Mathematics · Secondary 1

Active learning ideas

Ratio and Direct Proportion

Active learning helps students grasp ratio and direct proportion because they see quantities change in real time rather than just in abstract numbers. Comparing, scaling, and mixing materials make the relational aspect of ratios tangible and memorable for Secondary 1 students.

• MOE Syllabus Outcomes
• MOE: Ratio and Proportion - S1
• MOE: Numbers and Algebra - S1

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inside-Outside Circle
• 30 min · Pairs

Pairs: Paint Mixing Challenge

Pairs mix colours using ratios like 2:1 red to blue. They predict outcomes, mix small batches, then scale up to fill trays while keeping proportions. Compare results and adjust if colours shift.

How does a ratio represent a relationship rather than a fixed quantity?

Facilitation Tip

During the Paint Mixing Challenge, circulate to ask pairs, 'What happens to the color intensity if you keep the same ratio but increase the total amount?' to reinforce proportional reasoning.

What to look for

Present students with two scenarios: 'Scenario A: John has 3 apples and 5 oranges. Scenario B: Mary has 6 apples and 10 oranges.' Ask students to write the ratio of apples to oranges for each person and determine if the ratios are equivalent. Then, ask them to explain their reasoning using the concept of direct proportion.

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

Activity 02

• Inside-Outside Circle
• 45 min · Small Groups

Small Groups: Map Scale Hunt

Provide maps with scales. Groups measure distances between landmarks, convert to real-world km using ratios, and plot a route. They verify by checking actual distances online or with rulers.

Why is maintaining proportionality essential when scaling physical objects?

Facilitation Tip

For the Map Scale Hunt, provide rulers and colored pencils so groups can mark and measure distances directly on their maps.

What to look for

Provide students with a map scale (e.g., 1 cm : 2 km) and two points on a map with a measured distance (e.g., 4 cm). Ask them to calculate the actual distance between the two points. Include a follow-up question: 'If the map scale was changed to 1 cm : 4 km, would the actual distance be larger or smaller, and why?'

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

Activity 03

• Inside-Outside Circle
• 40 min · Whole Class

Whole Class: Recipe Scaling Relay

Display a recipe with ingredient ratios. Teams relay to scale it for 10 or 20 people, calculating amounts. Class discusses equivalent ratios and tests a batch together.

How do we distinguish between additive and multiplicative comparisons?

Facilitation Tip

In the Recipe Scaling Relay, assign clear roles so students rotate tasks and stay engaged during each scaling step.

What to look for

Pose the question: 'Imagine you are baking for a school fair. You have a recipe that serves 4 people, but you need to serve 20 people. How would you use ratios and direct proportion to figure out the new amounts for each ingredient? What is the multiplicative factor you are using?'

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

Activity 04

• Inside-Outside Circle
• 25 min · Individual

Individual: Model Scale Drawings

Students draw scaled models of classroom objects, like a 1:10 desk. They measure originals, apply ratios, draw, and check proportions with peers.

How does a ratio represent a relationship rather than a fixed quantity?

Facilitation Tip

With Model Scale Drawings, give each student grid paper and colored pencils to visualize how ratios translate into dimensions.

What to look for

Present students with two scenarios: 'Scenario A: John has 3 apples and 5 oranges. Scenario B: Mary has 6 apples and 10 oranges.' Ask students to write the ratio of apples to oranges for each person and determine if the ratios are equivalent. Then, ask them to explain their reasoning using the concept of direct proportion.

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

A few notes on teaching this unit

Teach ratio and direct proportion through concrete comparisons before moving to abstract symbols. Use visual aids like ratio bars and grids to show how quantities relate multiplicatively. Avoid rushing to formulas; let students discover the constant ratio through hands-on tasks. Research shows that students grasp proportional relationships better when they physically manipulate materials and discuss their observations.

Successful learning is evident when students confidently compare quantities, adjust scales multiplicatively, and explain why doubling one quantity requires doubling another. They should move from additive thinking to recognizing constant ratios in varied contexts.

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Watch Out for These Misconceptions

• During the Paint Mixing Challenge, watch for students dividing total quantities equally instead of maintaining the ratio.

  Have pairs use ratio bars to measure out paint and water separately, then mix and observe if the color matches their ratio expectation.

• During the Model Scale Drawings, watch for students adding the same length to each dimension instead of multiplying by the scale factor.

  Provide grid paper and ask them to double each side of a shape while counting squares to see the multiplicative change.

• During the Recipe Scaling Relay, watch for students assuming adding more of each ingredient increases servings proportionally without checking the ratio.

  Have groups compare their scaled recipes to the original and calculate the multiplicative factor together before mixing.

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Methods used in this brief

• Inside-Outside Circle