Grow your. Yellow 7. The wee Maths Book. Growth. of Big Brain. Guaranteed to make your brain grow, just add some effort and hard work

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1 Grow your Yellow 7 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! The wee Maths Book of Big Brain Growth Negatives, Multiples, Factors, Primes and Significant Figures 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.

2 Directions, Journeys and Scale Drawings (MTH 2-17c, MTH 2-17d) S20s I have prior knowledge of the 4 main compass points and can relate these to the associated bearings 1. (a) Copy the compass below into your jotter. (b) Beneath the four main compass points, write down the associated bearing. 2. Answer the following as True (T) or False (F) (a) The angle between North and South is 180º. (b) Bearings are always measured anti-clockwise from north. (c) The direction east is equivalent to a bearing of 90º. (d) The bearing of 175º is closest to travelling west. (e) Bearings are always given in three figures. (f) The direction west has a bearing of 270º. Page 2

3 S21s I can use an 8 point compass points, and their associated bearing, to describe, follow and record directions, routes and journeys 1. What bearing would you be on if you were travelling: (a) South (b) East (c) West (d) North East (e) South West (f) North West 2. Molly and her friends are going hillwalking. Molly tells her friends that they start their walk by heading southwest. (a) What is the 3-figure bearing for southwest? Later, Molly tells her friends that they need to walk on a bearing of 135. (b) What direction is represented by 135? 3. Alan is walking in a Northwest direction. Daniel is walking in the opposite direction. What direction is Daniel walking? 4. Katie is facing North. If Katie then turns to face Southwest, through how many degrees did she turn? Page 3

4 5. Ben is taking part in an outdoor training exercise. His task is to travel from the START to the FINISH visiting all checkpoints in order, as shown in the diagram below. (a) What bearing is Ben traveling in when he moving from the START to checkpoint 1? (b) What bearing is Ben traveling in when he moving from checkpoint 1 to checkpoint 2? (c) What bearing is Ben traveling in when he moving from checkpoint 2 to checkpoint 3? (d) What bearing is Ben traveling in when he moving from checkpoint 3 to checkpoint 4? (e) What bearing is Ben traveling in when he moving from checkpoint 4 to the FINISH? Page 4

5 S22s I can measure lengths on a scale drawing and use the scale to find the actual length (models, maps and plans) 1. The scale drawing below of a real car has been made using a scale of 1cm to 30cm (a) Measure the length of the car on the drawing in centimetres. (b) Use the scale to calculate the actual length of the real car in centimetres. (c) Write down this length in metres. 2. The scale drawing shown, of a concept car, has been made using a scale of 1cm to 10cm (a) Measure the distance between the two air inlets, indicated by the arrowed line, on the scale drawing. Give your answer in centimetres. (b) Use the scale to calculate this distance on the actual car in metres Page 5

6 3. The scale drawing below of a plane has been made using a scale of 1cm to 0 5m (a) Use the scale to calculate the actual length of the plane. (b) Use the scale to calculate the actual wingspan of the plane. 4. The map of shown has been drawn using a scale of 1cm to 50km. (a) Use the scale to find the distance between Garth and Kern (b) Use the scale to find the distance between Halo and Kern (c) Use the scale to find the distance between Halo and Garth Page 6

7 5. The map of Scotland below has been drawn using a scale of 1cm to 40km. (a) Use the scale to find the distance from Dundee to Aberdeen. (b) Use the scale to find the distance from Glasgow to Aberdeen. Page 7

8 S23t I can use directions to find my way around a street plan. 1. Look at the street plan below (a) What build would you be looking for, if these are the directions? Start at Mill Road looking towards Barnford Street; Walked straight ahead into Barnford Street; Turned left, then turned first right and then again first right; The building you are looking for is at the end of this road on your left. Page 8

9 (b) What build would you be looking for, if these are the directions? Start at the school; Take the second turning on the right; Go straight ahead until the end of the road; At the end of the road turn right and the building you are looking for is on your right. (c) What street would you end up in if these were the directions? Start in Gilmour Gardens; Turn right into Milford Avenue; Take second left, followed by first on the left; You have now reached your destination. (d) What street would you end up in if these were the directions? Start in Meadow Road; Turn first left, followed by a first right; At the end of the road take a left and then first right. You have now reached your destination. Page 9

10 2. Look at the street plan below. Give direction to travel from: (a) Tom s House to the Park. (b) The Swimming Pool to the School. (c) The Health Centre to the Railway Station. (d) The Car Park to the Bus Station. Page 10

11 Negative Numbers (3-04a) N29t I can add, subtract, multiply and divide with negative numbers in abstract contexts in preparation for their use in algebra. 1. The temperature in Glasgow on Monday was 7 C, but by Friday it had fallen to 4 C. (a) Which of these calculations do you think apply? (i) 7 + ( 4) (ii) 7 ( 4) (iii) (iv) 4 7 (b) How many degrees had the temperature fallen? 2. The temperature in East Kilbride was 13 C. The weather report said that the temperature would rise by 8 degrees. (a) Which of these calculations do you think apply? (i) (ii) 13 8 (iii) 8 + ( 13) (iv) 8 ( 13) (b) What would be the new temperature after this rise? Page 11

12 3. A liquid is stored at 30 C. If the temperature of the liquid is reduced by 11 degrees it would reach its freezing point. (a) Which of these calculations do you think apply? (i) (ii) (iii) 11 + ( 30) (iv) 11 ( 30) (b) What is the freezing point of this liquid? 4. It was extremely cold at midnight. During the morning, the temperature rose by 7 C. By midday, it had reached -6 C. What was the temperature at midnight? 5. The temperature at midnight was 12 C. By midday, the temperature was 7 C. What was the temperature change? Page 12

13 6. Write down the question then evaluate, (a) 4 + ( 11) (b) 2 12 (c) ( 6) + 16 (d) 6 + ( 9) (e) 7 15 (f) ( 6) 7 7. Write down the question then evaluate, (a) ( 50) + ( 70) (b) ( 42) + 42 (c) ( 11) 4 (d) 18 + ( 22) (e) 13 + ( 14) (f) 36 ( 14) 8. Write down the question then evaluate, (a) 9 ( 9) (b) ( 840) (c) 4 ( 3) (d) ( 3) ( 7) (e) ( 9) + ( 12) (f) 15 ( 15) 9. Write down the question then evaluate, (a) 6 ( 6) (b) 7 ( 8) (c) ( 8) 4 (d) 15 ( 4) (e) ( 7) ( 3) (f) ( 40) ( 8) 10. Write down the question then evaluate, (a) ( 63) 9 (b) 8 ( 4) (c) 56 ( 7) (d) ( 7) 3 (e) ( 5) ( 4) (f) ( 9) ( 8) 11. Write down the question then evaluate, (a) ( 3) ( 6) (b) ( 4) ( 12) (c) 10 ( 6) (d) 8 ( 8) (e) ( 27) 3 (f) ( 81) ( 9) (g) ( 63) ( 7) (h) ( 6) 2 (i) 6 ( 7) 3 Page 13

14 12. Write down the question then evaluate, (a) 4 ( 6) (b) ( 5) + ( 8) (c) 11 ( 3) (d) 2 ( 8) (e) ( 36) 9 (f) ( 7) + ( 5) (g) ( 35) ( 5) (h) 3 + ( 7) (i) ( 8) Write down the question then evaluate, (a) 3 ( 7) (b) ( 3) + ( 9) (c) 5 ( 2) (d) 17 ( 2) (e) ( 36) 6 (f) ( 8) + ( 12) (g) ( 40) ( 8) (h) 8 + ( 11) (i) ( 7) Write down the question then evaluate, (a) 7 ( 8) (b) ( 6) + ( 6) (c) 4 ( 3) (d) 3 ( 2) (e) ( 27) 3 (f) ( 2) + ( 2) (g) ( 18) ( 9) (h) 5 + ( 15) (i) ( 2) Write down the question then evaluate, (a) 7 ( 4) (b) ( 3) + ( 10) (c) 4 ( 10) (d) 5 ( 8) (e) ( 20) 4 (f) ( 11) + ( 1) (g) ( 24) ( 8) (h) 4 + ( 7) (i) ( 12) + 2 Page 14

15 Multiples and Factors (MTH 2-05a, 3-05a, 3-05b) N30s I know the meaning of the term multiple 1. Which of the following are multiples of 6. 4, 9, 12, 25, 32, 18, 61, 24, Which of the following are multiples of 2. 4, 9, 12, 5, 13, 18, 16, 17, Which of the following are multiples of 7. 4, 9, 14, 5, 13, 21, 16, 17, Copy the bingo card below into your jotter. (a) Cross out all the numbers which are multiples of two. (b) Cross out all the numbers which are multiples of three or four. (c) Cross out all the number which are multiples of five. (d) Is it a winning card? Page 15

16 N31s I can identify multiples of 2 to 9 (first 10 multiples only) 1. List the first 5 multiples of: (a) 3 (b) 5 (c) 4 (d) 9 (d) 7 (f) 8 2. List all the multiples of 7 between 30 and Copy out and fill in the blanks (missing multiples) below: (i) Multiples of two 2, 4, 6, 8,,,, 16. (ii) Multiples of three 3,, 9,, 15,,,. (iii) Multiples of six 6,,,, 30,, 42,. (iv) Multiples of nine, 18, 27,, 45, 54,. (v) Multiples of five 5,,,,,,,. Page 16

17 N32t I can find the lowest common multiple of two whole numbers. 1. Find the Lowest Common Multiple LCM of: (a) 2 and 5 (b) 3 and 7 (c) 4 and 6 (d) 7 and 10 (e) 13 and 3 (f) 2, 3 and 5 (g) 3, 6 and 7 (h) 2, 4 and 8 (i) 5, 15 and Pencils come in packages of 10 and Erasers come in packages of 12. Mr Kane wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil. How many packages of pencils and erasers should Mr Kane buy? 3. Cameron has swimming lessons every fifth day and diving lessons every third day. Cameron had a swimming lesson and a diving lesson on May 5. What will be the date, when he next has both swimming and diving lessons on the same day? 4. Three flashing lights are turned on at the same time. One flashes every 2 second, the second every 3 seconds and the third flashes every 5 seconds. How long, after they are first turned on, will they first flash again at the same time? Page 17

18 N33s I know the meaning of the term factor 1. Which of the following are factors of 40. 5, 6, 7, Which of the following are factors of 24. 5, 6, 7, Which of the following are factors of 21. 5, 6, 7, Copy the bingo card below into your jotter. (a) Cross out all the numbers which have two or three as a factor. (b) Now cross out all the numbers which have five or six as factors. (c) Finally, cross out all the number which have seven as a factor. (d) Is it a winning card? Page 18

19 N34s I can identify all the factors of any whole number less than or equal to Find the factors of, (a) 12 (b) 24 (c) 40 (d) 36 (e) 32 (f) Which number am I? (a) I am an odd number greater than five. (b) I am a multiple of three. (c) I am a factor of Which number am I? (a) I am an even number between 10 and 20. (b) I am a multiple of three. (c) I am a factor of Which number am I? (a) I am an odd number between 10 and 26. (b) I am a multiple of five. (c) I am a factor of 30. Page 19

20 N35t I can find the highest common factor of two whole numbers. 1. Find the Higher Common Factor (HCF) of, (a) 4 and 6 (b) 9 and 27 (c) 15 and 36 (d) 12 and 42 (e) 14, 35 and 42 (f) 32, 24 and Fraser has 6 cans of regular juice and 15 cans of diet juice. He wants to create some identical refreshment tables, operating during a Cup Final, and wants to use up all the cans. What is the greatest number of refreshment tables that Fraser can stock? 3. For a dinner party, Cara is creating individual servings of starters. She has 10 carrot sticks and 15 celery sticks. If she wants each serving to be identical, with no food left over, what is the greatest number of servings Cara can create? 4. Eva is making emergency-preparedness kits to share with friends. She has 20 bottles of water and 12 cans of food, which she would like to distribute equally among the kits, with nothing left over. What is the greatest number of kits Eva can make? Page 20

21 Angles (MTH 2 17a, MTH 2 17b) S24s I can classify angles in the environment 1. The bird shown has its beak slightly open. What type of angle does the bird s beak make? 2. The laptop shown can be flipped open for use. What type of angle does the keyboard and screen make? 3. Wind turbines are a very common sight in the Scottish landscape. What is the type of angle between blades? Page 21

22 4. Ben woke up during the night and checked his watch. (a) Write the time in 12-hour and 24-hour time. (b) What type of angle is the shaded clockwise angle between the hands of the watch. 5. Next time Ben checked his watch is when his alarm went off. (a) Write the time in 12-hour and 24-hour time. (b) What type of angle is the shaded angle. 6. Ben checked his watch when the bell sounded at the end of registration. (a) Write the time in 12-hour and 24-hour time. (b) What type of angle is the shaded angle. Page 22

23 7. Ben looked at his watch just before the bell for lunchtime. (a) Write the time in 12-hour and 24-hour time. (b) What type of angle is the shaded angle. 8. Ben checked his watch when his dad served his evening meal. (a) Write the time in 12-hour and 24-hour time. (b) What type of angle is the shaded angle. 9. Ben checked his watch when he finished his homework. (a) Write the time in 12-hour and 24-hour time. (b) What type of angle is the shaded angle. Page 23

24 10. For his birthday Ben got a new golf club. The angle shown in the diagram is known as the Bounce Angle. The manufacturers say that the bounce angle of the club is 8 degrees. Do you agree? Justify your answer. 11. The second diagram shows the loft angle of the club. Ben says his new club has a loft angle of 48 degrees. Is he correct? Justify your answer. Page 24

25 Quadrilaterals (MTH 2-16a) S25t I can identify quadrilaterals from their properties. Use the clues below to answer the question which quadrilateral am I? 1. I have 4 equal sides and my 4 angles are 90 degrees. 2. I have 4 equal sides, but my 4 angles are not 90 degrees. 3. I have 2 lines of symmetry, but they are not my diagonals. 4. I have 4 equal sides and have only 2 lines of symmetry. 5. My diagonals meet at 90 degrees, but only 1 bisects the other. 6. I have 4 lines of symmetry. 7. I have no lines of symmetry. 8. I have only 1 pair of parallel sides. Page 25

26 Drawing accurate 2D Shapes (MTH 3-16a) S26t I can draw triangles given 3 sides, 2 sides and an angle, 2 angles and one side using compasses, protractor and ruler. 1. Using only a ruler and a set of compasses draw accurately a triangle with sides of size (a) 3cm, 4cm and 5cm. (b) 6cm, 6cm and 6cm. 2. Using a ruler and a protractor, accurately draw the triangles sketched below. (a) (b) 38 5 cm 8 cm cm 7 cm (c) (d) cm cm 46 Page 26

27 S27t I can draw rhombi and kites accurately using compasses, protractor and ruler. 1. Using only a ruler and a set of compasses draw accurately the kite shown below 5 cm 6 cm 7 cm (a) What is the perimeter of this kite? (b) Calculate the area of the kite you have drawn. (Hint: You will need to make some measurements) 2. Using only a ruler and a set of compasses draw accurately the kite shown. 4 cm 6 cm (a) What is the perimeter of this kite? (b) Calculate the area of the kite you have drawn. 5 cm Page 27