Introduction to Ratio Notation

Active learning helps students grasp ratio notation because it moves beyond abstract numbers into tangible comparisons. When students manipulate objects or scale real drawings, they see how ratios describe relationships, not just quantities. Concrete experiences build a foundation for later abstract reasoning in scaling and proportionality.

• Year 6
• Mathematics
• 3 activities
• 15 min–45 min

Learning Objectives

1. Explain the difference between a ratio comparing two parts and a fraction comparing a part to a whole.
2. Simplify ratios to their lowest terms using common factors.
3. Calculate missing quantities in a ratio when one quantity is known.
4. Create a real-world scenario that can be represented using ratio notation.

Simulation Game

⏱ 45 min·Small Groups

Simulation Game: The Master Chef

Give groups a recipe for 4 people and ask them to adjust it for 6, 10, and 15 people. They must use ratio and scaling to ensure the proportions remain correct, then present their new ingredient lists to the 'Head Chef' (the teacher).

Prepare & details

Differentiate between a ratio (part to part) and a fraction (part to whole).

Facilitation Tip: During The Master Chef activity, circulate with counters and recipe cards to intervene immediately when students add instead of multiply ratios.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Inquiry Circle

⏱ 40 min·Pairs

Inquiry Circle: Scale My Drawing

Students draw a simple character on a 1cm grid. They then work in pairs to redraw the character on a 2cm grid (scale factor 2) and a 0.5cm grid (scale factor 0.5), discussing how the area and perimeter change as they scale.

Prepare & details

Explain how to simplify a ratio to its simplest form.

Facilitation Tip: In Scale My Drawing, circulate to check that students label their ratios clearly with the original and new dimensions before scaling.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: Ratio or Fraction?

Show a picture of 2 apples and 3 oranges. Ask: 'What is the ratio of apples to oranges?' and 'What fraction of the fruit are apples?' Students discuss in pairs why the numbers are different (2:3 vs 2/5) and share their reasoning.

Prepare & details

Construct a real-world problem that can be solved using ratio notation.

Facilitation Tip: For Ratio or Fraction? have students first write their own answers, then discuss in pairs before sharing with the class to uncover misconceptions.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Teach ratio notation by connecting it to real contexts students already understand, like recipes or drawings. Avoid starting with abstract symbols alone, as this often leads to rote memorization without understanding. Use concrete models first, then transition to symbolic notation only after students can explain the relationships in words. Research shows that students who begin with physical manipulatives or visual models develop stronger proportional reasoning than those who start with algorithms.

What to Expect

Students should confidently write ratios in correct notation, explain what the numbers represent in context, and apply scaling consistently. They should also distinguish between part-to-part and part-to-whole comparisons without confusing the order or using additive reasoning.

Watch Out for These Misconceptions

Common Misconception

During The Master Chef activity, watch for students who add the same amount to each part instead of multiplying the entire ratio. For example, doubling 2:3 as 4:5 instead of 4:6.

What to Teach Instead

Hand students physical counters representing 2 red and 3 blue beads. Ask them to create two identical batches and observe that the total is 4 red and 6 blue, not 4 red and 5 blue. Have them record the new ratio as 4:6 and relate it back to doubling the original.

Common Misconception

During Scale My Drawing, watch for students who reverse the order of the ratio when scaling. For example, scaling a 3:2 ratio to 6:4 instead of 4:6.

What to Teach Instead

Have students label each part of their drawing clearly with the original ratio before scaling. Provide a checklist with instructions to peer-check the order against the labels and adjust if necessary before proceeding.

Assessment Ideas

Exit Ticket

After The Master Chef activity, provide students with a recipe card that uses a ratio of 4 cups flour to 2 cups sugar. Ask them to write the ratio in simplest form and then scale it to make 12 cups of flour.

Quick Check

During Scale My Drawing, display a simple shape with a ratio of 5 cm to 3 cm and ask students to write the ratio. Then, ask them to scale it to 10 cm and explain how they found the new measurements.

Discussion Prompt

After Ratio or Fraction?, pose the prompt: 'In a bag of marbles, the ratio of red to blue is 3:7. If I add 6 more red marbles, what happens to the ratio? Is it still 3:7?' Have students discuss their reasoning in small groups and share conclusions with the class.

Extensions & Scaffolding

• Challenge: Ask students to create a scaled map of the school playground with a ratio of 1:50, including a legend and a key.
• Scaffolding: Provide labeled fraction strips or ratio bars for students to compare and scale step-by-step.
• Deeper exploration: Introduce a ratio challenge where students must find multiple possible scale factors that preserve the same ratio relationship in a real-world problem, such as resizing a photo without distortion.

Key Vocabulary

Ratio	A comparison of two quantities, often written using a colon (e.g., 2:3) or as a fraction (e.g., 2/3), showing the relative sizes of those quantities.
Ratio Notation	The standard way of writing ratios, typically using a colon to separate the numbers representing the quantities being compared (e.g., 1:2).
Simplest Form	A ratio where the numbers have no common factors other than one, meaning it cannot be divided further to represent the same relationship.
Part to Part Ratio	A ratio that compares two different parts of a whole, such as the number of boys to the number of girls in a class.
Part to Whole Ratio	A ratio that compares one part of a whole to the entire whole, similar to a fraction, such as the number of boys compared to the total number of students.