Year 9 Ratio Proportion Dr J Frost jfrosttiffin
![Year 9: Ratio & Proportion Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. Year 9: Ratio & Proportion Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths.](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-1.jpg)
![Starter Puzzles 1 (You can work in pairs) 3 ? ? 2 N ? Starter Puzzles 1 (You can work in pairs) 3 ? ? 2 N ?](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-2.jpg)
![Direct Proportion Iain wants to make a Baked Alaska. He requires 24 eggs to Direct Proportion Iain wants to make a Baked Alaska. He requires 24 eggs to](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-3.jpg)
![Test Your Understanding Solve the following using both the ‘unitary method’ (i. e. find Test Your Understanding Solve the following using both the ‘unitary method’ (i. e. find](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-4.jpg)
![Direct Proportion ! Two things are directly proportional if they in the same ratio. Direct Proportion ! Two things are directly proportional if they in the same ratio.](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-5.jpg)
![Exercise 1 1 (see provided sheet) 5 If it takes 3 men 5 hours Exercise 1 1 (see provided sheet) 5 If it takes 3 men 5 hours](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-6.jpg)
![Exercise 1 (see provided sheet) N 8 ? N ? ? 9 N ? Exercise 1 (see provided sheet) N 8 ? N ? ? 9 N ?](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-7.jpg)
![Inverse Proportion Suppose Mo runs at a speed of 8 m/s for second, and Inverse Proportion Suppose Mo runs at a speed of 8 m/s for second, and](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-8.jpg)
![Example Q Four bricklayers can build a certain wall in ten days. How long Example Q Four bricklayers can build a certain wall in ten days. How long](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-9.jpg)
![Test Your Understanding Q Eleven taps fill a tank in three hours. How long Test Your Understanding Q Eleven taps fill a tank in three hours. How long](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-10.jpg)
![Exercise 2 1 6 ? ? 2 7 ? 3 ? ? 4 8 Exercise 2 1 6 ? ? 2 7 ? 3 ? ? 4 8](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-11.jpg)
- Slides: 11
![Year 9 Ratio Proportion Dr J Frost jfrosttiffin kingston sch uk www drfrostmaths Year 9: Ratio & Proportion Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths.](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-1.jpg)
Year 9: Ratio & Proportion Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com Last modified: 10 th September 2015
![Starter Puzzles 1 You can work in pairs 3 2 N Starter Puzzles 1 (You can work in pairs) 3 ? ? 2 N ?](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-2.jpg)
Starter Puzzles 1 (You can work in pairs) 3 ? ? 2 N ? ?
![Direct Proportion Iain wants to make a Baked Alaska He requires 24 eggs to Direct Proportion Iain wants to make a Baked Alaska. He requires 24 eggs to](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-3.jpg)
Direct Proportion Iain wants to make a Baked Alaska. He requires 24 eggs to make 700 g of the pudding. How many eggs does he require to make 1250 g? Method 1: Unitary Method ? Method 2: Ratio Method We say that the number of eggs and the mass of the pudding are ‘directly proportional’. There is some underlying ‘scaling’ between the two things.
![Test Your Understanding Solve the following using both the unitary method i e find Test Your Understanding Solve the following using both the ‘unitary method’ (i. e. find](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-4.jpg)
Test Your Understanding Solve the following using both the ‘unitary method’ (i. e. find quantity for one unit) and the ‘ratio method’. The mass of 16 cm 3 of Neoginium is 24 g. What is the mass of Q 20 cm 3 of the same element? Unitary Method Ratio Method ? ? If you finish: Q ?
![Direct Proportion Two things are directly proportional if they in the same ratio Direct Proportion ! Two things are directly proportional if they in the same ratio.](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-5.jpg)
Direct Proportion ! Two things are directly proportional if they in the same ratio. Can you suggest variables that might be directly proportional? • Speed and distance travelled (if you double your speed, you double the distance travelled). • Total cost and quantity purchased. ? • Length of steel rod and weight. Why is “hours revised for maths exam” and “maths exam mark” not likely to be directly proportional? If we 5 hours revision resulted in 60%, then clearly 10 hours revision wouldn’t result in 120%! So while the two ? things are ‘correlated’, they are not directly proportional. Q Electricity cost is directly proportional to the hours of TV watched. If 2 hours are watched, a cost of 14 p is incurred. If 7 hours is watched, what cost is incurred? ?
![Exercise 1 1 see provided sheet 5 If it takes 3 men 5 hours Exercise 1 1 (see provided sheet) 5 If it takes 3 men 5 hours](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-6.jpg)
Exercise 1 1 (see provided sheet) 5 If it takes 3 men 5 hours to dig 12 holes, how many hours does it take for 3 men to dig 84 holes? 35 hours ? ? 6 [IMC 2009 Q 9] Joseph’s flock has 55% more sheep than goats. What is the ratio of goats to sheep in the flock? A 9: 11 B 20: 31 C 11: 20 D 5: 9 E 9: 20 Solution: B 2 ? ? 7 [IMC 2005 Q 6] A shop advertise ‘Buy one, get 3 ? ? ? 4 one at half price’. For this offer, the average cost per item is the same as: A Two for the price of one B Three for the price of one C Three for the price of 2. D Four for the price of three E Five for the price of four Solution: D (make the original cost of each item £ 1 for simplicity, and go from there) ? ?
![Exercise 1 see provided sheet N 8 N 9 N Exercise 1 (see provided sheet) N 8 ? N ? ? 9 N ?](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-7.jpg)
Exercise 1 (see provided sheet) N 8 ? N ? ? 9 N ? ?
![Inverse Proportion Suppose Mo runs at a speed of 8 ms for second and Inverse Proportion Suppose Mo runs at a speed of 8 m/s for second, and](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-8.jpg)
Inverse Proportion Suppose Mo runs at a speed of 8 m/s for second, and takes 120 seconds to finish. If he ran double the speed at 16 m/s, what happens to his time? It halves! ? And what do you notice about the speed multiplied by the time in the two cases? It remains the ? same. ! When two quantities are inversely (or ‘indirectly’) proportional, their product remains constant.
![Example Q Four bricklayers can build a certain wall in ten days How long Example Q Four bricklayers can build a certain wall in ten days. How long](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-9.jpg)
Example Q Four bricklayers can build a certain wall in ten days. How long would it take five bricklayers to build it? Method 1: Constant Product Method 2: Unitary Method Find how many days one bricklayer would take! ? ? 4 bricklayers take 10 days. 1 bricklayer takes 40 days 5 bricklayers take 8 days
![Test Your Understanding Q Eleven taps fill a tank in three hours How long Test Your Understanding Q Eleven taps fill a tank in three hours. How long](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-10.jpg)
Test Your Understanding Q Eleven taps fill a tank in three hours. How long would it take to fill the tank if only six taps are working? ? If you finish that quickly… Q If it takes 3 men 4 hours to dig 6 holes, how many hours does it take for 6 men to build 8 holes? Notice that “men” and “hours” are inversely 3 men 4 hours for 6 holes proportional but “hours” and “holes” are directly 6 men 2 hours for 6 holes ? proportional. 6 men 1/3 hours for 1 holes 6 men 8/3 hours for 8 holes (which is 2 hours 40 minutes)
![Exercise 2 1 6 2 7 3 4 8 Exercise 2 1 6 ? ? 2 7 ? 3 ? ? 4 8](https://slidetodoc.com/presentation_image/289fbe5a8b8f05c2e70b2a6a9d55eddc/image-11.jpg)
Exercise 2 1 6 ? ? 2 7 ? 3 ? ? 4 8 ? 5 ? ?