Mathematics · 3rd Class · Fractions · Summer Term

Naming and Writing Fractions

Practise reading and writing common fractions like halves, quarters, eighths, and tenths. We will connect the fraction name to its written number form.

TL;DR:Let's get practical with fractions! This topic introduces children to naming and writing common fractions by connecting words, symbols, and pictures.

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

About This Topic

This topic, Naming and Writing Fractions, is a foundational element within the Number strand of the Irish Primary School Mathematics Curriculum for Third Class. The curriculum emphasises a hands-on, exploratory approach, moving from the concrete to the pictorial and finally to the abstract. For this topic, the initial focus is strictly on unit fractions: halves (1/2), quarters (1/4), eighths (1/8), and tenths (1/10). The primary goal is to build a strong conceptual understanding of what a fraction represents, specifically how it denotes a part of a whole. This involves extensive work with concrete materials like fraction walls, paper folding, Cuisenaire rods, and everyday objects before moving to symbolic representation.

The core of the learning is connecting the spoken language, for example, 'one quarter', with its written form, 1/4. Teachers should facilitate activities where children physically divide wholes into equal parts and then label those parts using both words and numbers. This helps to solidify the meaning of the denominator as the total number of equal parts the whole has been divided into, and the numerator as the number of those parts being considered. This topic lays the groundwork for later work in comparing fractions, finding fractions of a set, and understanding equivalence.

Key Questions

1. Explain the relationship between the name 'one quarter' and the fraction 1/4.
2. Identify the fractions represented by various shaded diagrams.
3. Compare the written form of 'one half' and 'one eighth' and explain which represents a larger piece.

Learning Objectives

• Identify and name the fractions one half, one quarter, one eighth, and one tenth.
• Write the symbols for common fractions: 1/2, 1/4, 1/8, 1/10.
• Match the name of a fraction to its written symbol and pictorial representation.
• Explain that the denominator represents the total number of equal parts in a whole.
• Shade a given fraction of a shape for halves, quarters, eighths, and tenths.

Key Vocabulary

Fraction	A number that represents an equal part of a whole.
Whole	The entire object or amount that is being divided into parts.
Half	One of two equal parts of a whole, written as 1/2.
Quarter	One of four equal parts of a whole, written as 1/4.
Eighth	One of eight equal parts of a whole, written as 1/8.
Tenth	One of ten equal parts of a whole, written as 1/10.
Denominator	The bottom number in a fraction. It shows how many equal parts the whole is divided into.
Numerator	The top number in a fraction. It shows how many of the equal parts are being counted.

Watch Out for These Misconceptions

Common Misconception

A student believes that 1/8 is larger than 1/4 because the number 8 is larger than the number 4.

What to Teach Instead

Use a concrete example, like a bar of chocolate. Show that when you share it among 8 people (eighths), each person gets a much smaller piece than if you share it among only 4 people (quarters). Emphasise that the denominator tells us how many pieces we are sharing between, so the more people, the smaller the piece.

Common Misconception

A student reads 1/4 as 'one and four' or 'one over four' without understanding its name as 'one quarter'.

What to Teach Instead

Consistently model the correct language: 'one quarter', 'one half', 'one eighth'. Connect the word 'quarter' to other familiar concepts, like a quarter of an hour on the clock or four quarters in a euro.

Common Misconception

A student thinks that any two pieces of a shape make a half, even if they are not equal in size.

What to Teach Instead

Stress the term 'equal parts'. Use activities like paper folding to demonstrate that for a fraction to be a half, the two parts must be exactly the same size. Compare a correctly folded half with an unequally divided piece of paper.

Active Learning Ideas

Stations Rotation

Fraction Pizza Party

Give each group a paper plate 'pizza'. Call out a fraction, like 'one quarter', and have the children draw lines to divide their pizza into the correct number of equal slices and then shade in the fraction.

20 min·Small Groups

Stations Rotation

Fraction Wall Build

Using strips of coloured paper of the same length, children create their own fraction wall. They start with a 'whole' strip, then fold and cut other strips to make halves, quarters, and eighths, labelling each piece.

30 min·Pairs

Stations Rotation

Fraction Match-Up

Create a set of cards with fraction names (e.g., 'one half'), symbols (1/2), and pictorial representations (a shape shaded in). Children work in pairs to match the three corresponding cards.

15 min·Pairs

Real-World Connections

• Sharing a pizza or a birthday cake equally among friends.
• Telling the time, for example, 'quarter past three' or 'half past ten'.
• Following a recipe that calls for 'half a cup' of sugar or 'a quarter of a teaspoon' of salt.
• Understanding sales in shops, such as 'half-price' offers.
• Folding a piece of paper or a towel in half or in quarters.

Assessment Ideas

Quick Check

Use mini whiteboards. Show the class a shape with a fraction shaded (e.g., 1/4 of a square) and ask them to write down the fraction. This gives an instant check for understanding.

Discussion Prompt

Observe children during a practical activity, like building a fraction wall. Listen to their mathematical language and note any misconceptions as they discuss their work with a partner.

Quick Check

Provide a short worksheet at the end of the topic. Include tasks like matching fraction names to symbols, writing the fraction for a shaded shape, and shading a shape to represent a given fraction.

Frequently Asked Questions

Why is the bottom number in a fraction called the denominator?

The denominator tells us the 'denomination' or the 'name' of the fraction. It tells us what kind of parts we are talking about, like halves, quarters, or eighths. It shows how many equal parts the whole has been split into.

Can we only find fractions of shapes like circles and squares?

No, you can find a fraction of anything that can be considered a 'whole'. This could be a length of string, a group of people, a bar of chocolate, or a number. The important thing is that we always divide the whole into equal parts.

How do I help a child who struggles to write the fraction symbol correctly?

Use a simple template: a line with a box above it and a box below it. First, ask them, 'How many equal parts are there in total?' and guide them to write that number in the bottom box (the denominator). Then ask, 'How many of those parts are we talking about?' and have them write that in the top box (the numerator).