use of concrete and pictorial representations. The curriculum emphasises the use of fraction walls, paper folding, and diagrams to allow children to see and physically manipulate fractional parts, helping them to internalise the relationship between the denominator and the size of the part.

By engaging with these hands-on materials, pupils will discover for themselves that as the denominator increases, the size of the fractional part decreases (when the numerator is one). This visual and tactile approach is vital for preventing common misconceptions and for building the confidence needed for more complex fraction work in later classes. The learning experiences should be rooted in problem-solving and discussion, encouraging pupils to articulate their reasoning, for example, explaining why one-half is larger than one-quarter by referring to a shared pizza or a folded piece of paper. This ensures a deep, lasting understanding rather than rote memorisation of rules.

Key Questions

1. Explain how a fraction wall helps you compare 1/4 and 1/8.
2. Justify why 1/2 is greater than 1/3 using a diagram.
3. Compare two different fractions with the same numerator, like 1/5 and 1/10, and explain which is larger.

Learning Objectives

• Compare and order unit fractions (e.g., 1/2, 1/4, 1/8) and fractions with the same denominator.
• Use fraction walls, number lines, and diagrams to justify why one fraction is greater or less than another.
• Articulate the relationship between the denominator and the size of a fractional part for unit fractions.
• Solve simple word problems involving the comparison of fractions.
• Place simple, familiar fractions in order from smallest to largest.

Key Vocabulary

Fraction	A number that represents a part of a whole.
Numerator	The top number in a fraction. It tells us how many parts we have.
Denominator	The bottom number in a fraction. It tells us how many equal parts the whole is divided into.
Fraction Wall	A set of coloured rectangular bars used to represent and compare different fractions of the same whole.
Unit Fraction	A fraction where the numerator is one, like 1/2 or 1/8.
Greater than (>)	A symbol used to show that the first number or fraction is bigger than the second.

Watch Out for These Misconceptions

Common Misconception

A bigger denominator means a bigger fraction. For example, a pupil thinks 1/8 is larger than 1/4 because 8 is larger than 4.

What to Teach Instead

Explain that the denominator tells us how many equal pieces the whole is cut into. Use the analogy of sharing a cake: 'If we share a cake between 4 people, your slice will be bigger than if we share the same cake between 8 people. More sharing means smaller slices.'

Common Misconception

The size of the 'whole' doesn't matter. A pupil might think that 1/2 of a small chocolate bar is the same amount as 1/2 of a large one.

What to Teach Instead

Use concrete examples with different-sized 'wholes' (e.g., a small A5 paper and a large A3 paper). Show that while both can be folded in half, the resulting halves are very different sizes. Emphasise that a fraction is always relative to its whole.

Common Misconception

When comparing fractions like 2/5 and 2/8, the numerators are the same so the fractions are the same.

What to Teach Instead

Draw two identical bars. Divide one into 5 equal parts and shade 2. Divide the other into 8 equal parts and shade 2. Pupils can visually see that the parts in the first bar are larger, so 2/5 is greater than 2/8.

Active Learning Ideas

Think-Pair-Share

Fraction Wall Race

In pairs, pupils are given a fraction wall. The teacher calls out two fractions, and the first pupil to correctly point to the larger fraction on the wall and explain why wins a point. This encourages quick visual comparison.

15 min·Pairs

Think-Pair-Share

Play-Doh Portions

Give each pupil a ball of Play-Doh representing a 'whole'. Ask them to model different fractions, like 1/2 and 1/4, by splitting their 'whole' into equal parts. They can then directly compare the size of the resulting pieces.

20 min·Individual

Think-Pair-Share

Human Fraction Line

Give each pupil a card with a simple fraction on it. Challenge the class to arrange themselves in a line from the smallest fraction to the largest without talking, using only gestures and looking at each other's cards.

10 min·Whole Class

Real-World Connections

• Sharing a pizza or chocolate bar fairly among friends: 'Do I get more if we share it between two people or four people?'
• Measuring ingredients for baking: Using measuring cups for 1/2 cup of flour versus 1/4 cup of sugar.
• Comparing discounts in a shop: Figuring out if '1/3 off' is a better deal than '1/4 off'.
• Telling the time: Understanding that a quarter of an hour is less than half an hour.
• Filling a container: Knowing that a bottle that is 1/2 full has more in it than a bottle that is 1/3 full.

Assessment Ideas

Quick Check

Use 'Show Me' whiteboards. Call out two fractions (e.g., 1/3 and 1/5) and have pupils write down the larger one. Ask a few to explain their reasoning using a quick drawing.

Exit Ticket

Exit Ticket: Give pupils a slip of paper with two fractions. They must circle the larger fraction and draw a simple diagram (a bar or a circle) to prove their answer.

Quick Check

A short worksheet where pupils order sets of fractions from smallest to largest and solve a simple word problem requiring them to compare two fractions in a real-world context.

Frequently Asked Questions

Why is 1/10 smaller than 1/5? The number 10 is bigger than 5.

Think of it like a pizza. The bottom number, the denominator, tells you how many slices to cut. If you cut a pizza into 10 slices, each slice will be much smaller than if you only cut it into 5 slices.

How do I use a fraction wall to compare fractions?

Find the two fractions on the wall. Look at the length of their bars. The fraction with the longer bar is the bigger fraction. For example, the bar for 1/2 is longer than the bar for 1/3, so 1/2 is bigger.

Does it matter how I draw my diagram to compare fractions?

Yes, it's very important. The 'wholes' you start with must be the same size. If you are comparing 1/2 and 1/4 using circles, you must draw two circles that are the same size to begin with.