Mathematics · 3rd Class

Active learning ideas

Comparing and Ordering Fractions

Let's get hands-on with fractions! This topic moves beyond simply naming parts to figuring out which slice of the cake is actually bigger.

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

• 10–20 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Think-Pair-Share
• 15 min · Pairs

Fraction Wall Race

In pairs, pupils are given a fraction wall. The teacher calls out two fractions, and the first pupil to correctly point to the larger fraction on the wall and explain why wins a point. This encourages quick visual comparison.

Explain how a fraction wall helps you compare 1/4 and 1/8.

Facilitation Tip

Use laminated fraction walls and whiteboard markers so pupils can circle or shade the fractions.

What to look for

Use 'Show Me' whiteboards. Call out two fractions (e.g., 1/3 and 1/5) and have pupils write down the larger one. Ask a few to explain their reasoning using a quick drawing.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 20 min · Individual

Play-Doh Portions

Give each pupil a ball of Play-Doh representing a 'whole'. Ask them to model different fractions, like 1/2 and 1/4, by splitting their 'whole' into equal parts. They can then directly compare the size of the resulting pieces.

Justify why 1/2 is greater than 1/3 using a diagram.

Facilitation Tip

Encourage them to start with a fresh 'whole' for each new fraction to avoid confusion.

What to look for

Exit Ticket: Give pupils a slip of paper with two fractions. They must circle the larger fraction and draw a simple diagram (a bar or a circle) to prove their answer.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 10 min · Whole Class

Human Fraction Line

Give each pupil a card with a simple fraction on it. Challenge the class to arrange themselves in a line from the smallest fraction to the largest without talking, using only gestures and looking at each other's cards.

Compare two different fractions with the same numerator, like 1/5 and 1/10, and explain which is larger.

Facilitation Tip

Start with a smaller group of 5-6 pupils at the front of the class to model the process first.

What to look for

A short worksheet where pupils order sets of fractions from smallest to largest and solve a simple word problem requiring them to compare two fractions in a real-world context.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Always start with concrete materials like paper strips or Play-Doh before moving to diagrams. Constantly prompt pupils with 'How do you know?' to encourage them to explain their reasoning out loud. Using a think-pair-share strategy allows them to build confidence in their explanations before addressing the whole class.

By the end of these activities, your pupils will be able to confidently use visual aids like fraction walls and diagrams to compare and order common fractions.

---

Watch Out for These Misconceptions

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

  Explain that the denominator tells us how many equal pieces the whole is cut into. Use the analogy of sharing a cake: 'If we share a cake between 4 people, your slice will be bigger than if we share the same cake between 8 people. More sharing means smaller slices.'

• The size of the 'whole' doesn't matter. A pupil might think that 1/2 of a small chocolate bar is the same amount as 1/2 of a large one.

  Use concrete examples with different-sized 'wholes' (e.g., a small A5 paper and a large A3 paper). Show that while both can be folded in half, the resulting halves are very different sizes. Emphasise that a fraction is always relative to its whole.

• When comparing fractions like 2/5 and 2/8, the numerators are the same so the fractions are the same.

  Draw two identical bars. Divide one into 5 equal parts and shade 2. Divide the other into 8 equal parts and shade 2. Pupils can visually see that the parts in the first bar are larger, so 2/5 is greater than 2/8.

---

Methods used in this brief

• Think-Pair-Share