Mathematics · Year 3

Active learning ideas

Comparing and Ordering Fractions

Active learning turns abstract fraction comparisons into concrete, visual tasks. When students manipulate fraction strips or position themselves on a number line, they build mental models they can explain aloud. These hands-on moments reveal gaps in understanding faster than worksheets, letting you correct misconceptions in the moment.

• National Curriculum Attainment Targets
• KS2: Mathematics - Fractions

• 15–25 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inside-Outside Circle
• 25 min · Small Groups

Small Groups: Fraction Strip Matching

Provide paper strips for groups to fold into equal parts for denominators 3, 4, or 5. Students cut and label numerators, then lay strips side-by-side to compare and order sets like 1/5, 3/5, 2/5. Groups justify their orders on shared charts before swapping sets.

Explain how to compare two fractions with the same denominator.

Facilitation Tip

During Fraction Strip Matching, circulate and ask each group to verbalize why one strip is longer than another before they record the comparison symbol.

What to look for

Present students with two fraction cards, e.g., 3/5 and 4/5. Ask them to hold up the card representing the larger fraction and explain their choice using the terms numerator and denominator.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 02

• Inside-Outside Circle
• 20 min · Pairs

Pairs: Bar Model Relay

Pairs receive cards with fractions of the same denominator. One partner draws and shades a bar model while the other times them, then they switch to compare which fraction is larger and explain using 'greater than' language. Repeat with ordering three fractions.

Order a set of fractions from smallest to largest.

Facilitation Tip

In the Bar Model Relay, time the pairs so they feel the pressure to decide quickly, then immediately discuss any disagreements before moving to the next model.

What to look for

Give students a worksheet with three fractions, such as 1/6, 5/6, and 3/6. Ask them to draw a simple bar model for each and then write the fractions in order from smallest to largest.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 03

• Inside-Outside Circle
• 15 min · Whole Class

Whole Class: Human Number Line

Tape a large number line from 0 to 1 on the floor. Students draw fraction cards with same denominators, stand at positions to represent values, and adjust collaboratively until ordered correctly. Class discusses and photographs the final line.

Justify why three-fifths is greater than two-fifths.

Facilitation Tip

On the Human Number Line, insist that every child places their fraction card and states their reasoning aloud to the class before sitting down.

What to look for

Pose the question: 'Imagine you have two pizzas cut into 8 equal slices. One pizza has 3 slices left, and the other has 5 slices left. Which pizza has more slices left? How do you know?' Facilitate a class discussion using student explanations.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 04

• Inside-Outside Circle
• 15 min · Individual

Individual: Visual Ordering Sheets

Students receive printed grids or circles divided into equal parts. They shade fractions with the same denominator, cut them out, and glue in order from smallest to largest on a personal strip. Self-assess with a model answer key.

Explain how to compare two fractions with the same denominator.

What to look for

Present students with two fraction cards, e.g., 3/5 and 4/5. Ask them to hold up the card representing the larger fraction and explain their choice using the terms numerator and denominator.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teach this topic by isolating the denominator first. Keep the number of pieces constant while you vary the count of pieces selected. Use consistent visuals across activities so students link the bar model to the fraction strip and the number line. Avoid saying ‘bigger denominator means smaller pieces’ in isolation; instead, connect the visual size directly to the numerator comparison. Research shows that when students physically arrange items, their errors drop by half compared to symbolic-only tasks.

By the end of the session, pupils will confidently compare fractions with the same denominator by naming the numerator as the deciding factor. They will order three fractions correctly and justify each choice using the language of parts and wholes. You’ll hear clear statements such as, ‘Four-fifths is greater because four parts are shaded, not two.’

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Watch Out for These Misconceptions

• During Fraction Strip Matching, watch for pupils who declare that 1/4 equals 3/4 because the strips look the same length.

  Have the group place the two strips end to end and measure them with a blank strip of one-fourth. Ask them to describe how the shaded parts differ in count and why that changes the length.

• During Bar Model Relay, watch for pupils who insist that 1/5 is larger than 4/5 because the pieces are smaller.

  Prompt the pair to shade the models and count aloud: ‘One fifth means one out of five parts. Four fifths means four out of five parts.’ Ask them to compare the shaded areas directly.

• During Human Number Line, watch for children who focus on piece size rather than the count of pieces.

  Circle back to the bar models used earlier and ask students to trace the number line path with their finger while repeating the numerator count for each fraction.

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Methods used in this brief

• Inside-Outside Circle