1. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com Rate and Proportion www.mathsrevision.com Rates and Finding Rates Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 20151 Direct Proportion S4 Direct Proportion graphs Inverse Proportion

2. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com Starter Questions www.mathsrevision.com S4 Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 20152

3. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com Learning Intention Success Criteria 1.To understand the term ‘rate’ and calculate it. 1.To explain the term ‘rate’ is and how to find the rate. Rates S4 Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 20153

4. Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com 4 Per means for each. A phrase that contains the word ‘per’ is called a RATE. Example :Sean walks at 5 km per hour (km/hr) This means that if Sean walked at this speed for one hour he would travel 5km. Rates S4

5. www.mathsrevision.com We are often interested in rates Miles per gallon Goals per game £’s spent per day Calories per day Words per minute Rates Why are we interested in rates? www.mathsrevision.com S4

6. Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com 6 Example : Sean walks at 5 km per hour (km/hr) How far would he walk in : (a)4 hours(b)Half an hour (a)4 x 5 = (b)5 x 0.5 = 20km 2.5 km Rates S4

7. Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com 7 Finding the Rate Example : For 5 hours’ work Jennifer is paid £30. Calculate her rate of pay per hour. Answer : 5 hours  £30 1 hour  £30 ÷ 5 =£6 This means that Jennifer is paid a ‘rate’ of £6 per hour S4

8. Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com 8 Finding the Rate Example : 3 litres of paint covers a fence area of 36 m 2 How much will 1 litre cover. Answer : 3 litres  36 1 litre  36 ÷ 3 =12m 2 This means that 12m 2 requires 1 litre of paint. S4

9. Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com 9 Finding the Rate Example : Nicola gets paid £48 000 pounds a year. What is her monthly rate of pay. Answer : 12 months  £48 000 1 month  £48 000 ÷ 12 =£4 000 This means Nicola gets paid £4 000 per month S4

10. Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Wednesday, June 10, 2015Created by Mr. Lafferty @www.mathsrevision.com Now try Ex 1 Ch 2 (page 26) www.mathsrevision.com 10 Finding the Rate S4

11. 10-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com S4

12. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To explain the term Direct Proportion. 1. Understand the idea of Direct Proportion. Direct Proportion 2. Solve simple proportional problems. S4

13. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Direct Proportion “.. When you double the number of cakes you double the cost.” CakesCost Two quantities, (for example, number of cakes and total cost) are said to be in DIRECT PROPORTION, if : Example :The cost of 6 cakes is £4.20. find the cost of 5 cakes. 6  4.20 1  4.20 ÷ 6 = 0.70 5  0.70 x 5 = £3.50 S4 Easier method CakesPence 6  420 5 Are we expecting more or less (less)

14. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Direct Proportion £$ Example :On holiday I exchanged £30 for $45. How many $ will I get for £50. 30  45 1  45 ÷ 3 0 = 1.5 50  1.5 x 50 = $75 What name do we give to this value Exchange rate S4 Easier method £$ 30  45 50 Are we expecting more or less (more)

15. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Direct Proportion PencilsCost Sometimes it is easier to find the cost of 10,100 or 1000 items rather than 1. Example :300 pencils cost £6. How much will 200 cost. 300  £6.00 100  £6.00 ÷ 3 = £2.00 200  £2.00 x 2 = £4.00 S4 Easier method PencilPence 300  600 200 Are we expecting more or less (less)

16. 10-Jun-15Created by Mr. Lafferty Maths Dept. Now try Ex 2 Ch2 (page 28) www.mathsrevision.com Direct Proportion S4

17. 10-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com S4

18. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To explain how Direct Proportion Graph is always a straight line. 1. Understand that Direct Proportion Graph is a straight line. Proportion 2. Construct Direct Proportion Graphs. Direct Proportion Graphs S4

19. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Proportion The table below shows the cost of packets of “Biscuits”. Direct Proportion Graphs We can construct a graph to represent this data. What type of graph do we expect ? S4

20. 10-Jun-15Created by Mr. Lafferty Maths Dept. Direct Proportion Graphs Notice that the points lie on a straight line passing through the origin This is true for any two quantities which are in Direct Proportion.

21. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Proportion Direct Proportion Graphs KeyPoint Two quantities which are in DIRECT PROPORTION always lie on a straight line passing through the origin. S4

22. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Proportion Example : Plot the points in the table below. Are they in direct proportion? Direct Proportion Graphs We plot the points (1,3), (2,6), (3,19), (4,12)X1234y36912 S4

23. 10-Jun-15Created by Mr. Lafferty Maths Dept. 1 www.mathsrevision.com Proportion Plotting the points (1,3), (2,6), (3,9), (4,12) Direct Proportion Graphs 01234 10 11 12 2 3 4 5 6 7 8 9 Since we have a straight line passing through the origin x and y are in direct proportion. x y S4

24. 10-Jun-15Created by Mr. Lafferty Maths Dept. Now try TJ Extension booklet www.mathsrevision.com Proportion Direct Proportion S4

25. 10-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com S4

26. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To explain the term Inverse Proportion. 1. Understand the idea of Inverse Proportion. Proportion 2. Solve simple inverse proportion problems. Inverse Proportion S4

27. 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Proportion MenHours Inverse proportion is when one quantity increases and the other decreases. The two quantities are said to be INVERSELY PROPORTIONAL or (INDIRECTLY PROPORTIONAL) to each other. Example :If it takes 3 men 8 hours to build a wall. How long will it take 4 men. (Less time !!) 3  8 1  3 x 8 = 24 hours 4  24 ÷ 4 = 6 hours Inverse Proportion S4 Easier method Workers Hours 3  8 4 Are we expecting more or less (less)

28. 1  12 x 10 = 120 8  120 ÷ 8 = 15 months 10-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Proportion MenMonths Example :It takes 10 men 12 months to build a house. How long should it take 8 men. 10  12 Inverse Proportion S4 Easier method Workersmonths 10  12 8 Are we expecting more or less (more)

29. 10-Jun-15Created by Mr. Lafferty Maths Dept. Now try TJ Extension Booklet www.mathsrevision.com Proportion Inverse Proportion S4