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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.
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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 thediagram 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 £20 Working: 3:2 is 5 parts £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 M5.2 Complete the boxes:
Ratio problems 1 M5.3 • 1The 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?
1The 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 1The 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 7 litres + 7 litres= 14 litres of green
Ratio problems 1 M5.3 1The 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. Pedals Wheels x2 x5 Working: 2 X 2.5 5 150 ? 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
