Y9 BoosterLesson 5

Objectives – what you should be able to do by the end of the lesson

• Divide a quantity in a given ratio

• Solve simple problems using a unitary method

Equivalent ratios:

In the diagram below the ratio of blue beads to green beads is 3:2.

So for every five beads in the chain, 3 are blue and 2 are green.

3:2

6:4

9:6

If 3:2 = 6:4 = 9:6

Find 3 more equivalent ratios.

Complete this ratio: 150:?

Complete this ratio: ?:40

If the chain has 35 beads altogether how many are green and how many are blue?

Ratio spider diagram 1 M5.1

Find some equivalent ratios to 24:36:60

Unequal sharing:

Example: Share £20 in the ratio 3:2

Working: 3:2 is 5 parts£20

£4

£4 £4 £4£4

3 parts is 3 x £4 = £12

2 parts is 2 x £4 = £8

Answer: £20 in the ratio 3: 2 is £12 : £8

Ratio spider diagram 2 M5.2Complete the boxes:

Ratio problems 1 M5.3• 1 The angles in a triangle are in the ratio 9 : 5 : 4. Find the size of each angle.

• 2 Green paint is made by mixing 2 parts of blue paint with 5 parts of yellow.

A girl has 5 litres of blue paint and 10 litres of yellow paint. What is the maximum amount of green paint she can make?

• 3 This recipe for fruit squash is for 6 people. 300 g chopped oranges 1500 ml lemonade 750 ml orange juice

How much lemonade do you need to make fruit squash for: (a) 9 people? (b) 10 people?

1 The angles in a triangle are in the ratio 9 : 5 : 4. Find the size of each angle.

Angles in a triangle total: 180º

180º In the ratio 9: 5: 4 9 + 5+ 4 = 18 parts

180 ÷ 18 = 10º per part 9 :5: 4 = 90º: 50º: 40º

The angles in the triangle are 90º, 50º and 40º.

Ratio problems 1 M5.3• 1 The angles in a triangle are in the ratio 9 : 5 : 4. Find the size of each angle.

• 2 Green paint is made by mixing 2 parts of blue paint with 5 parts of yellow.

A girl has 5 litres of blue paint and 10 litres of yellow paint. What is the maximum amount of green paint she can make?

• 3 This recipe for fruit squash is for 6 people. 300 g chopped oranges 1500 ml lemonade 750 ml orange juice

How much lemonade do you need to make fruit squash for: (a) 9 people? (b) 10 people?

2 Green paint is made by mixing 2 parts of blue paint with 5 parts of yellow.

A girl has 5 litres of blue paint and 10 litres of yellow paint. What is the maximum amount of green paint she can make?

Blue paint: yellow paint = 2: 5

She has 5 litres of blue

And 10 litres of yellow

2 Green paint is made by mixing 2 parts of blue paint with 5 parts of yellow.

A girl has 5 litres of blue paint and 10 litres of yellow paint. What is the maximum amount of green paint she can make?

Blue paint: yellow paint = 2: 5

She has 5 litres of blue

And 10 litres of yellow

7 litres + 7 litres= 14 litres of green

7 litres7 litres

Ratio problems 1 M5.3• 1 The angles in a triangle are in the ratio 9 : 5 : 4. Find the size of each angle.

• 2 Green paint is made by mixing 2 parts of blue paint with 5 parts of yellow.

A girl has 5 litres of blue paint and 10 litres of yellow paint. What is the maximum amount of green paint she can make?

• 3 This recipe for fruit squash is for 6 people. 300 g chopped oranges 1500 ml lemonade 750 ml orange juice

How much lemonade do you need to make fruit squash for: (a) 9 people? (b) 10 people?

3 This recipe for fruit squash is for 6 people. 300 g chopped oranges 1500 ml lemonade 750 ml orange juice

How much lemonade do you need to make fruit squash for: (a) 9 people? (b) 10 people?

a) For 6 people you need 1500 ml of lemonade

For 9 people (6 + 3) we need: 1500 ml + 750 ml

Answer: 9 people would require 2250 ml of lemonade

b) For 6 people we need 1500 ml of lemonade

For each person we require 1500 ÷ 6 = 250 ml

10 people would require 250 ml x 10

Answer: 10 people would require 2500 ml of lemonade.

Ratio problems 2 M5.4 1 In a game of rugby Rob’s ratio of successful to

unsuccessful kicks was 5 : 3. Dave’s ratio was 3 : 2. Who was the more successful?

2 The gears of a bicycle travelling along a flat road are such that for every 2 turns of the pedals the rear wheel makes 5 turns.If the pedals make 150 turns, how many turns will the rear wheel make?

When travelling up a steep hill in a different gear, would you expect the rear wheel to make more or less than 5 turns for each 2 turns of the pedals?Explain your answer.

3 The answers to a survey are shown in a pie chart. The angle representing ‘Yes’ is 120°, the angle for ‘No’ is 150°, and the angle for ‘Don’t know’ is 90°.

If 300 people took part in the survey, how many replied ‘No’?

1. In a game of rugby Rob’s ratio of successful to unsuccessful kicks was 5 : 3. Dave’s ratio was 3 : 2. Who was the more successful?

Rob’s ratio of 5: 3 means he is successful for 5 out of every 8 kicks

5 out of 8 = 0.625 or 62.5% successful

Dave’s ratio of 3: 2 means he is successful for 3 out of every 5 kicks

3 out of 5 = 0.6 = 60% successful

Rob is the most successful with his ratio of 5: 3

Ratio problems 2 M5.4 1 In a game of rugby Rob’s ratio of successful to

unsuccessful kicks was 5 : 3. Dave’s ratio was 3 : 2. Who was the more successful?

2 The gears of a bicycle travelling along a flat road are such that for every 2 turns of the pedals the rear wheel makes 5 turns.If the pedals make 150 turns, how many turns will the rear wheel make?

When travelling up a steep hill in a different gear, would you expect the rear wheel to make more or less than 5 turns for each 2 turns of the pedals?Explain your answer.

3 The answers to a survey are shown in a pie chart. The angle representing ‘Yes’ is 120°, the angle for ‘No’ is 150°, and the angle for ‘Don’t know’ is 90°.

If 300 people took part in the survey, how many replied ‘No’?

2 The gears of a bicycle travelling along a flat road are such that for every 2 turns of the pedals the rear wheel makes 5 turns.If the pedals make 150 turns, how many turns will the rear wheel make?

When travelling up a steep hill in a different gear, would you expect the rear wheel to make more or less than 5 turns for each 2 turns of the pedals?Explain your answer.

x2 x5

150 ?

Pedals Wheels

Working:

2 X 2.5 5

150 X 2.5 375 The rear wheel will turn 375 times

I would expect the rear wheel to make more/less turns travelling up hill because:

Ratio problems 2 M5.4 1 In a game of rugby Rob’s ratio of successful to

unsuccessful kicks was 5 : 3. Dave’s ratio was 3 : 2. Who was the more successful?

2 The gears of a bicycle travelling along a flat road are such that for every 2 turns of the pedals the rear wheel makes 5 turns.If the pedals make 150 turns, how many turns will the rear wheel make?

When travelling up a steep hill in a different gear, would you expect the rear wheel to make more or less than 5 turns for each 2 turns of the pedals?Explain your answer.

3 The answers to a survey are shown in a pie chart. The angle representing ‘Yes’ is 120°, the angle for ‘No’ is 150°, and the angle for ‘Don’t know’ is 90°.

If 300 people took part in the survey, how many replied ‘No’?

3 The answers to a survey are shown in a pie chart. The angle representing ‘Yes’ is 120°, the angle for ‘No’ is 150°, and the angle for ‘Don’t know’ is 90°.

If 300 people took part in the survey, how many replied ‘No’?

150º / 360º = 15 / 36 = 5 / 12

We need 5/12 of 300 1/ 12 is 300 ÷ 12 = 25

5 / 12 is 5 x 25 = 125

Answer: 125 people in the survey said ‘no’.

Objectives – how have we done?

• Divide a quantity in a given ratio

• Solve simple problems using a unitary method

Thank you for your attention