**Understanding Proportion**

Starter

Understanding Proportion

Two quantities are in proportion if one is always the same multiple of the other i.e. the two are always in the same ratio.

Are these in Proportion?

Decide whether these quantities are in proportion. Show your working.

**L.O. - Understand what it means for two quantities to be in proportion, and use proportional relationships.**

How many times bigger is the orange area than the green area?

If I double the number of green and orange pieces, how many times bigger will the orange area be than the green area?

Starter

How many times bigger is the orange area than the green area?

2.5 x bigger

If I double the number of green and orange pieces, how many times bigger will the orange area be than the green area?

Still 2.5 x bigger

1 litre of milk costs 97p and 2 litres of milk costs £1.90

A 4 pack of toilet tissue costs £1.24 and a 6 pack costs £1.86.

A 300g pack of biscuits contains 15 biscuits, and a 500g pack of biscuits contains 25 biscuits.

Are these in Proportion?

Decide whether these quantities are in proportion. Show your working.

1 litre of milk costs 97p and 2 litres of milk costs £1.90

A 4 pack of toilet tissue costs £1.24 and a 6 pack costs £1.86.

A 300g pack of biscuits contains 15 biscuits, and a 500g pack of biscuits contains 25 biscuits.

No, they are not in proportion, 1 litre only costs 95p in the 2 litre bottle.

Yes, they are in proportion, each roll costs 31 pence in both packs.

Yes, they are in proportion, each biscuit weights 20g.

Are they in Proportion?

Red

Amber

Are the results for the 14 year olds and the results for the 15 year olds in proportion?

Green

Are they in Proportion?

Red

Amber

Are the results for the 14 year olds and the results for the 15 year olds in proportion?

Yes both ratios are 3:1.

Green

No, David's ratio is 4:5 but Jose's is 17:20.

The ratio of right to wrong is 27:4 in the first test

which is 6.75:1. In the second it would be 26:5 which is 5.2:1. So Sara is not correct.

Using a proportional relationship

A car travels 100 miles, using 12 litres of fuel.

How far would the car travel using 18 litres

of fuel?

A journey of 20km takes 5 hours at average walking pace. How long would a journey of

26 km take at average walking pace?

Using a proportional relationship

A car travels 100 miles, using 12 litres of fuel.

How far would the car travel using 18 litres

of fuel?

The ratio of litres to miles = 3:25.

This means every 3 litres takes us 25 miles. 18 litres is 6 x 3 litres so 6 x 25 miles = 150 miles.

A journey of 20km takes 5 hours at average walking pace. How long would a journey of

26 km take at average walking pace?

The ratio of hours to kilometres is 1:4. This means every hour takes us 4 km. 26 km = 6.5 x 5 so 6.5 x 1 = 6.5 hours (or 6 hours 30 minutes)

Main Activity

Find the required value in these proportional

relationships.

Red

Amber

Green

Main Activity

Find the required value in these proportional

relationships.

Red

Amber

Green

34 minutes

£30

42 seconds

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