**Practical Proportional Relationships**

Starter

A house takes 5 painters 3 days to paint. How long would it take 6 painters to paint?

A tin of paint covers 12 m . The house has a total area of 138 m that needs painting. How many tins of paint are required for the house?

Activity

Look at the cards and sort them into 'Proportional' (P), 'Inversely Proportional' (I) or 'Neither' (N). Try to solve the problem on each one.

Proportion and Inverse Proportion problems

A vehicle travels 220 miles in 5 hours. Work out the speed of the vehicle.

The vehicle travels the same 220 miles, but increases its speed to 50 miles an hour. How long will the vehicle take?

**L.O. - To review proportional relationships and solving practical problems.**

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Starter

A house takes 5 painters 3 days to paint. How long would it take 6 painters to paint?

2.5 days

A tin of paint covers 12 m . The house has a total area of 138 m that needs painting. How many tins of paint are required for the house?

11.5 tins. (12 tins)

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Proportional and Inversely Proporitonal Relationships

A house takes 5 painters 3 days to paint. What is the relationship between the number of painters and the number of days?

A tin of paint covers 12 m . What is the relationship between the number of tins of paint and the area covered?

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Proportional and Inversely Proporitonal Relationships

A house takes 5 painters 3 days to paint. What is the relationship between the number of painters and the number of days?

Number of painters x number of days = 15.

A tin of paint covers 12 m . What is the relationship between the number of tins of paint and the area covered?

Area covered = 12 x number of tins.

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Proportion and Inverse Proportion problems

A vehicle travels 220 miles in 5 hours. Work out the speed of the vehicle.

220/5 = 44 miles per hour.

The vehicle travels the same 220 miles, but increases its speed to 50 miles an hour. How long will the vehicle take?

220/50 = 4.4 hours (4 hours 24 minutes).

Activity

Cut out the cards and sort them into 'Proportional' or 'Inversely Proportional'. Try to solve the problem on each one.

1). Proportional, 95 miles.

2). Inversely Proportional, 5.3333... hours (5 hours 20 minutes).

3). Inversely Proportional, 50 pickers.

4). Proportional, £3.10.

5). Neither, 40 minutes.

6). Inversely Proportional, 5.25 days.

7). Proportional, £405.

Activity

Solve the problems on the worksheet

Activity

Solve the problems on the worksheet

1. $1280

2. £80

3. 15

4. 15 minutes

5. 40

6. As the length of one side doubles, the width has to be halved for the area to stay the

same.

E.g. a rectangle of 24 cm2 could be 12 cm × 2 cm or 6 cm × 4 cm.

7. 150 miles is half as much distance again so the time is half as much again. Half of 5

hours is 2.5 hours. Or 300 ÷ 5 = 60 miles, so (450 – 300) ÷ 60 = 2.5 hours oe

8. 5 × 12 = 60, so 1 person would take 60 days so 6 people will take 6

60 = 10 days oe

9. £78

10. 50 hours

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