Mathematics · Primary 4

Active learning ideas

Introduction to Ratios

Active learning helps students grasp ratios because they are inherently about relationships between quantities. When children physically handle objects or draw comparisons, they move beyond memorization to internalize the meaning of part-to-part relationships. This hands-on engagement builds the foundation for proportional reasoning and ensures no one feels lost in abstract symbols.

• MOE Syllabus Outcomes
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Decimals: Recognise that the tenth place is one-tenth of a whole, the hundredth place is one-hundredth of a whole, etc.
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Decimals: Read and write decimals up to three decimal places.
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Fractions: Express a fraction as a decimal.
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Decimals: Compare and order decimals up to three decimal places.

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 30 min · Pairs

Manipulative Sort: Candy Ratio Share

Provide bags of red and yellow candies in different ratios. Pairs sort and count candies, express the ratio in two forms, then simplify by sharing equally among group members. Discuss how the ratio stays the same after doubling the candies.

What is the difference between area and perimeter, and what units do you use to measure each?

Facilitation Tip

During Candy Ratio Share, circulate with a checklist to note who writes ratios correctly and who needs to revisit the physical division of candies.

What to look for

Present students with a collection of objects, like 6 red counters and 4 blue counters. Ask: 'Write the ratio of red counters to blue counters in colon notation. Then, simplify this ratio to its simplest form.'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Experiential Learning
• 35 min · Pairs

Drawing Scale: Map Ratios

Give students grid paper and simple maps. They draw enlarged versions using ratios like 1:2, marking distances and checking equivalence. Pairs compare drawings and simplify any complex ratios encountered.

How do you calculate the area and perimeter of a square and a rectangle using a formula?

Facilitation Tip

For Map Ratios, have students label their diagrams with both the ratio and the simplified form to reinforce equivalence.

What to look for

Pose the following scenario: 'Sarah used 2 cups of flour and 3 cups of sugar for a cake. John used 4 cups of flour and 6 cups of sugar for the same size cake. Are the ratios of flour to sugar the same for both Sarah and John? Explain your reasoning using equivalent ratios.'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Ratio Hunts

Set up stations with ratio problems: one for word forms using toys, one for simplifying with number lines, one for equivalent ratios with paint mixing cups. Small groups rotate, recording findings on a class chart.

Can you find the area and perimeter of a composite figure made from two or more rectangles?

Facilitation Tip

In Ratio Hunts, place a timer at each station so students practice efficiency while maintaining accuracy in their ratio recordings.

What to look for

Give each student a card with a ratio, for example, 5:10. Ask them to: 1. Write this ratio in fraction form. 2. Find one equivalent ratio. 3. Simplify the original ratio to its simplest form.

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

Activity 04

• Experiential Learning
• 20 min · Whole Class

Whole Class: Ratio Line-Up

Students hold cards with numbers to form ratios like 4:6. As a class, they simplify by removing common factors, reforming lines to show equivalence. Vote on real-life examples like team scores.

What is the difference between area and perimeter, and what units do you use to measure each?

What to look for

Present students with a collection of objects, like 6 red counters and 4 blue counters. Ask: 'Write the ratio of red counters to blue counters in colon notation. Then, simplify this ratio to its simplest form.'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Experienced teachers start with concrete objects before symbols, using manipulatives to build intuition about part-to-part comparisons. They avoid rushing to fraction notation until students can verbally explain ratios like 2:3 without confusion. Teachers also encourage peer discussion to surface misconceptions early, such as when one student thinks 2:3 means 5 parts total. This approach aligns with research showing that students need multiple representations to fully grasp ratios.

Successful learning looks like students confidently writing ratios in multiple forms and explaining why 2:3 is not the same as adding to 5. They should simplify ratios correctly and recognize equivalent ratios in real contexts. Students will also articulate the difference between ratios and fractions without prompting, using their own words and examples.

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Watch Out for These Misconceptions

• During Candy Ratio Share, watch for students who add the parts of the ratio to represent the total number of candies.

  Ask them to physically divide 10 candies into 2 groups of red and 3 groups of blue, then count each color separately. Emphasize that the ratio 2:3 compares red to blue, not the total.

• During Map Ratios, watch for students who confuse ratios with fractions representing parts of a single whole.

  Have them draw two separate tape diagrams side-by-side, labeling one for the ratio and one for a fraction. Ask them to shade 2 parts out of 3 on the fraction diagram and compare it to the ratio 2:3 on the other.

• During Ratio Hunts, watch for students who believe simplifying a ratio changes its value.

  In the group challenge, ask them to match equivalent ratio cards by grouping them. Then, have them verify the total for each group remains the same when simplified, using counters to confirm.

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Methods used in this brief

• Experiential Learning
• Stations Rotation