Understanding Ratios

Lesson Overview

Duration: 60 minutes
Class size: 30 students
Subject: Mathematics
Topic: Ratios
Year group: Year 6
Curriculum reference:

• National Curriculum for England - Mathematics
• Key Stage 2
• Number - Ratio and Proportion
• Pupils should be taught to:
  • Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts (Year 6 Programme of Study: Number - ratio and proportion)
  • Pupils should be able to express one quantity as a fraction of another, recognise and use ratio notation, and understand the concept of proportion.

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Learning Objectives

By the end of this lesson, pupils will be able to:

• Understand and use ratio notation (e.g., 3:2) to describe the relative size of two or more quantities.
• Explore and compare ratios in real-life contexts.
• Solve straightforward problems involving ratios using multiplication and division.
• Develop reasoning skills by discussing and justifying ratio comparisons.

National Curriculum links:

• Use, read and write ratio notation, including reduction to simplest form
• Solve problems involving ratio, including unequal sharing and grouping
• Recognise, use and appreciate the link between ratio and fractions

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Resources Needed

• Whiteboard and markers
• Printed worksheets with real-life ratio problems (30 copies)
• Sets of coloured counters (in two colours) per group (e.g., red and blue counters)
• Mini-whiteboards and pens for each student
• Visual aids with ratio examples (e.g., fruit bowls, simple recipe cards, sports team composition)
• Stopwatch or timer
• Sticky notes and pens for group work

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Lesson Structure

1. Introduction (10 minutes)

• Starter activity: Show pictures of two bowls of fruit. One has 6 apples and 4 bananas, the other has 3 apples and 8 bananas.
• Ask students: “How can we compare the numbers of apples and bananas in these bowls?”
• Introduce ratio notation, explaining that ratio compares the quantity of one thing to another, e.g., apples to bananas (6:4).
• Demonstrate how to simplify ratios by dividing both numbers by their greatest common factor (6:4 simplifies to 3:2).
• Link the ratio to fractions by explaining 6:4 means “6 parts to 4 parts,” similar conceptually to fractions.

2. Exploration and Group Discussion (15 minutes)

• Divide the class into groups of 5. Give each group coloured counters (e.g., red and blue).
• Provide different ratio cards for the groups to model using the counters: e.g., "Create a ratio of 5 red counters to 3 blue counters."
• Task groups to:
  • Model the ratio physically.
  • Express the ratio in simplest form using their counters.
  • Come up with a real-life example that matches their ratio (e.g., 5 red cars to 3 blue cars).
• Bring class together to share examples and discuss how each ratio describes quantities differently.

3. Problem Solving Activity (20 minutes)

• Hand out a worksheet with 5 real-life ratio problems for students to solve independently or in pairs (examples include: recipe scaling, mixing paint colours, sports teams composition, etc.). Problems increase in difficulty and involve:
  • Writing ratios from word problems.
  • Simplifying ratios.
  • Finding missing values to keep ratios equivalent (using multiplication or division).
• Circulate the room offering support; use formative assessment by listening to reasoning and noting common misconceptions.

4. Plenary and Formative Assessment (10 minutes)

• Use mini-whiteboards for a quick quiz: call out short ratio problems and ask students to write answers (e.g., “Simplify the ratio 12:8,” “If the ratio of boys to girls is 4:3 and there are 12 boys, how many girls are there?”).
• Collect responses with a show of mini-whiteboards and give immediate feedback.
• Summarise key points: importance of ratio notation, simplifying ratios, and solving problems.

5. Extension / Homework Suggestion (5 minutes)

• Ask students to observe ratios at home or in their surroundings (e.g., number of tea cups to plates at dinner, amount of sugar to drinks) and write a short paragraph describing the ratio using proper notation and explaining what it means.
• Encourage creativity: take photos and bring examples next lesson if possible.

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Differentiation

• Support: Work in pairs or small groups for modelling ratios with physical counters before attempting written problems.
• Challenge: Extension problems where ratios are applied to three quantities or where students find equivalent ratios showing proportional reasoning.

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Assessment Opportunities

• Observation during group work and problem-solving to note understanding and misconceptions about ratio notation and simplification.
• Mini-whiteboard quiz to quickly check individual understanding of key skills.
• Analysis of worksheet answers for accuracy and reasoning.

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Curriculum Mapping Summary

Curriculum Area	Coverage in Lesson
Ratio and Proportion	Use and write ratio notation, simplify ratios, solve problems involving relative sizes of quantities.
Number	Apply multiplication and division to find missing terms in ratio problems.
Mathematical Reasoning	Engage in group discussion to explain and justify ratio comparisons.

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By designing the lesson around hands-on materials, real-world contexts, and active discussions, this plan aims to deepen pupils’ conceptual understanding of ratio, fulfilling Year 6 National Curriculum ambitions and sparking engagement with these important mathematical ideas.