Mathematics · 3rd Class · Fractions · Summer Term

Understanding Equal Parts

Learn what a fraction is by dividing shapes and objects into equal parts. We will discover the meaning of the numerator and the denominator.

TL;DR:Let's get ready to slice, share, and see maths in a whole new way! This topic introduces fractions by focusing on the simple, hands-on idea of making fair shares.

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

About This Topic

This topic introduces pupils in Third Class to the foundational concept of fractions, aligning with the Number strand of the Irish Primary School Mathematics Curriculum (PSMC). The initial focus is on the concrete and pictorial understanding of fractions as equal parts of a whole. Before introducing formal notation, it is crucial that children have hands-on experience with sharing and dividing objects, shapes, and quantities into 'fair shares' or 'equal parts'. This practical grounding ensures they grasp that the equality of the parts is the defining characteristic of a fraction.

The lessons will bridge this concrete understanding to the semi-abstract by having pupils identify and create halves and quarters. Following this, the abstract notation is introduced, breaking down a fraction into its two components: the numerator and the denominator. Pupils will learn that the denominator signifies the total number of equal parts the whole has been divided into, while the numerator indicates the number of those parts being considered. This topic lays the essential groundwork for all future work with fractions, including equivalence, ordering, and operations in later classes.

Key Questions

1. Explain why a shape must be divided into equal parts to show a fraction.
2. Identify the numerator and denominator in the fraction 3/4 and describe what each number represents.
3. Compare a shape divided into halves with a shape divided into quarters.

Learning Objectives

• Divide a shape or object into two and four equal parts.
• Identify and name halves (1/2) and quarters (1/4).
• Recognise that fractions represent equal parts of a whole.
• Identify the numerator and the denominator in a written fraction.
• Explain the meaning of the numerator and denominator in the context of a shape or set.

Key Vocabulary

Fraction	A number that shows an equal part of a whole or a set.
Whole	The entire object, shape, or amount that is being divided.
Equal Part	One of the pieces of a whole that are all exactly the same size.
Numerator	The top number in a fraction. It tells us how many equal parts we have.
Denominator	The bottom number in a fraction. It tells us the total number of equal parts the whole is divided into.
Half	One of two equal parts of a whole (1/2).
Quarter	One of four equal parts of a whole (1/4).

Watch Out for These Misconceptions

Common Misconception

Any shape that is cut into parts shows a fraction.

What to Teach Instead

A fraction can only be used to describe a whole that has been divided into equal parts. If the parts are not the same size, they are not fractions of the whole.

Common Misconception

The bigger the number on the bottom (denominator), the bigger the piece.

What to Teach Instead

The denominator tells us how many equal pieces the whole is split into. The more pieces we have, the smaller each piece must be. So, 1/4 is smaller than 1/2.

Common Misconception

Confusing the roles of the numerator and denominator.

What to Teach Instead

Remember, the denominator down below tells us the total number of parts. The numerator up on top tells us how many of those parts we are counting or looking at.

Active Learning Ideas

Think-Pair-Share

Pizza Fractions Party

Pupils use paper plate 'pizzas' and cut them into equal slices to represent halves and quarters. They can then decorate the slices and discuss how many slices make up the whole pizza.

20 min·Small Groups

Think-Pair-Share

Fraction Folding

Give each pupil several identical strips of coloured paper. They fold one in half, another into quarters, and leave one as the 'whole' to visually compare the sizes of the parts.

15 min·Pairs

Think-Pair-Share

Play-Doh Portions

Each pupil gets a ball of Play-Doh and is asked to divide it into two, then four, equal portions. This tactile activity reinforces the concept that the parts must be the same size.

15 min·Individual

Real-World Connections

• Sharing a pizza or cake fairly among friends.
• Telling the time, for example, 'half past two' or 'a quarter to three'.
• Following a recipe that asks for 'half a cup' of sugar.
• Folding a sheet of paper in half to make a card.
• Noticing that a chocolate bar is divided into equal squares.

Assessment Ideas

Quick Check

Circulate and observe as pupils complete the 'Fraction Folding' activity. Note their ability to create equal parts and use the correct vocabulary to describe them.

Exit Ticket

Use an 'exit ticket': provide pupils with a drawing of a circle and ask them to divide it into quarters and shade 3/4.

Quick Check

A simple worksheet showing various shapes. Pupils must circle the shapes that are divided into equal parts and write the fraction for the shaded area.

Frequently Asked Questions

Why do the parts have to be equal?

Think about sharing a chocolate bar with a friend. If you want it to be fair, you both get the same amount. Fractions are like that, they are all about fair, equal shares of something.

Can we only find fractions of shapes?

Not at all! We can find a fraction of anything we can divide equally. We can find a fraction of a group of people, a bag of marbles, or a piece of string.

What do the two numbers in a fraction mean?

The bottom number, the denominator, tells you how many equal pieces the whole thing is cut into. The top number, the numerator, tells you how many of those pieces you have.