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

Are They Equal Halves?

Not every line that cuts something in two makes halves. We will look at different pictures and decide if they are split into two equal halves or not.

TL;DR:Today we're going to be fairness detectives! Our job is to investigate shapes and objects to see if they have been shared fairly into two equal halves.

• NCCA Curriculum Specifications
• PSMC: Number - Fractions

About This Topic

This topic introduces First Class pupils to the foundational concept of fractions through the exploration of halves. Within the Irish Primary School Mathematics Curriculum (PSMC), this falls under the 'Fractions' strand unit in the 'Number' strand. The primary focus at this stage is not on symbolic notation (like ½) but on developing a deep conceptual understanding that a half represents one of two strictly equal parts of a whole. The learning is grounded in hands-on, practical experiences using familiar objects and shapes.

The core idea is to move beyond the simple act of cutting something in two and to critically assess the equality of the resulting parts. By using language like 'fair shares', 'equal parts', and 'the same size', pupils connect the mathematical concept to their real-world experiences of sharing. Activities should encourage manipulation, discussion, and justification, allowing children to construct their own understanding of what constitutes a 'half'. This visual and tactile exploration builds the essential groundwork for more formal work with fractions in later classes.

Key Questions

1. Identify which shape is correctly cut in half.
2. Explain why a shape cut into two unequal pieces does not show halves.
3. Justify your decision about whether a picture shows a fair half.

Learning Objectives

• Visually identify whether a shape is divided into two equal or unequal parts.
• Use the vocabulary 'half', 'equal', and 'whole' appropriately in discussions.
• Justify why a shape is or is not correctly divided into halves.
• Demonstrate how to create a half by folding, drawing, or dividing a concrete object.
• Sort objects and images into groups of 'halves' and 'not halves'.

Key Vocabulary

Half	One of two equal parts that make up a whole.
Equal	Exactly the same in amount, size, or value.
Whole	A complete thing, with no parts missing.
Fair Share	A way of dividing something so that everyone gets an equal amount.
Divide	To split or separate something into parts.

Watch Out for These Misconceptions

Common Misconception

Any line that splits something into two pieces makes halves.

What to Teach Instead

Explain that 'half' is a special word in maths that means the two pieces must be exactly the same size. Use a balance scale with Play-Doh to show that two unequal pieces do not weigh the same, so they are not halves.

Common Misconception

A shape can only be halved by cutting it down the middle from top to bottom.

What to Teach Instead

Show examples of halving a square or rectangle with a horizontal or diagonal line. As long as the two resulting pieces are equal in size, it is a half.

Common Misconception

You can't have a half of a group of things, only a half of one thing.

What to Teach Instead

Use counters or blocks. Show a group of 6 counters and explain that you can split them into two equal groups of 3. Each group is a half of the original big group.

Active Learning Ideas

Four Corners

Play-Doh Fair Share

Each pair of pupils gets a ball of Play-Doh and is asked to split it into two equal halves to share. They must then compare their two pieces to see if they are a 'fair share' and adjust if necessary.

15 min·Pairs

Four Corners

The Fold Test

Provide pupils with various paper shapes like squares, rectangles, and circles. They must investigate if they can fold the shapes exactly in half so that the two parts match up perfectly.

10 min·Individual

Four Corners

Sorting Halves and Not-Halves

Give small groups a collection of picture cards showing shapes and objects. Some are divided into equal halves, others into unequal parts. The group must work together to sort the cards into two piles: 'Halves' and 'Not Halves'.

20 min·Small Groups

Real-World Connections

• Sharing a chocolate bar or sandwich equally with a friend.
• Filling a glass so it is 'half full'.
• Folding a towel or a sheet of paper in half.
• Following a recipe that asks for 'half a cup' of flour.
• Knowing when it is 'half past' the hour on a clock.

Assessment Ideas

Quick Check

Teacher observation during hands-on activities. Listen for pupils' use of key vocabulary and the reasoning they give to their partners.

Quick Check

Provide a worksheet with various shapes. Pupils must colour in the shapes that are correctly cut in half.

Quick Check

Show a series of images on the board. Pupils use thumbs up/thumbs down to indicate if the image shows correct halves.

Frequently Asked Questions

If I cut the cake and my piece is bigger, is it still a half?

No, for it to be a half, both pieces must be the exact same size. We would call that an unfair share, not a half.

What if I cut it into three pieces?

When we cut something into two equal pieces, we call them halves. If we cut it into three equal pieces, we call them thirds. That's something we'll learn more about when you're a bit older.

Does the cutting line have to be straight?

Usually, for simple shapes, a straight line is the easiest way to make two equal halves. The most important rule is not about the line, but that the two pieces it creates are identical.