www mathsrevision com Rate and Proportion Rates and

www. mathsrevision. com Rate and Proportion Rates and Unit Value Finding the Rate Using the Rate Best Buys In Proportion Scales and models Graphs in Proportion Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 1

Starter Questions www. mathsrevision. com S 4 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 2

Rates www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain the term rate and unit value. 1. To understand the term rate and unit value. 2. Solve problems including rate and unit value. Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 3

Rates www. mathsrevision. com S 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 5 km. Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 4

Rates S 4 www. mathsrevision. com Example : Sean walks at 5 km per hour (km/hr) How far would he walk in : (a) 4 hours (a) 4 x 5 = 20 km (b) 5 x 0. 5 = 2. 5 km Thursday, March 15, 2018 (b) Half an hour Created by Mr. Lafferty @www. mathsrevision. com 5

Rates www. mathsrevision. com S 4 Now try Ex 2. 1 Ch 2 (page 21) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 6

Starter Questions www. mathsrevision. com S 4 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 7

Proportion www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain how to find the rate. Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 1. To be able to find the term rate from information given. 8

Finding the Rate www. mathsrevision. com Example : For 5 hours’ work Darius is paid £ 30. Calculate his rate of pay per hour. Answer : 5 hours £ 30 1 hour Thursday, March 15, 2018 £ 30 ÷ 5 = £ 6 Created by Mr. Lafferty @www. mathsrevision. com 9

Finding the Rate www. mathsrevision. com 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 Thursday, March 15, 2018 36 ÷ 3 = Created by Mr. Lafferty @www. mathsrevision. com 12 m 2 10

Finding the Rate www. mathsrevision. com Example : I get paid £ 48 000 pounds a year. What is my monthly rate of pay. Answer : 12 months £ 48 000 1 month £ 48 000 ÷ 12 = £ 4 000 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 11

www. mathsrevision. com Finding the Rate Now try Ex 3. 1 Ch 2 (page 22) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 12

Starter Questions www. mathsrevision. com S 4 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 13

Using the Rate www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain how to use the rate to solve problems. Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 1. To be able to find the term rate from information given. 14

Using the Rate www. mathsrevision. com 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) 15 ÷ 5 = 1 secs 3 litres 8 secs Thursday, March 15, 2018 15 litres 1 secs Answer : (b) 5 secs 8 x 3= Created by Mr. Lafferty @www. mathsrevision. com 3 litres 24 litres 15

Using the Rate www. mathsrevision. com 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 1 secs Answer : (b) 20 ÷ 10 = 2 words 1 secs 2 words 14 secs 14 x 2 = Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 28 words 16

Using the Rate www. mathsrevision. com 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) 200 ÷ 5 = £ 40 1 day £ 40 8 days Thursday, March 15, 2018 £ 200 1 day Answer : (b) 5 days 40 x 8 = Created by Mr. Lafferty @www. mathsrevision. com £ 320 17

www. mathsrevision. com Using the Rate Now try Ex 4. 1 Ch 2 (page 23) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 18

Starter Questions www. mathsrevision. com S 4 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 19

Using the Rate www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To work out harder type rate problems. Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 1. To be able to work out t harder type rate problems. 20

Using the Rate www. mathsrevision. com Example : Nicola exchanges £ 10 into Euros. She receives 16 Euros. How many Euros will she get for £ 200. Answer : £ 10 € 16 £ 1 16 ÷ 10 = € 1. 60 £ 200 Thursday, March 15, 2018 200 x 1. 60 = € 320 Created by Mr. Lafferty @www. mathsrevision. com 21

Using the Rate www. mathsrevision. com Example : Joseph’s library book is 4 days overdue. He pays a fine for each day. In total he pays 28 p. Alana’s book is 5 days overdue how much did she have to pay. Answer : 28 p 1 day 28 ÷ 4 = 7 p 5 days Thursday, March 15, 2018 4 days 5 x 7 = 35 p Created by Mr. Lafferty @www. mathsrevision. com 22

www. mathsrevision. com Using the Rate Now try Ex 4. 2 Ch 2 (page 24) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 23

Starter Questions www. mathsrevision. com S 4 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 24

Best Buys www. mathsrevision. com S 4 Learning Intention Success Criteria 1. Calculating the Best Buys for household goods. 1. To be able to find the price t of one product. 2. Decide which is the best buy. Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 25

2 for 1 Best Buys www. mathsrevision. com S 4 50% We often see lots of special offers at various off supermarkets. Example : Which is the better buy? 2 light bulbs for 90 p or 5 light bulbs for £ 2. 00 Answer : (i) (ii) 1 bulb 90 ÷ 2 = 45 p 2. 00 ÷ 5 = 40 p or £ 0. 40 Best buy is 5 bulbs at 40 p Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 26

Best Buys S 4 www. mathsrevision. com Example : Which is the better buy? 5 balloons for £ 1. 20 or 6 balloons for £ 1. 50 Answer : (i) (ii) 1 balloon 1. 20 ÷ 5 = 24 p or £ 0. 24 1. 50 ÷ 6 = 25 p or £ 0. 25 Best buy is 5 balloons at 24 p Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 27

Using the Rate www. mathsrevision. com S 4 Now try Ex 5. 1 Ch 2 (page 26) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 28

Starter Questions www. mathsrevision. com S 4 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 29

Best Buys Harder example S 4 www. mathsrevision. com 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) (ii) Box A £ 2. 88 ÷ 160 = 1. 8 p per bag Box B £ 3. 84 ÷ 240 = 1. 6 p per bag Best buy is Box B since it costs only 1. 6 p per bag Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 30

Using the Rate www. mathsrevision. com S 4 Now try Ex 5. 1 Ch 2 (page 25) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 31

Starter Questions www. mathsrevision. com S 4 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 32

In Proportion www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To be able to identify simple connections between two quantities. Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 1. Understand the term proportion. 2. Solve problems using proportion. 33

In Proportion www. mathsrevision. com S 4 If two quantities are in proportion there is a connection between them. Example : Jake mixes sand cement to make a patio. He uses 1 part sand 3 parts cement. This means for every shovel of sand he must use 3 shovels of cement OR For every 1 kg of sand he must use 3 kg of cement. How much cement for 5 kg of sand : Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 5 x 3 = 15 kg 34

In Proportion S 4 www. mathsrevision. com Example : To make a healthy fruit drink Darius uses 4 parts apple and 1 part water. Complete the table Part Water 1 2 Part Apple 4 8 12 3 4 10 Thursday, March 15, 2018 16 40 Created by Mr. Lafferty @www. mathsrevision. com 35

In Proportion www. mathsrevision. com S 4 Now try Ex 6. 1 Ch 2 (page 29) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 36

How much ingredients S 4 for 2 portions In Proportion Example : www. mathsrevision. com Half the ingredients Flour 110 g Sugar 75 g Harder Example Butter Almond 40 g Scott makes an almond mobile cake which makes 4 portions. The ingredients are: Complete the table Makes 4 Portions How much Flour 220 g Multiply 2 portions ingredients by 3 for 6 portions Sugar 150 g Flour 330 g Butter Almond 80 g Sugar 225 g Butter Almond 120 g Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 37

In Proportion www. mathsrevision. com S 4 Now try Ex 6. 2 Ch 2 (page 30) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 38

www. mathsrevision. com Starter Questions 15 -Mar-18 Created by Mr. Lafferty Maths Dept.

Scales and Models www. mathsrevision. com S 4 Learning Intention 1. 15 -Mar-18 To understand the term scale and how they are used in real life. Success Criteria 1. To be able to understand the term scales. 2. Interpret scales into reallife measurements. Created by Mr. Lafferty Maths Dept.

Scales and Models www. mathsrevision. com S 4 Definition A scale of 1 cm = 2 m This simply means for every 1 cm measured on a drawing this represents 2 m in real-life. 15 -Mar-18 Created by Mr. Lafferty Maths Dept.

Scales and Models www. mathsrevision. com S 4 4 x 25= 100 cm 4 cm 2 x 25 = 50 cm The scale of this drawing is 1 cm = 25 cm What is the actual length and breadth of the TV ? 15 -Mar-18 Created by Mr. Lafferty Maths Dept.

Scales and Models www. mathsrevision. com S 4 12 cm 12 x 50 = 600 cm = 6 m Living room 8 cm 8 x 50 = 400 cm =4 m The scale of this drawing living room is 1 cm = 50 cm What is the actual length and breadth of the room ? 15 -Mar-18 Created by Mr. Lafferty Maths Dept.

Scales and Models www. mathsrevision. com S 4 Now try Ex 7. 1 Ch 2 (page 31) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 44

Starter Questions www. mathsrevision. com S 4 15 -Mar-18 Created by Mr. Lafferty Maths Dept.

Scales and Models www. mathsrevision. com S 4 Learning Intention 1. 15 -Mar-18 To explain how to calculate the scale of a model. Success Criteria 1. To be able to calculate the scale of a model. Created by Mr. Lafferty Maths Dept.

Scales and Models www. mathsrevision. com S 4 Example : Answer : A model bicycle is 30 cm long. The real length of the bicycle is 150 cm. What is the scale of the model. 150 ÷ 30 = 5 Scale is 1 to 5 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 47

Scales and Models www. mathsrevision. com S 4 Example : A model car is 10 cm long. The real length of the car is 300 cm. What is the scale of the model. Answer : 300 ÷ 10 = 30 Scale is 1 to 30 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 48

Scales and Models www. mathsrevision. com S 4 Now try Ex 7. 2 Ch 2 (page 32) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 49

Starter Questions www. mathsrevision. com S 4 15 -Mar-18 Created by Mr. Lafferty Maths Dept.

Proportion graphs www. mathsrevision. com S 4 Learning Intention 1. 15 -Mar-18 To explain the main features of a proportion graph and used it to solve problems. Success Criteria 1. To be able to identify a proportion graph. 2. Use graph to solve problems. Created by Mr. Lafferty Maths Dept.

How much How far can I petrol do I travel with 6 need to travel litres of petrol is always a straight line graph through the origin A proportion graph 80 km. Proportion graphs S 4 120 km 1 minute to come up with a question 4 litres Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 52

Proportion graphs How Euros How many for £ 80 S 4 Pounds for 25 € 100 € £ 20 Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 53

Proportion graphs www. mathsrevision. com S 4 Now try Ex 8. 1 Ch 2 (page 34) Thursday, March 15, 2018 Created by Mr. Lafferty @www. mathsrevision. com 54