Y9 Booster Lesson 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. 3:23:2 6:46:4 9:69:6

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 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 2M5.2 Complete the boxes:

Ratio problems 1M5.3 1The angles in a triangle are in the ratio 9 : 5 : 4. Find the size of each angle. 2Green 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? 3This recipe for fruit squash is for 6 people. 300 gchopped oranges 1500 ml lemonade 750 mlorange juice How much lemonade do you need to make fruit squash for: (a)9 people?(b)10 people?

1The angles in a triangle are in the ratio 9 : 5 : 4. Find the size of each angle. Angles in a triangle total:180 º 180 º In the ratio 9: 5: = 18 parts 180 ÷ 18 = 10 º per part 9 :5: 4 = 90º: 50º: 40º The angles in the triangle are 90 º, 50 º and 40 º.

Ratio problems 1M5.3 1The angles in a triangle are in the ratio 9 : 5 : 4. Find the size of each angle. 2Green 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? 3This recipe for fruit squash is for 6 people. 300 gchopped oranges 1500 ml lemonade 750 mlorange 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 litres

Ratio problems 1M5.3 1The angles in a triangle are in the ratio 9 : 5 : 4. Find the size of each angle. 2Green 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? 3This recipe for fruit squash is for 6 people. 300 gchopped oranges 1500 ml lemonade 750 mlorange 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 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 2M5.4 1In 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? 2The 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. 3The 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 = 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 2M5.4 1In 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? 2The 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. 3The 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’?

2The 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? PedalsWheels Working: 2 X X The rear wheel will turn 375 times I would expect the rear wheel to make more/less turns travelling up hill because:

Ratio problems 2M5.4 1In 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? 2The 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. 3The 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 3001/ 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