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

Finding Half of a Set

How do you find half of a group of things? We will practice sharing sets of counters, blocks, or toys into two equal groups to find out what half is.

TL;DR:Let's become experts at fair sharing! Today we'll discover a special maths word for sharing a group of things equally between two people: 'half'.

• NCCA Curriculum Specifications
• PSMC: Number - Fractions

About This Topic

This topic, Finding Half of a Set, is a foundational element within the Number strand of the Irish Primary School Mathematics Curriculum (PSMC) for First Class. It introduces pupils to the concept of fractions through the practical and relatable idea of 'halving' as fair sharing. The focus at this stage is purely on concrete manipulation and language development, aligning with the curriculum's emphasis on an active, hands-on approach. Pupils will engage with sets of familiar objects like counters, cubes, and toys, physically partitioning them into two equal groups. This process builds a strong conceptual understanding before any formal notation (like ½) is introduced.

The pedagogical approach should follow the Concrete-Pictorial-Abstract (CPA) sequence. This topic resides firmly in the 'Concrete' phase. By sharing items one by one ('one for you, one for me'), pupils internalise the meaning of 'equal' and 'half'. This exploration links directly to early division concepts and develops problem-solving skills. The activities are designed to be collaborative and play-based, fostering mathematical discourse as pupils explain their reasoning and compare their results with peers. The goal is for pupils to confidently and accurately find half of any even-numbered set up to 20.

Key Questions

1. Identify half of a group of 8 counters.
2. Explain the steps you take to find half of 10 blocks.
3. Compare finding half of 6 items with finding half of 4 items.

Learning Objectives

• Partition a set of up to 20 objects into two equal groups.
• Identify and name half of a set of objects.
• Explain the process of finding half using the language of 'sharing' and 'equal groups'.
• Demonstrate that two halves make a whole set by recombining the groups.
• Solve simple oral problems involving finding half.

Key Vocabulary

Half	One of two equal parts that make a whole group.
Share	To give a part of something to others; to divide things among people.
Equal	Being the same in amount, number, or size.
Group / Set	A number of things that are put together.
Fair	Treating everyone in the same way, so everyone gets the same amount.

Watch Out for These Misconceptions

Common Misconception

Half just means splitting a set into any two smaller groups, regardless of whether they are equal.

What to Teach Instead

Explain that 'half' is a special word in maths that means splitting something into two perfectly fair or equal shares. Use a balance scale with cubes to demonstrate that the two groups must 'weigh' the same.

Common Misconception

When asked to find half of 8, the pupil says the answer is 2 because there are two groups.

What to Teach Instead

Clarify that we want to know how many are in *one* of the groups after we have shared them out. Count the items in one of the two equal groups together to find the answer.

Common Misconception

Believing that odd numbers can be halved just as easily, resulting in a 'messy' answer or frustration.

What to Teach Instead

Acknowledge that it's tricky. Use objects to show that with an odd number, there is always one 'left over' after sharing. For now, explain that in First Class maths, we only find half of even numbers to keep it fair and simple.

Active Learning Ideas

Stations Rotation

Teddy Bear's Picnic

Pupils are tasked with preparing for a picnic for two teddy bears. They must share out items like counters (biscuits) or cubes (sandwiches) equally between the two bears to ensure each gets half.

15 min·Pairs

Stations Rotation

Halving Station Sorting

Set up stations with different quantities of objects (e.g., 6 pencils, 8 erasers, 10 beads). In pairs, pupils visit each station, divide the set in half, and record their findings by drawing the two equal groups.

20 min·Small Groups

Stations Rotation

Building Block Halves

Give each pupil a set of an even number of building blocks. Ask them to build two towers that are the exact same height, thereby splitting the set in half. They can then count the blocks in one tower to find what half is.

10 min·Individual

Real-World Connections

• Sharing a bag of sweets or crisps equally with a friend.
• Splitting a team of players into two equal teams for a game in the yard.
• Sharing out playing cards or game pieces so two players have the same number.
• Understanding 'half-time' in a football or hurling match.
• Cutting a sandwich or a piece of fruit in half to share.

Assessment Ideas

Quick Check

Teacher observation during activities. Use a checklist to note which pupils can successfully partition a set and use the correct vocabulary.

Exit Ticket

Exit Ticket: Give each pupil a small drawing of a set of objects (e.g., 8 ladybirds) and ask them to circle half of them.

Quick Check

Thumbs up, middle, or down. Ask pupils: 'Show me with your thumb how confident you feel about finding half of a set of 10 cubes.'

Frequently Asked Questions

Why can't we find half of 5?

When we share 5 things between two people, one person gets 3 and the other gets 2. That's not a fair share, so it's not half. We need the groups to be exactly the same.

Is finding half the same as sharing?

It's a special kind of sharing. Finding half is when you share something equally between exactly two people or into two groups.

Does the teacher need to introduce the fraction symbol ½ at this stage?

No, the First Class curriculum focuses on the language and concept of 'half'. Formal symbolic representation is introduced in later classes. The emphasis should remain on hands-on activities and oral language.