Grow your brain N4 Numeracy Book 5 The wee Maths Book of Big Brain Growth Guaranteed to make your brain grow, just add some effort and hard work Don t be afraid if you don t know how to do it, yet! It s not how fast you finish, but that you finish. It s always better to try something than to try nothing. Don t be worried about getting it wrong, getting it wrong is just part of the process known better as learning. Numeracy 1.3, 1.4 and 1.5
K Recording measurements using a straightforward scale on an instrument K1 I have revised reading scales to the nearest graduation. 1. What numbers are located at positions a) to i) on theses number lines? 2. On squared paper (your jotter) draw a line to indicate the following Page 2 (i) Minimum of 0, maximum of 1000, Grid step 50, Numbered step 100. (ii) Minimum of 0, maximum of 100, Grid step 5, Numbered step 20. (iii) Minimum of 0, maximum of 100, Grid step 5, Numbered step 10.
3. (i) Minimum of 0, maximum of 50, Grid step 2, Numbered step 10. (ii) Minimum of 0, maximum of 100, Grid step 4, Numbered step 20. (iii) Minimum of 0, maximum of 10, Grid step 0 5, Numbered step 2. 4. On squared paper (your jotter) draw a line to indicate the following (i) Minimum of 400, maximum of 1200, Grid step 50, Numbered step 100. (ii) Minimum of 40, maximum of 160, Grid step 5, Numbered step 20. (iii) Minimum of 20, maximum of 120, Grid step 5, Numbered step 10. 5. (i) Minimum of 40, maximum of 120, Grid step 2, Numbered step 10. (ii) Minimum of 60, maximum of 140, Grid step 4, Numbered step 20. (iii) Minimum of 12, maximum of 24, Grid step 0 5, Numbered step 2. 6. Jack made some mistakes in his number line (a) Copy the line and re-number it the way you think it should be? (b) What advice could you give Jack for the next time he draws a number line? Page 3
7. You will learn about measuring mass in Science. Write down the mass shown on each scale (a) (b) (c) (d) 8. Write down the weight indicated on each of these scales: (a) 2k 0 2kg (c) 1kg 3k 0 1kg 0 3kg 0 4k (b) (d) 0 0 4kg Page 4
9. Write down the volumes (in ml) indicated on these measuring jugs: (a) (b) (c) 200 160 250 200 100 80 120 80 40 150 100 50 60 40 20 10. (a) What speed is shown on this speedometer? (b) How long will a train take to travel 175 kilometres at this speed? Give your answer in hours and minutes. Page 5
11. The scale below shows speed in miles per hour and kilometres per hour. speed in miles per speed in kilometres per Use the information given to change each of the following. (a) 80 miles per hour into kilometres per hour. (b) 140 miles per hour into kilometres per hour. (c) 25 miles per hour into kilometres per hour. (d) 95 miles per hour into kilometres per hour. 12. The shaded part of the scale below shows the amount of oil, in gallons, in an oil tank. 0 20 40 60 80 empty full How many gallons are in the tank? Page 6
K2 I can use a ruler and a protractor to measure and draw accurate lines and angles 13. Using a ruler, find the perimeter of each of these shapes in centimetres. (a) (b) 14. Using a ruler, find the perimeter of each of these shapes in millimetres. (a) (b) Page 7
15. Use a protractor to measure the angles below. (a) (b) (c) (d) 16. Draw angles which are of the following sizes: (a) 43º (b) 127º (c) 53º (d) 151º Page 8
17. Below are four sketches of angles. Make and accurate drawing of each of the sketches. 18. The sketch below shows the dimensions of a mobile phone s screen. Make an accurate drawing of the phone s outline. Page 9
19. For each diagram below, measure both of the angles which make up each straight angle and show that they add up to 180. (a) (b) 8. For each diagram below, measure all the angles around the point and show that they add up to 360. (a) (b) * Page 10
20. In Technical, Cara uses two types of set-square to make her drawings. The first type has angles of 90, 45 and 45. Which of the triangles below could be used as this type of set square. Each of your answers must include measurements of three angles which add up to 180 and a conclusion. (a) (b) (c) (d) Page 11
21. The second type has angles of 90, 30 and 60. Which of the triangles below could be used as this type of set square. Each of your answers must include measurements of three angles which add up to 180 and a conclusion. (a) (b) (c) (d) Page 12
K3 In the context of measure, I have revised and understood that digits after the decimal point represent tenths and hundredths respectively. 22. What numbers are located at a) to h) on these number lines 23. On squared paper (your jotter) draw a line to indicate the following (i) Minimum of 0, maximum of 1, Grid step 0 1, Numbered step 0 2. (ii) Minimum of 0, maximum of 5, Grid step 0 25, Numbered step 0 1. (iii) Minimum of 0, maximum of 1, Grid step 0 02, Numbered step 0 1. Page 13
24. On squared paper (your jotter) draw a line to indicate the following (i) Minimum of 0, maximum of 2, Grid step 0 2, Numbered step 0 5. (ii) Minimum of 0, maximum of 0 5, Grid step 0 05, Numbered step 0 1. (iii) Minimum of 0, maximum of 0 2, Grid step 0 01, Numbered step 0 05. 25. (a) Draw the following number line Minimum of 0, maximum of 1, Grid step 0 05, Numbered step 0 2. (b) On your number line, indicate with an arrow the following (i) 0 3 (ii) 0.7 (iii) 0 24 (iv) 0 68 (v) 0 91 (vi) 0 42 26. (a) Draw the following number line Minimum of 0, maximum of 0 5, Grid step 0 02, Numbered step 0 1. (b) On your number line, indicate with an arrow the following (i) 0 15 (ii) 0.45 (iii) 0 31 (iv) 0 42 (v) 0 38 (vi) 0 07 (c) Calculate 0 38 + 0 02 and show the addition as a step on your number line. (d) Calculate 0 42 0 02 and show the subtraction as a step on your number line. Page 14
27. The rulers below are calibrated in tenths of a centimetres. Write down, to the nearest tenth of a centimetre, the measurements indicated by the arrows. (a) (b) (c) (d) (e) (f) (g) (h) (i) 28. The three stopwatches below measure time intervals to the nearest hundredth of a second. (a) For each stopwatch write down the digit that indicates tenths of a second. (b) Now write down the digit that indicates hundredths of a second. (i) (ii) (iii) Page 15
Cara measures length (or distance) regularly in four of her subjects. In technical she uses a steel rule to measure lengths in millimetres. In Home Economics she uses a measuring tape to measure fabric in centimetres. In Physical Education she uses a large measuring tape to measure distances in metres. In Mathematics she uses a plastic ruler to measure in millimetres or centimetres. 29. For each diagram, read off the measurements and say which subject it is most likely to be in. (a) 7m 10 20 30 40 50 60 70 80 90 8m 10 20 30 40 50 60 70 80 90 9m 10 20 (b) (c) (d) Page 16
30. For each diagram, read off the measurements to the most appropriate units and say which subject it is most likely to be in. (a) (b) (c) (d) 2m 10 20 30 40 50 60 70 80 90 3m 10 20 30 40 50 60 70 80 90 4m 10 20 Page 17
L Interpreting measurements to make decisions L1 I can interpret measurements to the nearest graduation allowing me to make a decision. 1. Some water will be added to the measuring jars below to fill them to the top graduation. How much water is needed to fill each jar to the top graduation? (a) (b) (c) 150ml 75ml 300ml 100ml 50ml 200ml 50ml 25ml 100ml 2. The line in the diagram has to be extended to be 9 5cm. By what length must the line be extended? Page 18
3. Alan wants 250ml of water. What adjustment must he make to the three jars below so that each contains 250ml? (a) (b) (c) 750ml 300ml 600ml 500ml 200ml 400ml 100ml 200ml 250ml 4. The diagram shows the scale used for measuring a boy s height. The arrow indicates his height. How much more does he need to grow to be 2 metres tall? Page 19
5. The best angle of release for a javelin is between 32º and 36º to the horizontal, but this is tough to achieve consistently. Which of these throws are at the correct angle of release? In each case justify your answer. (a) (b) (c) (d) Page 20
6. The thermometer below shows the temperature in degrees Fahrenheit. (a) What temperature does the thermometer show? (b) If the temperature rises by 15 what would the new temperature be? (c) If the temperature fell by 23 what would the new temperature be? 7. John is a coach driver. The speedometer shows the speed of his coach on a trip to France. (a) Write down the speed shown (b) To make the best time, John wants to drive at the maximum speed limit of 100 kilometres per hour. How much faster does he need to drive to reach this? Page 21
M Interpreting the results of calculations to make decisions M1 I have investigated problems involving container packaging. 1. Ben works for an electrical manufacturer packing items in boxes. He is packing a product, in their box, into larger boxes for delivery. 5 cm 40 cm 80 cm 180 cm 100 cm 30 cm What is the maximum number of product boxes that can be fitted into the large box? Justify your answer Page 22
2. Cereal boxes are transported in larger boxes to ship around the country. A cereal manufacturer has two options as show below. 13 50 35 250 245 260 420 400 260 Option A Option B If they want to transport the most cereal boxes at once should they choose option A or B? Justify your answer. Page 23
3. Packaging is cut out of cardboard in the form of a net, and then folded to create a box. A net for a box is shown below. 40 cm 30 cm 50 cm These boxes are then filled with pens and put into a larger box shown below for transporting. 90 cm 160 cm 250 cm What is the maximum number of small boxes that can be fitted into the large box? Justify your answer. Page 24
4. A library gets a new bookcase delivered. 22 cm 195 cm 16 cm If all the books are the size shown, how many books can they fit into the bookcase? Justify your answer. 3 cm 20 cm 14 cm Page 25
M2 Calculations involving Mean and Range 5. Mark is a 100 metres sprinter. In five races he recorded the times, in seconds, shown. 10 23, 11 02, 10 59, 11 64, 11 42. (a) Calculate Mark s mean time for the five races. (b) Ben had a mean of 10 96 seconds in the five races. The sprinter with the best average time was to represent Scotland at a sprint event. Who would represent Scotland, Mark or Ben? Justify your answer Page 26
M3 I can decide on which deals constitute best buy 6. Supermarkets can present a problem over deciding which buy is the Best Buy. Look at the Special Offers below for a brand of hand wash. Special Offer 1 500ml bottles on offer at 3 for 2 Price for each 1.90 Special Offer 2 300ml bottles on offer at buy one get one free Price for each 1.88 State which offer represents the best buy. You must justify your answer. 7. A store offers these two deals on 330ml cans of fruit juice. 10 cans 4 90 18 cans 8 10 (a) Which deal offers the best buy per can? (b) A school trip plans to give every child on the trip a can of juice. There are 44 children going on the trip. What would be the cheapest way to by at least 44 cans of juice. Justify your answer. Page 27
M4 I can make a decision based on a measurement and a calculation involving a formula 8. The temperature in a room is controlled by a thermostat. John says he likes the room to be about 70 F. The thermostat is set at 18. The formula to change from Celsius to Fahrenheit is F = 1 8C + 32 Is the thermostat set correctly for John? Justify your answer 9. Pierre is told by his football coach that his perfect weight is between 55 and 58 kilograms. Pierre weighs himself in pounds as shown. The formula for converting from pounds to kilograms is given by K = P 2 2 Comment on Pierre s weight. Page 28
M5 I can make a justify a decision with a calculation 10. Jordan has a lemonade stall at the school fete. He makes up 12 jugs of lemonade. Each jug can fill 6 cups. The cost of making 12 jugs is 16 40. Jordan wants to charge 40p per cup. If he sells all 12 jugs will he make a profit? 11. The MacDonald family, Mr and Mrs MacDonald and their 3 children, are planning a trip to Spain. Mrs MacDonald reads the following information in a holiday brochure. Hotel Excelsior - Cost for 7 days all inclusive Adults 520 Children 300 The MacDonald s budget can afford to spend up to 2000 on the holiday. Is the Hotel Excelsior in their price range? Page 29
N Explaining decisions based on the results of measurements or calculations 1. An airline charges 8 per kilograms on any baggage over 15 kilograms. Margo arrives at the Airport with one large bag weighing 23 kilograms. How much will she be asked to pay for her excess baggage? 2. The total cost of a school the trip for 42 children is 9400. The Parent Teacher Association has agreed to pay 1410 of this and each child is asked to pay 180. Is this enough to cover the cost of the trip? Give a reason for your answer. 3. A college group of 165 students are planning to travel to an event using hired buses. A bus company offers two sizes of bus: Size A 48 seats Price 200 Size B 25 seats Price 130 The group wants to pay the lowest total hire charge available. (a) How many buses of each size should they hire? (b) How much will this cost? 4. The total cost of a school ski trip for 30 children is 16000. Page 30 The Parent Teacher Association has agreed to pay 1200 of this and each child is asked to pay 500. Is this enough to cover the cost of the trip? Give a reason for your answer.