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Rate and Proportion

Rate and Proportion. Rates and Unit Value. Finding the Rate. Using the Rate. Best Buys. www.mathsrevision.com. In Proportion. Scales and models. Graphs in Proportion. S4. Starter Questions. www.mathsrevision.com. S4. Rates. Learning Intention. Success Criteria.

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Rate and Proportion

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  1. Rate and Proportion Rates and Unit Value Finding the Rate Using the Rate Best Buys www.mathsrevision.com In Proportion Scales and models Graphs in Proportion Created by Mr. Lafferty @www.mathsrevision.com

  2. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  3. S4 Rates Learning Intention Success Criteria • To understand the term rate and unit value. • 2. Solve problems including rate and unit value. • To explain the term rate and unit value. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  4. Rates S4 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) www.mathsrevision.com This means that if Sean walked at this speed for one hour he would travel 5km. Created by Mr. Lafferty @www.mathsrevision.com

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

  6. Rates S4 Now try Ex 2.1 Ch 2 (page 21) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  7. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  8. Proportion S4 Learning Intention Success Criteria • To be able to find the term rate from information given. • To explain how to find the rate. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  9. Finding the Rate Example : For 5 hours’ work Darius is paid £30. Calculate his rate of pay per hour. Answer : 5 hours  £30 www.mathsrevision.com 1 hour  £30 ÷ 5 = £6 Created by Mr. Lafferty @www.mathsrevision.com

  10. Finding the Rate Example : 3 litres of paint covers a fence area of 36 m2 How much will 1 litre cover. Answer : 3 litres  36 www.mathsrevision.com 1 litre  36 ÷ 3 = 12m2 Created by Mr. Lafferty @www.mathsrevision.com

  11. Finding the Rate Example : I get paid £48 000 pounds a year. What is my monthly rate of pay. Answer : 12 months  £48 000 www.mathsrevision.com 1 month  £48 000 ÷ 12 = £4 000 Created by Mr. Lafferty @www.mathsrevision.com

  12. Finding the Rate Now try Ex 3.1 Ch 2 (page 22) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  13. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  14. Using the Rate S4 Learning Intention Success Criteria • To be able to find the term rate from information given. • To explain how to use the rate to solve problems. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  15. Using the Rate Example : A pipeline delivers 15 litres of water in 5 secs. (a) Calculate the rate of flow per second. (b) How many litres will the pipeline deliver in 8 secs Answer : (a) 5 secs  15 litres www.mathsrevision.com 1 secs  15 ÷ 5 = 3 litres Answer : (b) 1 secs  3 litres 8 secs  8 x 3 = 24 litres Created by Mr. Lafferty @www.mathsrevision.com

  16. Using the Rate Example : A pupil can type 20 words in 10 seconds. (a) Calculate how many words typed per second. (b) How many words typed in 14 seconds. Answer : (a) 10 secs  20 words www.mathsrevision.com 1 secs  20 ÷ 10 = 2 words Answer : (b) 1 secs  2 words 14 secs  14 x 2 = 28 words Created by Mr. Lafferty @www.mathsrevision.com

  17. Using the Rate Example : To hire a car for 5 days costs £200. (a) Calculate the cost to hire for 1 day. (b) Calculate the cost for 8 days. Answer : (a) 5 days  £200 www.mathsrevision.com 1 day  200 ÷ 5 = £40 Answer : (b) 1 day  £40 8 days  40 x 8 = £320 Created by Mr. Lafferty @www.mathsrevision.com

  18. Using the Rate Now try Ex 4.1 Ch 2 (page 23) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  19. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  20. Using the Rate S4 Learning Intention Success Criteria • To be able to work out harder type rate problems. • To work out harder type rate problems. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  21. Using the Rate Example : Nicola exchanges £10 into Euros. She receives 16 Euros. How many Euros will she get for £200. Answer : £10  € 16 www.mathsrevision.com £1  16 ÷ 10 = € 1.60 £200  200 x 1.60 = € 320 Created by Mr. Lafferty @www.mathsrevision.com

  22. Using the Rate Example : Joseph’s library book is 4 days overdue. He pays a fine for each day. In total he pays 28p. Alana’s book is 5 days overdue how much did she have to pay. Answer : www.mathsrevision.com 4 days  28p 1 day  28 ÷ 4 = 7p 5 days  5 x 7 = 35p Created by Mr. Lafferty @www.mathsrevision.com

  23. Using the Rate Now try Ex 4.2 Ch 2 (page 24) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  24. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  25. Best Buys S4 Learning Intention Success Criteria • To be able to find the price of one product. • Calculating the Best Buys for household goods. • 2. Decide which is the best buy. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  26. 50% off 2 for 1 Best Buys S4 We often see lots of special offers at various supermarkets. Example : Which is the better buy? 2 light bulbs for 90p or 5 light bulbs for £2.00 www.mathsrevision.com Answer : (i) 1 bulb  90 ÷ 2 = 45p (ii) 40p or £0.40 1 bulb  2.00 ÷ 5 = Best buy is 5 bulbs at 40p Created by Mr. Lafferty @www.mathsrevision.com

  27. Best Buys S4 Example : Which is the better buy? 5 balloons for £1.20 or 6 balloons for £1.50 Answer : (i) 1 balloon  1.20 ÷ 5 = 24p or £0.24 (ii) 25p or £0.25 1 balloon  1.50 ÷ 6 = www.mathsrevision.com Best buy is 5 balloons at 24p Created by Mr. Lafferty @www.mathsrevision.com

  28. Using the Rate S4 Now try Ex 5.1 Ch 2 (page 26) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  29. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  30. Best Buys Harder example S4 Example : Which is the better buy? Tea box A costs £2.88 and holds 160 tea bags. Tea box B costs £3.84 and holds 240 tea bags. Answer : (i) Box A  £2.88 ÷ 160 = 1.8p per bag www.mathsrevision.com (ii) 1.6p per bag Box B  £3.84 ÷ 240 = Best buy is Box B since it costs only 1.6p per bag Created by Mr. Lafferty @www.mathsrevision.com

  31. Using the Rate S4 Now try Ex 5.1 Ch 2 (page 25) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  32. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  33. In Proportion S4 Learning Intention Success Criteria • Understand the term proportion. • To be able to identify simple connections between two quantities. • 2. Solve problems using proportion. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  34. In Proportion S4 If two quantities are in proportion then there is a connection between them. Example : Jake mixes sand and cement to make a patio. He uses 1 part sand and 3 parts cement. This means for every shovel of sand he must use 3 shovels of cement www.mathsrevision.com OR For every 1kg of sand he must use 3 kg of cement. How much cement for 5kg of sand : 5 x 3 = 15 kg Created by Mr. Lafferty @www.mathsrevision.com

  35. In Proportion S4 Example : To make a healthy fruit drink Darius uses 4 parts apple and 1 part water. Complete the table www.mathsrevision.com 8 3 16 40 Created by Mr. Lafferty @www.mathsrevision.com

  36. In Proportion S4 Now try Ex 6.1 Ch 2 (page 29) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  37. How much ingredients for 2 portions Half the ingredients Flour 110g Sugar 75g Butter Almond 40g In Proportion Harder Example S4 Example : Scott makes an almond mobile cake which makes 4 portions. The ingredients are: Complete the table How much ingredients for 6 portions Multiply 2 portions by 3 Flour 330g Sugar 225g Butter Almond 120g www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  38. In Proportion S4 Now try Ex 6.2 Ch 2 (page 30) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  39. Starter Questions Created by Mr. Lafferty Maths Dept.

  40. Scales and Models S4 Learning Intention Success Criteria • To be able to understand the term scales. • 1. To understand the term scale and how they are used in real life. 2. Interpret scales into real-life measurements. Created by Mr. Lafferty Maths Dept.

  41. Scales and Models S4 Definition A scale of 1 cm = 2m www.mathsrevision.com This simply means for every 1cm measured on a drawing this represents 2m in real-life. Created by Mr. Lafferty Maths Dept.

  42. Scales and Models S4 4x25= 100cm 4cm 2cm www.mathsrevision.com 2x25 = 50cm The scale of this drawing is 1cm = 25cm What is the actual length and breadth of the TV ? Created by Mr. Lafferty Maths Dept.

  43. Scales and Models S4 12x50 = 600cm = 6m 12cm Living room 8cm 8x50 = 400cm =4m www.mathsrevision.com The scale of this drawing living room is 1cm = 50cm What is the actual length and breadth of the room ? Created by Mr. Lafferty Maths Dept.

  44. Scales and Models S4 Now try Ex 7.1 Ch 2 (page 31) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  45. S4 Starter Questions Created by Mr. Lafferty Maths Dept.

  46. Scales and Models S4 Learning Intention Success Criteria • To be able to calculate the scale of a model. • 1. To explain how to calculate the scale of a model. Created by Mr. Lafferty Maths Dept.

  47. Scales and Models S4 Example : A model bicycle is 30cm long. The real length of the bicycle is 150cm. What is the scale of the model. Answer : www.mathsrevision.com 150 ÷ 30 = 5 Scale is 1 to 5 Created by Mr. Lafferty @www.mathsrevision.com

  48. Scales and Models S4 Example : A model car is 10cm long. The real length of the car is 300cm. What is the scale of the model. Answer : www.mathsrevision.com 300 ÷ 10 = 30 Scale is 1 to 30 Created by Mr. Lafferty @www.mathsrevision.com

  49. Scales and Models S4 Now try Ex 7.2 Ch 2 (page 32) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  50. S4 Starter Questions Created by Mr. Lafferty Maths Dept.

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