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.

• Primary 4
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Write ratios comparing two quantities in word form, colon notation, and fraction form.
2. Simplify ratios by dividing both quantities by their greatest common divisor.
3. Identify equivalent ratios by multiplying or dividing both quantities by the same non-zero number.
4. Compare the ratio of two quantities in different scenarios to determine which is greater.

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Candy Ratio Share, present students with a collection of 8 green counters and 12 yellow counters. Ask them to write the ratio of green to yellow in colon notation and simplify it.

Discussion Prompt

During Map Ratios, pose the scenario: 'A map shows 1 cm represents 5 km. Another map uses 2 cm for 10 km. Are these ratios equivalent? Explain using the diagrams you drew and the ratios you wrote.'

Exit Ticket

After Ratio Line-Up, give each student a card with the ratio 8:12. Ask them to write this ratio as a fraction, find one equivalent ratio, and simplify it to its simplest form.

Extensions & Scaffolding

• Challenge early finishers to create a real-world ratio problem using items in the classroom, then exchange with a partner to solve.
• Scaffolding for struggling students: Provide ratio strips with pre-divided sections so they can physically see 2:3 as two equal parts to three equal parts.
• Deeper exploration: Ask students to research and present on how ratios are used in a profession, such as cooking, art, or architecture, connecting math to careers.

Key Vocabulary

Ratio	A comparison of two quantities that tells us how much of one thing there is compared to another.
Colon Notation	A way to write a ratio using two numbers separated by a colon, such as 3:5.
Fraction Notation	A way to write a ratio using one number over another, like 3/5.
Simplest Form	A ratio where the two numbers have no common factors other than 1, meaning it cannot be divided further.
Equivalent Ratios	Ratios that represent the same comparison, even though the numbers may be different, like 1:2 and 2:4.