S4_Foundation_Proportion_MIA

S4_Foundation_Proportion_MIA - Rate and Proportion Rates...

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Unformatted text preview: Rate and Proportion Rates and Unit Value www.mathsrevision.com Finding the Rate Using the Rate Best Buys In Proportion Scales and models Graphs in Proportion Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 1 Starter Questions S4 1. Find 5% of 140 www.mathsrevision.com 2. Round to 1 decimal place (a) 1.24 (b) 2.35 3. I work 20 hours a week and my rate of pay is 8 per hour. What is my total weekly pay. 1 4. of 72 8 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 2 Rates S4 Learning Intention Success Criteria 1. To understand the term rate and unit value. 2. Solve problems including rate and unit value. www.mathsrevision.com 1. To explain the term rate and unit value. Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 3 Rates S4 www.mathsrevision.com 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. Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 4 Rates S4 Example : Sean walks at 5 km per hour (km/hr) www.mathsrevision.com How far would he walk in : (a) 4 hours (b) Half an hour (a) (b) 4 x 5 = 20km 5 x 0.5 = 2.5 km Created by Mr. Lafferty @www.mathsrevision.com Monday, February 13, 2012 5 Rates S4 www.mathsrevision.com Now try Ex 2.1 Ch 2 (page 21) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 6 Starter Questions S4 1. Find 5% of 360 www.mathsrevision.com 2. Round to 1 decimal place (a) 17.55 (b) 0.85 3. I work 40 hours a week and my rate of pay is 9 per hour. What is my total weekly pay. 1 4. of 246 6 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 7 Proportion S4 Learning Intention Success Criteria 1. To be able to find the term rate from information given. www.mathsrevision.com 1. To explain how to find the rate. Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 8 Finding the Rate Example : For 5 hours' work Darius is paid 30. Calculate his rate of pay per hour. www.mathsrevision.com Answer : 5 hours 1 hour 30 30 5 = 6 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 9 Finding the Rate Example : 3 litres of paint covers a fence area of 36 m2 How much will 1 litre cover. www.mathsrevision.com Answer : 3 litres 1 litre 36 36 3 = 12m2 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 10 Finding the Rate Example : I get paid 48 000 pounds a year. What is my monthly rate of pay. www.mathsrevision.com Answer : 12 months 1 month 48 000 48 000 12 = 4 000 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 11 Finding the Rate www.mathsrevision.com Now try Ex 3.1 Ch 2 (page 22) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 12 Starter Questions S4 1. Find 20% of 650 www.mathsrevision.com 2. Round to 1 decimal place (a) 172.66 (b) 2.78 3. I got paid 364 for 7 days work. What is my daily rate of pay. 1 4. of 210 7 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 13 Using the Rate S4 Learning Intention Success Criteria 1. To be able to find the term rate from information given. www.mathsrevision.com 1. To explain how to use the rate to solve problems. Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 14 Using the Rate Example : A pipeline delivers 15 litres of water in 5 secs. www.mathsrevision.com (a) (b) Answer : (a) Calculate the rate of flow per second. How many litres will the pipeline deliver in 8 secs 5 secs 1 secs 15 litres 15 5 = 3 litres 8 x 3 = 24 litres 15 3 litres Answer : (b) Monday, February 13, 2012 1 secs 8 secs Created by Mr. Lafferty @www.mathsrevision.com Using the Rate Example : A pupil can type 20 words in 10 seconds. www.mathsrevision.com (a) (b) Answer : (a) Calculate how many words typed per second. How many words typed in 14 seconds. 10 secs 1 secs 20 words 20 10 = 2 words 14 x 2 = 28 words 16 2 words Answer : (b) Monday, February 13, 2012 1 secs 14 secs Created by Mr. Lafferty @www.mathsrevision.com Using the Rate Example : To hire a car for 5 days costs 200. www.mathsrevision.com (a) (b) Answer : (a) Calculate the cost to hire for 1 day. Calculate the cost for 8 days. 5 days 1 day 200 200 5 = 40 40 x 8 = 320 17 40 Answer : (b) Monday, February 13, 2012 1 day 8 days Created by Mr. Lafferty @www.mathsrevision.com Using the Rate www.mathsrevision.com Now try Ex 4.1 Ch 2 (page 23) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 18 Starter Questions S4 1. Find 25% of 640 www.mathsrevision.com 2. Round to 1 decimal place (a) 163.82 (b) 72.38 3. I got paid 54 for 9 hours work. What is my hourly rate of pay. 1 4. of 450 9 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 19 Using the Rate S4 Learning Intention Success Criteria 1. To be able to work out harder type rate To be able t problems. www.mathsrevision.com 1. To work out harder type rate problems. Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 20 Using the Rate Example : Nicola exchanges 10 into Euros. She receives 16 Euros. www.mathsrevision.com How many Euros will she get for 200. Answer : 10 1 200 Monday, February 13, 2012 16 16 10 = 200 x 1.60 = 1.60 320 21 Created by Mr. Lafferty @www.mathsrevision.com 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 : 4 days 28p 1 day 28 4 = 7p 5 days 5 x 7 = 35p Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com 22 Using the Rate www.mathsrevision.com Now try Ex 4.2 Ch 2 (page 24) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 23 Starter Questions S4 1. Find 7 5 % o f 18 0 www.mathsrevision.com 2 . I f 3 pint s o f m ilk c o s t 9 . Ho w m uc h f o r 2 pint s . 3 . I g o t paid 6 3 f o r 7 h o ur s wo r k . W h at is m y h o ur ly r at e o f pay . 4 . 1 o f 2 8 0 7 Created by Mr. Lafferty @www.mathsrevision.com 24 Monday, February 13, 2012 Best Buys S4 Learning Intention Success Criteria 1. To be able to find the price of one To be able t product. 2. Decide which is the best buy. www.mathsrevision.com 1. Calculating the Best Buys for household goods. Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 25 2 for 1 Best Buys S4 We often see lots of special offers at various supermarkets. Example : Which is the better buy? 50% off www.mathsrevision.com 2 light bulbs for 90p or 5 light bulbs for 2.00 Answer : (i) (ii) 1 bulb 1 bulb 90 2 = 45p 2.00 5 = 40p or 0.40 Best buy is 5 bulbs at 40p Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 26 Best Buys S4 Example : Which is the better buy? www.mathsrevision.com 5 balloons for 1.20 or 6 balloons for 1.50 Answer : (i) (ii) 1 balloon 1.20 5 = 24p or 0.24 25p or 0.25 1 balloon 1.50 6 = Best buy is 5 balloons at 24p Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 27 Using the Rate S4 www.mathsrevision.com Now try Ex 5.1 Ch 2 (page 26) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 28 Starter Questions S4 1. Find 4 0 % o f 2 0 0 2 . I f 3 pint s o f m ilk c o s t 1.2 0 . Ho w m uc h f o r 2 pint s . 3 . I g e t paid 5 .5 0 an h o ur . Ho w will i g e t paid f o r 10 h o ur s wo r k . 1 4 . o f 3 6 0 8 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 29 www.mathsrevision.com Best Buys S4 Harder example Example : Which is the better buy? www.mathsrevision.com 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 Box B 2.88 160 = 1.8p per bag 3.84 240 = 1.6p per bag Best buy is Box B since it costs only 1.6p per bag Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 30 Using the Rate S4 www.mathsrevision.com Now try Ex 5.1 Ch 2 (page 25) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 31 Starter Questions S4 1. Find 5 0 % o f 9 5 2 . f ind t h e t im e d if f e r e nc e b e t we e n 0 8 .3 0 and 16 .3 9 3 . W h at is t h e b e t t e r d e al 3 b ar s o f s o ap f o r 9 9 p o r 4 b ar s o f 1.4 0 4 . Monday, February 13, 2012 www.mathsrevision.com 1 o f 2 4 0 5 Created by Mr. Lafferty @www.mathsrevision.com 32 In Proportion S4 Learning Intention Success Criteria 1. Understand the term proportion. 2. Solve problems using proportion. www.mathsrevision.com 1. To be able to identify simple connections between two quantities. Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 33 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 For every 1kg of sand he must use 3 kg of cement. How much cement for 5kg of sand : Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com OR 5 x 3 = 15 kg 34 In Proportion S4 Example : To make a healthy fruit drink Darius uses 4 parts apple and 1 part water. Complete the table Part Apple 4 8 12 16 40 Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com Part Water 1 2 3 4 10 Monday, February 13, 2012 35 In Proportion S4 www.mathsrevision.com Now try Ex 6.1 Ch 2 (page 29) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 36 S4 How much ingredients for 2 portions In Proportion Example : Half the ingredients Flour 110g Sugar 75g Harder Example Butter Almond 40g Scott makes an almond mobile cake which makes 4 portions. The ingredients are: www.mathsrevision.com Complete the table Makes 4 Portions 220g Multiply 2 portions by 3 150g Flour 330g Sugar 225g 80g Butter Almond 120g Created by Mr. Lafferty @www.mathsrevision.com How much Flour ingredients for 6 portions Sugar Butter Almond Monday, February 13, 2012 37 In Proportion S4 www.mathsrevision.com Now try Ex 6.2 Ch 2 (page 30) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 38 Starter Questions 1. 99. 6 + 7. 27 www.mathsrevision.com 2 . C a lc ula t e 7 0 % o f 8 4 3. 4. 25% of 160p Round t o 1 decimal place (a) 2. 67 13 Feb 2012 (b) 3. 23 Created by Mr. Lafferty Maths Dept. (c) 2. 9 1 Scales and Models S4 Learning Intention Success Criteria 1. To be able to understand the term scales. 2. Interpret scales into reallife measurements. www.mathsrevision.com 1. To understand the term scale and how they are used in real life. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Scales and Models S4 www.mathsrevision.com Definition A scale of This simply means for every 1cm measured on a drawing this represents 2m in reallife. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 1 cm = 2m Scales and Models S4 4cm www.mathsrevision.com 4x25= 100cm 2cm 2x25 = 50cm The scale of this drawing is 1cm = 25cm What is the actual length and breadth of the TV ? 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Scales and Models S4 12cm www.mathsrevision.com 12x50 = 600cm = 6m Living room 8cm 8x50 = 400cm =4m The scale of this drawing living room is 1cm = 50cm What is the actual length and breadth of the room ? 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Scales and Models S4 www.mathsrevision.com Now try Ex 7.1 Ch 2 (page 31) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 44 Starter Questions S4 1. 13. 6 + 7. 9 www.mathsrevision.com 2 . C a lc ula t e 2 0 % o f 6 4 3. W hat is t he best buy 3 cans of beans f or 57p or 4 cans 72p Explain your answer . 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Scales and Models S4 Learning Intention Success Criteria 1. To be able to calculate the scale of a model. www.mathsrevision.com 1. To explain how to calculate the scale of a model. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Scales and Models S4 Example : www.mathsrevision.com A model bicycle is 30cm long. The real length of the bicycle is 150cm. What is the scale of the model. Answer : 150 30 = 5 Scale is 1 to 5 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 47 Scales and Models S4 Example : www.mathsrevision.com A model car is 10cm long. The real length of the car is 300cm. What is the scale of the model. Answer : 300 10 = 30 Scale is 1 to 30 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 48 Scales and Models S4 www.mathsrevision.com Now try Ex 7.2 Ch 2 (page 32) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 49 Starter Questions S4 1. 18. 7 + 12. 9 www.mathsrevision.com 2 . C a lc ula t e 3 0 % o f 4 0 3. W hat is t he best buy 5 bot t les of wat er f or 3. 50 or 4 cans 2. 88 Explain your answer . 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Proportion graphs S4 Learning Intention Success Criteria 1. To be able to identify a proportion graph. 2. Use graph to solve problems. www.mathsrevision.com 1. To explain the main features of a proportion graph and used it to solve problems. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. S4 How much petrol do How far can I travel I need to travel 80 with 6 litres of petrol km. A proportion graph is always a straight line graph through the origin Proportion graphs 200 180 160 140 120 100 80 60 40 20 0 0 1 2 3 4 5 6 7 8 120km 1 minute to come up with a question 4 litres 9 10 ) m K ( e c n a t s i D Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com Pe t r o l Lit r e s 52 S4 How Euros for How many Pounds 80 for 25 140 120 100 Proportion graphs 80 60 40 20 0 0 s o r u E 100 20 20 40 60 80 100 Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com Po und s 53 Proportion graphs S4 www.mathsrevision.com Now try Ex 8.1 Ch 2 (page 34) Monday, February 13, 2012 Created by Mr. Lafferty @www.mathsrevision.com 54 ...
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