Year 8 Term 1 Week 2 - Ratio and Scale
- Sallyann Clark
- Aug 31
- 4 min read
Ratio and Scale
Introduction
Last week you learned the basics of ratio: simplifying, finding equivalent ratios, sharing in a ratio, and linking ratios to fractions. You also started exploring proportional reasoning through recipe scaling and fair sharing.
This week, we extend those ideas to include scale drawings, inverse proportion, and linear conversions. These skills will help you solve real-world problems like reading maps, converting measurements, and understanding relationships where one value increases as the other decreases.
Real-World Application – Why This Maths Matters
Scale, proportion, and conversions are key in everyday life. Builders and designers use scale drawings. Scientists and engineers work with inverse proportion when studying speed, density, and pressure. Linear conversions are used in cooking, travel, and shopping — from converting miles to kilometres, to turning pounds into kilograms.
Day 1 – Understanding Scale
What am I Learning Today?
I will be learning to interpret scales on drawings and maps, as well as convert between real-life measurements and scaled ones.
Revision reminder
You should already know how to simplify ratios from last week, and convert metric units (cm, m, km).
If you need to revise converting metric units watch Maths with Mr J: Metric units of length.
Game
Play MathsPlayground: Ratio Stadium
Learn
Work through BBC Bitesize KS3: Scale Drawings
Have a go at using Mathspad: Ratio Maps interactive.
Task
Answer the following questions:
A scale of 1:100 means 1 cm on a drawing represents how many cm in real life?
On a 1:50 scale drawing, a wall is shown as 8 cm long. What is the real length?
A map has a scale 1 cm = 5 km. If two towns are 12 cm apart on the map, how far apart are they in real life?
Conclusion
You can now use scale ratios to move between real measurements and scaled ones.
Day 2 – Scale Drawings
What am I learning Today?
I will be learning to create scale drawings using a given ratio and represent large objects on paper accurately.
Revision reminder:
You should already know how to multiply and divide by 10, 100, and 1000 to convert units. If you need to revise this watch The Maths Guy!: How to multiple by 10, 100 and 1,000.
Game
Play Wordwall: Multiple and divide by 10,100 and 1000.
Learn
Work your way through Khan Academy: 7th Grade Unit 8
Task
I think you did enough in the learn section today!
Conclusion
You can now draw scaled versions of real objects and spaces using ratio.
Day 3 – Inverse Proportion
What am I Learning Today?
I will be learning to recognise when quantities are in inverse proportion and solve problems where one value increases as the other decreases.
Revision reminder
You should already know how to solve direct proportion problems (from Week 1).
Game
Play the Wordwall game: Ratio, Proportion and Scale.
Learn
Work through BBC Bitesize KS3: Inverse Proportion.
Task:
In your journal:
record a definition for inverse proportion with three examples.
Complete MEP Unit 7 Ratios and Proportions exercise 7.5.
Conclusion
You can now solve inverse proportion problems where one value decreases as the other increases.
Day 4 – Linear Conversions
What am I learning Today?
I will be learning to convert between units using linear conversion rates and solve problems involving currencies, measures, and everyday conversions.
Revision reminder
You should already know how to multiply and divide with decimals. If you need a recap watch Maths with Mr J: Multiplying and Dividing Decimals.
Game
Play Mathpup Hop Decimal Multiplication on Math Nook.
Learn
Complete MEP Unit 7 Ratios and Proportions exercise 7.4.
Task
In your Journal:
Look at your Ratio page and add Proportions to the title.
Is there anything else you can add to your page that you have learned about ratios and proportions these past two weeks? Add it if there is.
Solve these problems:
Convert 5 miles into km, given 1 mile = 1.6 km.
Convert £200 into euros if £1 = €1.15.
A recipe needs 500 ml of milk. How many litres is this?
Challenge: A runner covers 10 km. Convert this into miles (1 mile ≈ 1.6 km).
Conclusion
You can now perform linear conversions in measures and currencies, applying them to real-life problems.
Day 5 – Project: The Travel Challenge
What am I Learning Today?
I will be learning to apply scale, inverse proportion, and linear conversions to real-life travel problems and decide when to use each proportional reasoning method.
Introduction
Imagine you are planning a school trip. You must work out distances, travel times, and convert between units.
Task – The Travel Challenge
Map Scale:
On a map with scale 1 cm = 10 km, two cities are 18 cm apart. What is the real distance?
Linear Conversion:
The journey is 180 km. Convert this into miles (1 mile = 1.6 km).
Inverse Proportion:
A coach takes 6 hours at 50 km/h. If the speed increases to 75 km/h, how long will the journey take?
Challenge – Combined Skills:
A train can carry 240 passengers. The number of carriages is inversely proportional to the number of passengers per carriage.
If 8 carriages carry 30 passengers each, how many passengers per carriage would 6 carriages hold?
Conclusion
Today you applied your knowledge of scale, inverse proportion, and linear conversions in a travel planning scenario. These skills show how proportional reasoning is used in journeys, budgeting, and logistics.
