1. GCSE Maths (Higher Tier) Inverse Proportion

2. Direct proportion what does it mean? £ 102030405060708090100 Percentage 306090120150180210240270300 Both of the lines are travelling in the same direction. As the percentage values goes up so does the amount (£) go up.

3. Direct proportion what does it mean? £ 102030405060708090100 Percentage 306090120150180210240270300 This type of relationship when both lines are going in the same directions are said to be in DIRECT PROPORTION to each other. The sign for direct proportion is :

4. What type of proportion is this? What is our strategy to work it out? We want to find the equivalent measurement in miles for 3 km. Km Miles 8 5 3 ?

5. Strategy Lines to extract information Answer There are 4.8 kilometres in 3 miles Calculation Lines to extract informationQuestion How many kilometres are there in 3 miles? Km Miles 8 5 3 ? The equivalent fractions are

6. Do you expect the time to be more, less or the same? Why? Time in mins. mph 90 60 ? 70 More Speed Less Speed More Time Less Time

7. They still have a relationship but this relationship is described as inverse proportion Time in mins. mph 90 60 ? 70 More Speed Less Speed More Time Less Time

8. It takes one person 8 days to complete a job. How many days will it take 2 people? 4 people? Why do you know this? Time in days. Number of people 8 1 2 4 More people Less people More Time Less Time 2 4

9. What else can you notice? Time in days. Number of people 8 1 2 4 More people Less people More Time Less Time 2 4 4 x 2 = 82 x 4 = 81 x 8 = 8 Equal products

10. Percentage £ 102030405060708090100 306090120150180210240270300 Direct proportion relationships have equivalent fractions. Direct proportion relationships have equivalent fractions We used this to solve questions relating to direct proportion.

11. We know that inverse proportion relationships have the same product, we can use this to solve questions that have arrows going in different directions. Time in days. Number of people 8 1 2 4 More people Less people More Time Less Time 2 4 4 x 2 = 82 x 4 = 81 x 8 = 8 Equal products

12. Start by putting the sums equal to each other. Then divide both sides by what ever is multiplying the ? Time in mins. mph 90 60 ? 70 More Speed Less Speed More Time Less Time

13. As always don’t forget to put the answer in context of the question. Time in mins. mph 90 60 ? 70 It takes approximately 77 minutes to get to my destination if I use the faster train.

14. Strategy Lines to extract information Answer It takes approximately 77 minutes to get to my destination if I use the faster train. Calculation – to get method marks Lines to extract information Question – read it carefully There is a fast and a slow train to get to my destination. One travels at a speed.of 60mph and takes 90 mins, the other train travels at 70mph. How long will my journey take if I choose the faster train. mph Time in min 60 90 ? 70 The equivalent products are

15. When you do some questions. Remember the strategy is: Lines to extract information Answer Put answer in context! Calculation – to get method marks Lines to extract information Question – read it carefully mph Time in min A? The equivalent products are C B