Mathematics · Year 6 · Ratio and Proportion · Spring Term

Introduction to Ratio Notation

Students will solve problems involving the relative sizes of two quantities using ratio notation.

• National Curriculum Attainment Targets
• KS2: Mathematics - Ratio and Proportion

About This Topic

Ratio and scaling introduce students to the idea of relative size and multiplicative relationships. Unlike fractions, which usually compare a part to a whole, ratios often compare one part to another part (e.g., 2 red beads for every 3 blue beads). In Year 6, the National Curriculum focuses on using ratio notation and scale factors to solve problems in contexts such as recipes, maps, and similar shapes.

This topic is a bridge to more advanced proportional reasoning. Students must understand that while the numbers in a ratio change when scaled, the relationship between them remains constant. This topic comes alive when students can physically model the ratios using concrete objects or use scaling to create larger versions of small designs, allowing them to see the proportional growth in action.

Key Questions

1. Differentiate between a ratio (part to part) and a fraction (part to whole).
2. Explain how to simplify a ratio to its simplest form.
3. Construct a real-world problem that can be solved using ratio notation.

Learning Objectives

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

Before You Start

Fractions as Division

Why: Students need to understand that a fraction represents a division of the numerator by the denominator to grasp the concept of comparing quantities.

Finding Common Factors

Why: Simplifying ratios relies on identifying and dividing by common factors, a skill developed when working with fractions and multiples.

Multiplication and Division Facts

Why: Accurate recall of multiplication and division facts is essential for simplifying ratios and calculating proportional amounts.

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.

Watch Out for These Misconceptions

Common Misconception

Using additive instead of multiplicative reasoning (e.g., to double a ratio of 2:3, adding 2 to both to get 4:5).

What to Teach Instead

This is a very common error. Use physical counters to show that if you have two groups of 2:3, you actually have 4:6. Peer discussion during scaling activities helps students see that the 'relationship' must be multiplied, not added to.

Common Misconception

Confusing the order of the ratio (e.g., writing 3:2 instead of 2:3).

What to Teach Instead

Students often think the order doesn't matter. Use specific labels in all activities (e.g., 'Flour:Sugar') and have students peer-check each other's work to ensure the numbers match the labels correctly.

Active Learning Ideas

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).

45 min·Small Groups

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.

40 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.

15 min·Pairs

Real-World Connections

• Chefs use ratios to scale recipes up or down. For example, if a recipe for 4 people calls for 200g of flour, a chef might use a ratio of 50g of flour per person (200g:4 people, simplified to 50g:1 person) to quickly calculate the flour needed for 10 people.
• Architects and designers use ratios to create scale drawings and models. A common scale might be 1:50, meaning 1 centimeter on the drawing represents 50 centimeters in reality, allowing them to represent large buildings or furniture accurately on paper.

Assessment Ideas

Exit Ticket

Provide students with two scenarios: 'For every 3 red marbles, there are 5 blue marbles' and '3 out of every 8 marbles are red'. Ask students to write the ratio notation for each and identify which is a part to part ratio and which is a part to whole ratio.

Quick Check

Display a ratio, for example, 12:18. Ask students to write the ratio in its simplest form on a mini-whiteboard. Then, present a simple word problem like, 'In a class, the ratio of teachers to students is 1:15. If there are 3 teachers, how many students are there?'

Discussion Prompt

Pose the question: 'Imagine you are making fruit punch. You have a recipe that uses 2 parts orange juice to 3 parts cranberry juice. What does this ratio tell you about the ingredients? How would you change the recipe if you wanted to make a much larger batch but keep the same taste?'

Frequently Asked Questions

How can active learning help students understand ratio?

Active learning, such as the 'Master Chef' recipe challenge, makes the abstract concept of 'parts' tangible. When students have to scale a recipe, they see that every ingredient must be multiplied by the same factor to keep the taste the same. This practical application reinforces multiplicative reasoning and helps them distinguish it from the additive reasoning they are more familiar with.

What is the difference between ratio and proportion?

Ratio is a comparison of two or more parts (e.g., 2 parts blue to 1 part yellow). Proportion is the equality of two ratios (e.g., 2:1 is the same proportion as 4:2). In Year 6, we use ratio to describe the relationship and proportion to solve for missing values.

How do I teach scale factors for shapes?

Use grid paper. If a rectangle is 2 squares by 3 squares, a scale factor of 3 means the new rectangle must be 6 squares by 9 squares. Students often forget to scale both dimensions, so the visual grid provides immediate feedback.

Why is ratio notation (a:b) used?

The colon notation is a universal way to show how quantities relate to each other without using words. It is efficient and allows for easy comparison between multiple parts, which is essential for more complex maths and science in the future.