1. © T Madas

2. What do we mean when we say two quantities are in proportion? It means that if: one of them doubles, the other one also doubles. one of them trebles, the other one also trebles. one of them x4, the other one also x4. one of them halves, the other one also halves. one of them ÷4, the other one also ÷4.

3. © T Madas 3 pens cost £2 6 pens cost £4 9 pens cost £6 12 pens cost £8 etc 15 pens cost £10 3 2 6 4 9 6 12 8 15 10 :::::::::: What do you notice? Cost of pens Pens £

4. © T Madas 3 pens cost £2 6 pens cost £4 9 pens cost £6 12 pens cost £8 etc 15 pens cost £10 3 2 6 4 9 6 12 8 15 10 :::::::::: Cost of pens Pens £ How much do 30 pens cost? …… 30 20 £20 x 10

5. © T Madas 3 pens cost £2 6 pens cost £4 9 pens cost £6 12 pens cost £8 etc 15 pens cost £10 3 2 6 4 9 6 12 8 15 10 :::::::::: Cost of pens Pens £ How much do 30 pens cost? …… 30 20 £20 x 2

6. © T Madas 3 pens cost £2 6 pens cost £4 9 pens cost £6 12 pens cost £8 etc 15 pens cost £10 3 2 6 4 9 6 12 8 15 10 :::::::::: Cost of pens Pens £ How much do 30 pens cost? …… 30 20 £20 x 5

7. © T Madas 2 laps in 5 minutes 4 laps in 10 minutes 6 laps in 15 minutes 8 laps in 20 minutes etc 10 laps in 25 minutes 2 5 410 615 820 10 25 :::::::::: What do you notice? Laps in Racing Cars Laps Min

8. © T Madas 2 laps in 5 minutes 4 laps in 10 minutes 6 laps in 15 minutes 8 laps in 20 minutes etc 10 laps in 25 minutes 2 5 410 615 820 10 25 :::::::::: Laps in Racing Cars Laps Min How many minutes does it take to cover 18 laps? …… 18 45 x 9

9. © T Madas 2 laps in 5 minutes 4 laps in 10 minutes 6 laps in 15 minutes 8 laps in 20 minutes etc 10 laps in 25 minutes 2 5 410 615 820 10 25 :::::::::: Laps in Racing Cars Laps Min How many minutes does it take to cover 18 laps? …… 18 45 x 3

10. © T Madas 2 laps in 5 minutes 4 laps in 10 minutes 6 laps in 15 minutes 8 laps in 20 minutes etc 10 laps in 25 minutes 2 5 410 615 820 10 25 :::::::::: Laps in Racing Cars Laps Min How many laps does it cover in 60 minutes? …… 24 60 24 x 6

11. © T Madas 2 laps in 5 minutes 4 laps in 10 minutes 6 laps in 15 minutes 8 laps in 20 minutes etc 10 laps in 25 minutes 2 5 410 615 820 10 25 :::::::::: Laps in Racing Cars Laps Min How many laps does it cover in 60 minutes? …… 24 60 24 x 12

12. © T Madas 2 laps in 5 minutes 4 laps in 10 minutes 6 laps in 15 minutes 8 laps in 20 minutes etc 10 laps in 25 minutes 2 5 410 615 820 10 25 :::::::::: Laps in Racing Cars Laps Min In how many minutes does it cover 5 laps? 12.5 5

13. © T Madas € 7 = £5 € 14 = £10 € 21 = £15 € 28 = £20 etc € 35 = £25 7 5 14 10 21 15 28 20 3525 :::::::::: How many Euros are equal to £100? 140 …… 140 100 € £ Money Conversions x 10

14. © T Madas € 7 = £5 € 14 = £10 € 21 = £15 € 28 = £20 etc € 35 = £25 7 5 14 10 21 15 28 20 3525 :::::::::: How many £ are equal to €56? 40 …… 56 40 € £ Money Conversions x 8

15. © T Madas

16. = 10p 3 :10 6 : 20 9 : 30 12 : 40 15 : 50 What are the next 4 ratios?

17. © T Madas = 10p 3 :10 6 : 20 9 : 30 12 : 40 15 : 50 How much do 30 sweets cost? …… 30 : 100 x 10

18. © T Madas = 40p 3 :40 6 : 80 9 : 120 12 : 160 15 : 200 What are the next 4 ratios?

19. © T Madas = 40p 3 :40 6 : 80 9 : 120 12 : 160 15 : 200 …… 24 : 320 x2x2 x2x2 How much do 24 lollipops cost?

20. © T Madas = £2 3 :2 6 : 4 9 : 6 12 : 8 15 : 10 What are the next 4 ratios?

21. © T Madas = £2 3 :2 6 : 4 9 : 6 12 : 8 15 : 10 How much do 24 boxes cost? …… 24 : 16 x8x8 x8x8

22. © T Madas = £2 3 :2 6 : 4 9 : 6 12 : 8 15 : 10 …… 45 : 30 x3x3 x3x3 How many boxes do I buy with £30?

23. © T Madas = £3 5 :3 10 : 6 15 : 9 20 : 12 25 : 15 What are the next 4 ratios?

24. © T Madas = £3 5 :3 10 : 6 15 : 9 20 : 12 25 : 15 How much do 35 ice creams cost? …… 35 : 21 x7x7 x7x7

25. © T Madas = £3 5 :3 10 : 6 15 : 9 20 : 12 25 : 15 …… 50 : 30 x 10 How many ice creams do I get with £30?

26. © T Madas What are the next 4 ratios? 3 :4 6 : 8 9 : 12 : 16 15 : 20 3 laps in 4 minutes L : M

27. © T Madas 3 :4 6 : 8 9 : 12 12 : 16 15 : 20 3 laps in 4 minutes L : M How long does he take for 24 laps? …… 24 : 32 x8x8 x8x8

28. © T Madas 3 :4 6 : 8 9 : 12 12 : 16 15 : 20 3 laps in 4 minutes L : M How long does he take for 39 laps? …… 39 : 52 x 13

29. © T Madas 3 :4 6 : 8 9 : 12 12 : 16 15 : 20 3 laps in 4 minutes L : M …… 45 : 60 x3x3 x3x3 How many laps does he do in 60 min?

30. © T Madas 3 :4 6 : 8 9 : 12 12 : 16 15 : 20 3 laps in 4 minutes L : M 4.5 6 How many laps does he do in 6 min?

31. © T Madas = 7 :5 € : £ If I change €21, how many £s will I get? …… 21 : x3x3 x3x3 15

32. © T Madas = 7 :5 € : £ If I change £25, how many €s will I get? …… 35 x5x5 x5x5 : 25

33. © T Madas 5 :8 5 laps in 8 minutes L : M How long does it take for 40 laps? …… 40 : x8x8 x8x8 64

34. © T Madas 5 :8 5 laps in 8 minutes L : M How many laps does it cover in 32 min? …… 20 x4x4 x4x4 : 32

35. © T Madas 5 :8 5 laps in 8 minutes L : M How many laps does it cover in 20 min? …… 12.5 x 2.5 : 20

36. © T Madas

38. With every 30 pupil textbooks that are bought, 2 teacher books are supplied. If we order 90 pupil textbooks how many teacher books do we get? If another order contains 9 teacher books how many pupil textbooks should be there? Pupil 30 60 90 120 150 180 Teacher 2 4 6 8 10 12 : : : : : : : 6 teacher books

39. © T Madas With every 30 pupil textbooks that are bought, 2 teacher books are supplied. If we order 90 pupil textbooks how many teacher books do we get? If another order contains 9 teacher books how many pupil textbooks should be there? Pupil 30 60 90 120 150 180 Teacher 2 4 6 8 10 12 :::::::::::::: 6 teacher books 135 textbooks Another Method 30 textbooks 15 textbooks 135 textbooks 2 teacher books 1 teacher book 9 teacher books (9 x 15) a a a

40. © T Madas

41. 3 : 4 1500 Yellow ……… Red 2000 2000 ml of yellow paint are needed To make a certain shade of orange paint we must mix 3 parts red with 4 parts yellow. If we use 1500 ml of red paint how many ml of yellow paint must we use? x 500

42. © T Madas

43. Washing powder is sold in E3 and E10 sizes which are in the ratio of 3 : 10. If the E3 size weighs 1.5 kg how much does the E10 size weigh? 3 : 10 1.5 E10 ……… E3 5 The E10 size weighs 5 kg ÷ 2

44. © T Madas

45. An orange drink is made up of pure orange juice and water. 1000 ml of that drink contains 200 ml of pure orange juice. How much water must we mix with 500 ml of orange juice in order to make this drink? 200 500 Water ……… Orange 2000 2000 ml of water must be mixed x 2.5 drink 1000: 800

46. © T Madas

47. 10 9 8 7 6 5 4 3 2 1 0 A water barrel with a scale next to it is shown below. When 75 litres of water are poured into the barrel, the water level rises from mark 5 to mark 8. 1. How many litres of water were originally in the barrel? 2. What is the total capacity of the water barrel? 3 marks = 1 mark = 5 marks = 10 marks = 75 litres 25 litres 125 litres 250 litres ÷3÷3 x5x5 x2x2

48. © T Madas

49. 30 80 mph B A C The needle of the speedometer of a car turns through 90° when the speed increases from 30 mph to 80 mph. Write down the readings at the points A, B and C. By how many degrees does the needle turn when the speed increases from 20 mph to 60 mph? 0 130 160 50 90° 180° 18° 72° 50 mph = 100 mph = 10 mph = 40 mph = The needle turns by 72° when the speed increases from 20 mph to 60 mph.

50. © T Madas