Mathematics · 1st Class · Fractions: Halves · Summer Term

Fair Sharing

Let's explore what it means to share something fairly between two friends. We will practice dividing things so that each person gets the same amount.

TL;DR:Get ready to make maths delicious and fun as we explore the world of fair sharing! This topic uses familiar objects to introduce your pupils to the foundational fraction concept of a half.

• NCCA Curriculum Specifications
• PSMC: Number - Fractions

About This Topic

This topic, 'Fair Sharing', is a pupil's first formal introduction to fractions within the Irish Primary School Mathematics Curriculum (PSMC). It aligns with the Number strand and the Fractions strand unit for First Class. The focus is entirely on the concept of 'half' as one of two equal parts of a whole. The approach should be highly practical and language-focused, using concrete materials and real-world scenarios that are familiar to young children in Ireland.

The core idea is to move from the informal understanding of 'sharing' to the more precise mathematical concept of 'fair sharing' where each part is equal. Activities should involve pupils physically dividing objects, folding shapes, and identifying halves in their immediate environment. This foundational, hands-on experience is crucial before introducing any formal notation (like ½), which typically comes later. The emphasis is on developing conceptual understanding and the correct vocabulary, such as 'whole', 'half', and 'equal parts', through exploration and discussion.

Key Questions

1. Explain what 'fair' means when you are sharing sweets.
2. Identify if a sharing of 6 blocks into a group of 4 and a group of 2 is fair.
3. Justify why it is important to share equally.

Learning Objectives

• Identify a half of a single item or shape.
• Divide a whole shape or object into two equal parts.
• Use the vocabulary 'whole' and 'half' correctly when describing objects.
• Distinguish between a whole object and an object that has been halved.
• Recognise that halves must be equal parts.

Key Vocabulary

Half	One of two equal parts that together make a whole.
Whole	The full object or entire amount, before it is divided.
Equal	Exactly the same in size, amount, or value.
Fair Share	Dividing something up so that everyone gets an equal amount.
Divide	To split something into parts or pieces.

Watch Out for These Misconceptions

Common Misconception

Any two pieces of an object are 'halves'.

What to Teach Instead

Explain that 'half' is a special word in maths that means two parts that are exactly the same size, or 'equal'. Cutting a cake into a big piece and a small piece means you have two pieces, but they are not halves.

Common Misconception

An object can only be halved in one specific way (e.g., vertically).

What to Teach Instead

Show through paper folding that a square or rectangle can be halved vertically, horizontally, and even diagonally. As long as the fold creates two identical, overlapping parts, you have made halves.

Common Misconception

Taller or longer always means bigger.

What to Teach Instead

When a rectangle is halved in two different ways (vertically vs horizontally), the resulting halves have different dimensions but are the same area. Show this by cutting them out and placing one on top of the other to prove they are the same amount.

Active Learning Ideas

Practical Life Work

Play-Doh Halves

Give each pair of pupils a ball of Play-Doh and a plastic knife. Challenge them to cut the ball in half to share it fairly between them. They can then check if their halves are equal by placing them on a balance scale.

15 min·Pairs

Practical Life Work

The Halves Hunt

Pupils become detectives and hunt around the classroom and school grounds for examples of halves. They could find a book open to the middle, a window with two panes, or a sandwich cut in two.

20 min·Small Groups

Practical Life Work

Folding Fun

Provide pupils with various paper shapes like squares, rectangles, and circles. They must explore different ways to fold them to create two perfect halves, colouring in one half afterwards.

10 min·Individual

Real-World Connections

• Sharing a chocolate bar or pizza fairly with a friend or sibling.
• Telling the time, such as 'half past three'.
• Following a recipe that calls for 'half a cup' of an ingredient.
• Folding clothes or paper in half.
• Filling a bottle or glass 'half full'.

Assessment Ideas

Quick Check

Observe pupils during hands-on activities. Note the language they use and their ability to physically create two equal shares from a whole object like Play-Doh or a piece of paper.

Quick Check

Provide a worksheet with images of various objects. Pupils must circle the objects that are correctly cut in half and put an 'X' on those that are not.

Quick Check

Ask pupils to draw a smiley face if they understand halves, a straight face if they are a bit unsure, and a sad face if they are confused. This provides a quick snapshot of class confidence.

Frequently Asked Questions

If I cut my apple into two pieces, is it always in half?

Not always! For it to be in half, you have to cut it very carefully so that both pieces are the exact same size. That's what makes it a 'fair share'.

Can we have half of a group of things?

Yes, you can! If you have four crayons and you give me two, you've given me half of your crayons. We can have half of one thing, or half of a set of things.

Why is it called a 'half'?

It's a very old word that means a 'part' or a 'side'. When you split something into two equal parts, you have one part, or one side, of the whole thing.