Mathematics · 3rd Class · Fractions · Summer Term

Discovering Equivalent Fractions

Investigate fractions that look different but have the same value. We will find different names for the same fractional amount, like 1/2 and 2/4.

TL;DR:Let's become fraction detectives! Today, we're going to investigate fractions that are in disguise, looking different but actually having the very same value.

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

About This Topic

This topic, 'Discovering Equivalent Fractions', is a crucial step for pupils in Third Class within the Number strand of the Primary School Mathematics Curriculum (PSMC). Building on their initial understanding of fractions from First and Second Class, where they identified and named halves and quarters, pupils now delve into the more abstract concept that different fractions can represent the same value. The focus is on developing a deep conceptual understanding through hands-on, concrete experiences rather than rote learning of procedures. Using tools like paper folding, fraction walls, and Cuisenaire rods, pupils will visually and physically manipulate parts of a whole to see for themselves why 1/2 is the same as 2/4, 3/6, and so on.

The investigation of equivalence lays the groundwork for more complex fractional operations in later classes, such as comparing, adding, and subtracting fractions with different denominators. It is vital that pupils are given ample time to explore, discuss their findings, and articulate their reasoning. This topic encourages problem-solving and communicating skills as pupils justify their answers using diagrams and concrete materials. The goal is for pupils to internalize the idea that a fraction's value is determined by the relationship between the numerator and the denominator, not just the numbers themselves.

Key Questions

1. Explain why 1/2 is equivalent to 2/4 using a drawing.
2. Identify two fractions that are equivalent to 1/2 from a given list.
3. Justify how you can use a fraction wall to find fractions that are equal to 3/6.

Learning Objectives

• Identify equivalent fractions using concrete materials like fraction walls and paper strips.
• Record pairs of equivalent fractions for halves, quarters, and eighths.
• Explain why two fractions are equivalent by referring to a diagram or model.
• Use a fraction wall to compare fractions and find those with the same value.
• Generate a simple equivalent fraction for a given unit fraction.

Key Vocabulary

Fraction	A number that represents part of a whole.
Equivalent	Having the same amount, value, or meaning.
Equivalent Fractions	Fractions which have the same value, even though they may look different (e.g., 1/2 and 2/4).
Numerator	The top number in a fraction. It shows how many parts of the whole we have.
Denominator	The bottom number in a fraction. It shows the total number of equal parts the whole is divided into.
Fraction Wall	A set of coloured rectangular bars used to show different fractions of the same whole and their relationships.

Watch Out for These Misconceptions

Common Misconception

A bigger denominator means a bigger fraction. For example, a pupil might think 1/8 is larger than 1/4 because 8 is larger than 4.

What to Teach Instead

Use concrete materials to show that the denominator tells us how many equal pieces the whole is split into. The more pieces you split it into, the smaller each individual piece becomes.

Common Misconception

To find an equivalent fraction, you can just add the same number to the top and bottom, e.g., 1/2 becomes 2/3 by adding 1.

What to Teach Instead

Demonstrate with a diagram that 1/2 and 2/3 are not the same amount. Emphasise that we are splitting the existing pieces, which is a multiplicative action (doubling the pieces means doubling the numerator and denominator), not an additive one.

Common Misconception

The fractions 2/4 and 4/2 are the same because they use the same numbers.

What to Teach Instead

Reinforce the meaning of the numerator and denominator. Use a real-world example: 'Would you rather have 2 pieces of a pizza cut into 4 (2/4), or 4 whole pizzas cut in half (4/2)?' This clarifies their very different values.

Active Learning Ideas

Think-Pair-Share

Fraction Strip Folding

Give each pupil several paper strips of the same length. They leave one whole, fold another in half, another into quarters, and another into eighths, labelling each part. By lining up the strips, they can visually identify which fractions are equivalent.

20 min·Pairs

Think-Pair-Share

Lego Fraction Builders

Using Lego bricks, pupils build a 'whole' with a large brick (e.g., an 8-stud brick). They then find how many smaller bricks (4-stud, 2-stud) are needed to make an equivalent length, discovering relationships like 1/2 = 2/4.

25 min·Small Groups

Think-Pair-Share

Equivalent Fraction Snap

Create a set of cards with pictorial representations of fractions and their symbolic forms (e.g., a picture of 1/2, the fraction 2/4). Pupils play a game of Snap, shouting 'Snap!' when two equivalent fractions are turned over.

15 min·Pairs

Real-World Connections

• Sharing a pizza: 4 slices out of an 8-slice pizza (4/8) is the same amount as 1/2 of the pizza.
• Baking and cooking: Measuring 2/4 of a cup of sugar is the same as measuring 1/2 a cup.
• Telling time: A quarter of an hour (1/4) is the same as 15 minutes (15/60).
• Shopping sales: A 'half-price' sale means the same as a '50% off' sale (50/100).
• Measuring length: Half a metre (1/2) is the same as 50 centimetres (50/100).

Assessment Ideas

Quick Check

Observe pupils during the paper folding activity. Ask them to show you two strips that are the same length and explain how they know the fractions are equivalent.

Quick Check

Provide a worksheet with shaded shapes. Pupils write the fraction for each shaded part and then draw lines connecting the shapes that show equivalent fractions.

Exit Ticket

Pupils complete an 'exit ticket' with a single problem, such as 'Draw a picture to show that 1/3 is the same as 2/6'. This gives a quick snapshot of individual understanding.

Frequently Asked Questions

Why do we need different names for the same fraction? Isn't 1/2 just easier?

That's a great question. Sometimes we need to compare or combine fractions. If a recipe asks for 1/2 a cup of flour and you only have a 1/4 cup measure, knowing that 2/4 is the same as 1/2 is very helpful!

How can I find an equivalent fraction without drawing it every time?

Once you understand it with drawings, you can use a rule. Whatever you multiply the top number (numerator) by, you must multiply the bottom number (denominator) by the same amount to keep the fraction's value the same.

Is there a limit to how many equivalent fractions there are for 1/2?

No, there isn't! You can keep multiplying the top and bottom by any number, forever, and you will always create a new fraction that is equivalent to 1/2. They are infinite.