Mathematics · Primary 6

Active learning ideas

Ratio and Fraction Interplay

Active learning lets students see ratio and fraction relationships in concrete ways. When they manipulate visuals, mix real solutions, or debate notations, they build mental models that abstract symbols cannot provide alone. This hands-on approach turns confusion about totals versus parts into clear understanding through repeated, meaningful practice.

• MOE Syllabus Outcomes
• MOE: Ratio - S1
• MOE: Fractions - S1

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Small Groups

Bar Model Matching: Ratio-Fraction Pairs

Provide cards with ratios like 3:5 and bar models divided into 8 parts. Students match ratios to fraction labels (3/8, 5/8) and justify with drawings. Extend by creating their own pairs and solving sharing problems.

Explain how a ratio can be expressed as a fraction of the whole and vice versa.

Facilitation Tip

For the Scale Drawing Challenge, provide grid paper and rulers to help students maintain proportional accuracy when scaling down or up.

What to look for

Present students with a ratio, such as 3:5. Ask them to write the ratio as two fractions of the whole. Then, pose a scenario: 'If these parts represent 80 items, how many items are in each part?'

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

Activity 02

• Stations Rotation
• 35 min · Small Groups

Recipe Scaling Relay: Proportional Mixes

Groups scale paint or juice recipes from a 2:3 ratio to total 20 units, expressing parts as fractions. One student calculates, another draws bars, third verifies proportionality. Rotate roles and share results.

Compare the utility of ratio units versus fractions in different problem scenarios.

What to look for

Provide two problems: Problem A asks to divide $120 in the ratio 2:3. Problem B asks to find the number of boys if they make up 2/5 of a class of 30 students. Ask students: 'Which problem is easier to solve using ratio units, and which is easier using fractions of the whole? Explain your reasoning.'

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

Activity 03

• Stations Rotation
• 25 min · Pairs

Notation Debate: Ratio vs Fraction Scenarios

Pairs solve five problems, like dividing 120 sweets in 4:5 ratio, using both notations. Discuss which form simplifies the task and why, then present to class. Vote on best approaches.

Analyze how maintaining proportionality affects the total number of units in a ratio problem.

What to look for

Give students a ratio of 4:1. Ask them to: 1. Write this ratio as fractions of the whole. 2. If the total number of items is increased from 5 to 15, what is the new ratio? Show your work.

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

Activity 04

• Stations Rotation
• 20 min · Individual

Scale Drawing Challenge: Map Ratios

Individuals draw maps scaling distances in 1:4 ratio, label fraction equivalents of total lengths. Share and check proportionality with peers using rulers.

Explain how a ratio can be expressed as a fraction of the whole and vice versa.

What to look for

Present students with a ratio, such as 3:5. Ask them to write the ratio as two fractions of the whole. Then, pose a scenario: 'If these parts represent 80 items, how many items are in each part?'

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

A few notes on teaching this unit

Teachers should start with visual models before symbols. Research shows students grasp the difference between parts and the whole when they partition bars or shapes by hand. Avoid rushing to algorithms; instead, use questioning to push students to explain their visual reasoning. Emphasize equivalence early—simplified ratios and fractions of the same total represent the same relationship.

Students will confidently explain how a ratio like 2:3 relates to fractions 2/5 and 3/5 of the whole. They will choose the best notation—ratio or fraction—for a given scenario and justify their choice. Missteps will be caught early through peer discussion and teacher observation during activities.

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Watch Out for These Misconceptions

• During Bar Model Matching, watch for students who label a ratio of 1:2 as 1/3 of the whole.

  Ask these students to count the total number of parts in their bar model and rewrite the fractions based on the actual total, using the visual to correct their misunderstanding.

• During Scale Drawing Challenge, watch for students who assume simplifying a ratio like 4:6 to 2:3 changes the actual quantities in the drawing.

  Have them measure their original drawing, simplify the ratio on paper, and verify that the scaled version maintains the same physical proportions as the original.

• During Recipe Scaling Relay, watch for students who try to add ratios directly, such as 2:3 + 1:4 = 3:7.

  Prompt them to convert the ratios to fractions first, find a common total, and then convert back to a ratio, using the recipe ingredients to test their method.

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Methods used in this brief

• Stations Rotation