Mathematics · Year 3

Active learning ideas

Understanding Non-Unit Fractions

Active learning helps Year 3 students grasp non-unit fractions because it shifts abstract symbols into tangible experiences. When students partition shapes with their hands or move fraction pieces, they build mental images that connect numerators to real quantities, reducing confusion between parts and wholes.

• National Curriculum Attainment Targets
• KS2: Mathematics - Fractions

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Pairs

Manipulative Build: Fraction Walls

Give students pre-cut fraction strips for denominators 2 to 5. Instruct them to build walls showing 1/4, 2/4, 3/4 and compare heights. Pairs discuss why 3/4 is larger than 1/4, noting numerator changes.

Explain how three quarters is different from one quarter.

Facilitation Tip

During Fraction Walls, ask students to explain why 3/4 is larger than 2/4 by comparing the height of the strips directly next to each other.

What to look for

Provide students with a circle divided into 4 equal parts and a rectangle divided into 3 equal parts. Ask them to shade 3/4 of the circle and 2/3 of the rectangle. Then, ask them to write one sentence explaining the difference between the numerator and denominator.

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

Activity 02

• Stations Rotation
• 25 min · Small Groups

Sharing Task: Chocolate Bar Fractions

Provide chocolate bar diagrams or real bars divided into grids. Students shade two-thirds or three-quarters, then explain to partners using numerator and denominator terms. Regroup to share visuals on the board.

Construct a visual representation of two-thirds.

Facilitation Tip

In Chocolate Bar Fractions, prompt students to name the fraction of pieces they received before eating any, linking the written fraction to the physical count.

What to look for

Display several shaded shapes (e.g., a rectangle with 2 out of 5 parts shaded, a circle with 1 out of 3 parts shaded). Ask students to write the fraction represented by the shaded area for each shape and identify the numerator and denominator.

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

Activity 03

• Stations Rotation
• 35 min · Individual

Visual Draw: Number Line Fractions

Draw number lines divided into 3, 4, or 5 equal parts. Students mark and label 2/3 or 3/5, then compare two fractions on parallel lines. Whole class discusses comparisons.

Compare the meaning of the numerator and the denominator in a non-unit fraction.

Facilitation Tip

For Number Line Fractions, have students mark a unit fraction first, then extend it to show how each added part increases the total size.

What to look for

Present two visual representations: one showing 1/4 of a pizza and another showing 3/4 of the same pizza. Ask students: 'How are these different?', 'What does the 4 tell us in both cases?', and 'What does the 1 tell us in the first picture and the 3 in the second?'

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

Activity 04

• Stations Rotation
• 40 min · Small Groups

Stations Rotation: Fraction Stations

Set up stations with shapes, sets of objects, and strips. At each, students represent a given non-unit fraction and record with drawings. Groups rotate every 7 minutes.

Explain how three quarters is different from one quarter.

Facilitation Tip

At Fraction Stations, circulate and ask one student per group to justify why their shaded model matches the fraction card before moving on.

What to look for

Provide students with a circle divided into 4 equal parts and a rectangle divided into 3 equal parts. Ask them to shade 3/4 of the circle and 2/3 of the rectangle. Then, ask them to write one sentence explaining the difference between the numerator and denominator.

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

A few notes on teaching this unit

Teach non-unit fractions by starting with unit fractions to establish the meaning of the denominator, then layer the numerator as repeated parts. Use consistent visuals across activities so students see that 3/4 always means three equal parts out of four, whether shaded in a circle or marked on a number line. Avoid rushing to rules; instead, let students discover patterns through repeated, varied practice with manipulatives and drawings.

Students will confidently identify and represent non-unit fractions using multiple models, explaining how the numerator and denominator work together to show size. They will compare fractions with the same denominator and justify their reasoning using visual evidence from the activities.

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Watch Out for These Misconceptions

• During Fraction Walls, watch for students who count the total number of blocks instead of understanding the denominator as the number of equal parts in one whole.

  Have students cover one whole strip with unit fractions first, then build upward to show how the numerator accumulates parts within the same whole. Ask them to point to the whole each time before adding more parts.

• During Chocolate Bar Fractions, listen for students who say two-thirds is smaller than one-half because 2 is less than the implied 10 in half.

  Give students a 12-piece chocolate bar and ask them to break it into thirds and halves, then shade and compare. Use the physical pieces to show that two-thirds equals eight pieces, while one-half equals six, making it clearly larger.

• During Number Line Fractions, notice students who assume that three-quarters is always bigger than one-quarter simply because 3 is greater than 1, regardless of placement.

  Have students draw two number lines side by side, one labeled 1/4 and the other 3/4, then mark both on the same line to see that 3/4 extends further. Ask them to explain how the denominator keeps the parts the same size while the numerator grows the total distance.

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Methods used in this brief

• Stations Rotation