Ratio and Proportion — Year 6 Lesson Plan
National Curriculum: Mathematics — Ratio and proportion, Year 6
Overview
Pupils are introduced to ratio and proportion as ways of comparing quantities. They learn to write and simplify ratios, solve problems involving recipes and scale, and connect ratio to fractions and percentages. They apply these ideas to real-world contexts such as scaling recipes and mixing solutions.
Learning Objectives
- Understand and use ratio notation to compare two quantities.
- Simplify ratios by dividing both parts by a common factor.
- Solve problems involving ratio, including scaling up and down.
- Connect ratio to fractions and use both to solve proportion problems.
Key Vocabulary
Suggested Lesson Structure
Display a recipe for 4 people. Ask: how would you adapt it for 8 people? For 6 people? Establish the concept of scaling a relationship rather than adding a fixed amount.
Introduce ratio notation (a:b). Model simplifying: 6:9 → 2:3. Solve a scaling problem using the unitary method: if 3 pencils cost 90p, how much do 7 cost? Connect to fractions: in a ratio of 2:3, the first quantity is 2/5 of the total.
Pupils simplify ratios, scale recipes, and find missing values in equivalent ratios. Discuss: how is ratio different from just adding more of something?
Pupils solve a set of ratio word problems including scaling (recipe, map scale, mixing paint) and a challenge: share £56 in the ratio 3:5.
A map scale is 1:50,000. A road measures 3 cm on the map — how long is it in real life? Pupils share methods and discuss the connection to multiplication.
Common Misconceptions
- Confusing ratio with fraction: in a 2:3 ratio, the first part is 2/5 (not ½) of the total — ratio compares parts to parts, fractions compare part to whole.
- Scaling by adding rather than multiplying: if the ratio is 1:2, doubling a recipe means multiplying, not adding 2 to each ingredient.
Prior Knowledge
Pupils should already be able to:
- Understanding of fractions and percentages.
- Ability to simplify fractions using common factors.
- Knowledge of multiplication and division.
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