Module 4 Proportion

Proportion - Teacher Notes

Solvemymaths has produced pages like this for lots of topics


NRICH: Cereal Mix
NRICH: Orange Drink
NRICH: Blackcurrantiest
NRICH: Rule of Three
Mixing Paints
Mixing More Paints
NRICH: Adding Triangles 
Trapezium Four

NRICH: Fractions Jigsaw
Peaches Today, Peaches...
NRICH: Matching FDP 
Fraction Card Game 4
NRICH: Andy’s Marbles
NRICH: Would you Rather?
NRICH: Mathland Election 
A Change in Code 
NRICH: An Unhappy End 
NRICH: John's Train Is on Time 
 Up and Across 
NRICH: Far horizon
NRICH: Swings and Roundabouts
NRICH: Cubestick
NRICH: Three by One
NRICH: Nicely Similar
NRICH: Two Ladders




Links in Proportional Reasoning - Watch this Video


All of these topics can be taught using one technique as they all involve scaling numbers up and down.  This approach requires pupils to summarise the question, identify and interpret the key pieces of information and pair up the given values and then to perform a single division and multiplication each time. 








Number of books







This method should be introduced by using some simple examples such as 1 book costs £4 leading to


These are 4 examples of completed questions using the previous grid


Proportion Problems

Compare the prices of various liquids – milk, petrol etc…


Introducing the link between Fractions, Decimals and Percentages

  Artwork and FDP – Click here


Unitary Method

Find a calculation that starts with 300 and ends with 50 by only moving horizontally or vertically.
For example: 300 ÷ 100 ÷ 3 x 5 x 10 = 50
Find other calculations


This then leads onto the following method which shows the functions to say calculate the price of 11 cakes given the price of 8

Speed Camera Maths

Speed Cameras are so last century: discerning law enforcement agencies favour the Average Speed Camera!

These motorway delights timestamp when you go through certain checkpoints and calculate your speed between them. No complicated laser guns required, just number plate recognition and a little distance/time calculation

For lesson ideas - Click here


Which lemonade is stronger?

200ml lemon juice and 300ml of water or
100ml lemon juice and 200ml of water

Random generator of different problems -
Click here



The Golden Ratio
Excellent site with a range of interesting activities -
Click here
NRICH: A first trail through the mysterious world of the Golden Section -
Click here

Ratios with Multilink

Using multilink provides pupils with an opportunity to manipulate the cubes to develop a deeper understanding of the concept of ratio

Percentages  [Thanks to Jo @mathsjam]

Percentage of an amount - ever wondered why? - JustMaths

Percentage Change Chain - Michael Sharman on TES 

Key Stage 3 percentages activities from Teachit Maths

Compound percentages activities from Teachit Maths

Percentages Inquiry - Inquiry Maths

Percentages Revision -


Complete the receipt - Teachit Maths

Ratio and Proportion
[Thanks to Jo @mathsjam]

Ratio and Proportion match cards - Mr Barton

Simplifying ratio bingo/match cardsstudent sheetnotesslides - Nuffield Foundation

Ratio code breaker - Teachit Maths

Simplifying ratio hidden message - jhofmannmaths on TES

Making shortbread - Teachit Maths

Proportion bursts - Teachit Maths

The language of ratio - Teachit Maths

Direct or inverse proportion? - Teachit Maths

Proportion matching cards - source unknown (apologies to author)

Ratio and Proportion workout - Teachit Maths

Breakfast shift - real-life inverse proportion lesson - Nyima Drayang on TES


Speed  [Thanks to Jo @mathsjam]

Speed activity - The Chalk Face

Interpreting Distance-Time Graphs - Maths Assessment Project (activities at the back)
RNLI speed distance time IWB activity - RNLI



Are these bars in proportion and how can you convince someone?


Enlargement Length, Area and Volume Scale Factors

Great starter activity – Click here