Mathematics · Primary 4

Active learning ideas

Equivalent Fractions

Active learning works for equivalent fractions because students need to see, touch, and manipulate parts to trust the abstract rule that multiplying or dividing the numerator and denominator by the same number does not change the fraction's value. When students fold paper, line up strips, or partition sets, they build mental images that replace misconceptions with concrete evidence.

• MOE Syllabus Outcomes
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Fractions: Recognise and write equivalent fractions.
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Fractions: Express a fraction in its simplest form.
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Fractions: Compare and order fractions.

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

Activity 01

• Peer Teaching
• 30 min · Pairs

Card Matching: Fraction Equivalents

Prepare cards with fractions like 1/2, 2/4, 3/6 and matching visual models or multiplication equations. Students work in pairs to match sets, then explain their pairings to the group. Extend by creating new equivalents from given fractions.

What are equivalent fractions, and how do you find them by multiplying or dividing?

Facilitation Tip

During Card Matching, circulate and ask, 'How did you decide these two fractions belong together? Show me on the strips.' to push verbal reasoning.

What to look for

Present students with a fraction, such as 2/3. Ask them to write two equivalent fractions by multiplying the numerator and denominator by different numbers. Then, ask them to write the fraction in simplest form if it is not already. Check their calculations and understanding of the process.

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

Activity 02

• Peer Teaching
• 35 min · Small Groups

Fraction Strip Relay

Provide pre-cut fraction strips. Teams line up and simplify a fraction on the board using strips to verify, then pass to the next teammate. First team to correctly simplify five fractions wins. Discuss strategies as a class afterward.

How do you simplify a fraction to its lowest terms?

Facilitation Tip

For Fraction Strip Relay, set a timer so teams must agree on placements before moving on, forcing peer discussion.

What to look for

Give each student a card with a fraction (e.g., 4/8). Ask them to draw a visual model (like a rectangle or a set of objects) to represent the fraction, and then write the fraction in its simplest form. Collect these to gauge individual understanding of simplification and representation.

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

Activity 03

• Peer Teaching
• 40 min · Pairs

Number Line Builds

Students draw number lines from 0 to 1 and mark equivalents like 1/4, 2/8, 3/12 by jumping equal intervals. Pairs compare and justify why points overlap. Share on class number line mural.

Can you show that two fractions are equivalent using both diagrams and multiplication?

Facilitation Tip

With Number Line Builds, require students to label both the fraction and its equivalent at each step to reinforce the connection.

What to look for

Pose the question: 'If Sarah ate 3/6 of a pizza and John ate 1/2 of the same pizza, did they eat the same amount?' Ask students to explain their reasoning using diagrams or by finding equivalent fractions. Facilitate a class discussion to compare their methods and conclusions.

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

Activity 04

• Peer Teaching
• 25 min · Small Groups

Set Partition Challenge

Give sets of 12 items like counters. Students partition into equivalent fractions such as 3/12 = 1/4 and record with drawings. Rotate sets and compare results in whole class debrief.

What are equivalent fractions, and how do you find them by multiplying or dividing?

What to look for

Present students with a fraction, such as 2/3. Ask them to write two equivalent fractions by multiplying the numerator and denominator by different numbers. Then, ask them to write the fraction in simplest form if it is not already. Check their calculations and understanding of the process.

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

A few notes on teaching this unit

Teach by starting with visual models before symbols, because research shows students who work with area models and number lines first internalize equivalence more deeply. Avoid rushing to rules; instead, let students discover the pattern through repeated exposure to concrete examples. Emphasize communication by pairing students to explain their reasoning with models in hand.

Successful learning looks like students confidently generating equivalent fractions by multiplying or dividing, simplifying fractions to lowest terms without prompting, and explaining equivalence using diagrams or number lines. Students should also demonstrate flexibility by choosing multiple methods to verify the same value.

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Watch Out for These Misconceptions

• During Card Matching, watch for students matching fractions based on similar numerators or denominators instead of value.

  Ask them to place two strips side by side to visually confirm the areas cover the same portion, then prompt, 'What did you multiply the numerator and denominator by here?'

• During Fraction Strip Relay, watch for students incorrectly placing strips because they believe larger denominators mean larger fractions.

  Have them cover one strip with another to see which fraction takes up more space, then ask, 'If we cut a pizza into 8 slices instead of 4, do the slices get bigger or smaller?'

• During Number Line Builds, watch for students placing equivalent fractions at different points on the line due to confusion about scaling.

  Pause the activity and ask, 'If 1/2 is at 0.5, where should 3/6 go? Let's measure with a ruler to check the distance from zero.'

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Methods used in this brief

• Peer Teaching