Grow your. Yellow 9. 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 9 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 Circle; Area of Quadrilaterals; Ratio and Proportion; Patterns and Sequences; Finance; More non-calculator skills 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 Circle (4-16a) M19f I can calculate the circumference of a circle by applying a formula and given the diameter or radius. 1. Calculate the circumference of these circles. Make sure you set down all the working. Remember to provide units in your answers (a) (b) (c) 6m 12mm 25cm (d) (e) (f) 4 2cm 7mm 1 5m 2. The London Eye, is a giant Ferris Wheel with a diameter of 120 metres. How far does a passenger on the London Eye travel in one rotation? Page 2

3 3. An ant is walking around the rim of a circular pot. The pot has a radius of 6 centimetres. How far will the ant walk in one lap of the pot? 4. A bike has a wheel with a diameter 65 centimetres. How far would this wheel go in one revolution (turn)? Give your answer in metres. 65 cm 5. Eva has a trundle wheel with a radius of 18 centimetres. How far would this wheel go in one revolution (turn)? Page 3

4 6. A farmer found a crop circle in his field one day. He measured the circle and found it had a radius of 20 metres. Calculate the circumference of the circle. 7. The average radius of the iris of a human eye is 5 9 mm. What is the average circumference of the human iris? 8. On Pi Day, Eva baked a circular cake. She wanted to put a ribbon around the cake. The cake was 30 centimetres in diameter and Eva had 1 metre of ribbon. Is this enough to go around the cake? Justify your answer Page 4

5 M20f I can calculate the area of a circle by applying a formula and given the diameter or radius. 1. Find the area of each circle below (a) (b) (c) 25cm 6m 7mm 2. The diagram shows the cross section of an orange. The cross section is a circle with diameter 7 centimetres. Calculate the area of the cross section of the orange. 3. The average radius of the iris of a human eye is 5 9 mm. What is the average area of a human iris? Page 5

6 4. Cara makes pizzas in a restaurant. The pizzas have a diameter of 18 centimetres. Calculate the area of the pizza. 5. A farmer found a crop circle in his field one day. He measured the circle and found it had a radius of 20 metres. The crop circle was reported in the local newspaper with the heading huge crop circle with an area of nearly 5000 square metres found in a farmers field. Comment on the accuracy of the newspaper headline. Page 6

7 Area of Quadrilaterals (4-11a) M21f I can find the area of a kite and rhombus using composite shapes. 1. Find the area of the kites below. (a) (b) 2 3cm 7 2m 3 4cm 9 8m 4 2cm 10 6m 2. Find the area of the rhombuses below. (a) (b) 120mm 2 3m 80mm 120cm Page 7

8 M22t I can find the area of a parallelogram using composite shapes. 1. Find the area of these parallelograms (a) 40m 30m 40m 110m (b) 25cm 80cm 50cm 25cm Page 8

9 M23t I can find the area of a trapezium using composite shapes. 1. Find the area of these trapeziums (a) 80cm 25cm 70cm 30cm (b) 9m 12m 8m Page 9

10 Ratio and Proportion (3-08a) N48t I understand how to express a ratio and can simplify ratios. 1. Write these ratios in their simplest form. (a) 2 4 (b) 6 4 (c) 4 6 (d) 8 6 (e) 3 6 (f) 9 3 (g) 6 9 (h) 15 6 (i) 6 3 (j) 4 6 (k) 3 6 (l) Write the number which should replace the?. (a) 3 6 = 12? (b)? 5 = (c) 18 4 =? 2 (d) 3 5 = 15? (e) 1 6 =? 18 (f) 5 13 =? 26 (g) 6? = 30 5 (h)? 9 = 6 27 (i) 2 17 = 4? (j) 23 7 =? 14 (k) = 15? (l) 7? = Page 10

11 N49t I can distribute a total amount in a given ratio. 1. Morven mixes tins of red paint with tins of white paint in the ratio 2:3. She needs 15 tins of paint altogether. How many tins of red paint does she need? 2. Sandy works with the council. Last week his duties were split between photocopying and working on reception in the ratio of 3:4. If Sandy worked for 35 hours last week how much time did he spend on photocopying? 3. Eva works with her dad. Last week her duties were split between office work and deliveries in the ratio of 3:5. If Eva worked for 40 hours last week, how much time was spent on office work? 4. Cara knows that to make a good mortar for bricklaying she should mix the cement and sand in a ratio of 1:3. If Cara follows this rule how much cement does she need for 2 kilograms of mortar? Page 11

12 5. Jillian s recipe mixes flour and sugar in the ratio of 3:2. How many grams of flour are required for 100 grams of this mixture? 6. Ben makes purple paint from mixing blue and red in the ratio of 3:2. To stick to this ratio what volume of blue paint does he require to make 30 ml of purple paint? 7. David feeds 32 fish to a mother seal and her baby. The mother seal has 5 fish for every 3 fish for the baby seal. (a) Write the number of fish the mother has, compared to the number of fish the baby has, as a ratio. (b) How many fish does David feed the mother seal? 8. Pranav has 3 shirts for every pair of suit trousers he owns. (a) Write this as a ratio of shirts to trousers. (b) He has a pair of trousers for every day of the week. How many shirts does he own? Page 12

13 N50t I can use direct proportion. 22. Five bars of soap cost What will be the cost of: (a) 1 bar of soap (b) 7 bars of soap (c) 20 bars of soap? 23. Four textbooks cost What will be the cost of: (a) 1 textbook (b) 15 text books (c) 30 text books? 24. A car uses 4 litres of petrol to travel 52km. (a) How far will it travel on 8 litres of petrol? (b) How far will it travel on 20 litres of petrol? (c) How much petrol will it need for a journey of 442 km? 25. Ten loaves weigh 7 kilogrammes. What would be the weight of: (a) 1 loaf (b) 12 loaves (one dozen). Page 13

14 Patterns and Sequences (2-13a, 3-13a, 3-15b) N51s I can extend a straightforward sequence. 1. List the next two terms in each sequence. (a) 6, 13, 20, 27, 34.. (b) 2, 5, 8, 11, 14.. (c) 10, 14, 18, 22, 26.. (d) 7, 9, 11, 13, 15.. (e) 10, 14, 18, 22, 26.. (f) 2, 6, 10, 14, List the next three terms in each sequence. (a) 0, 4, 8, 12, 16.. (b) 16, 22, 28, 34, 40.. (c) 8, 15, 22, 29, 36.. (d) 19, 29, 39, 49, 59.. (e) 20, 30, 40, 50, 60.. (f) 15, 23, 31, 39, 47.. (g) 10, 16, 22, 28, 34.. (h) 10, 13, 16, 19, List the next four terms in each sequence. (a) 9, 18, 27, 36, 45.. (b) 4, 6, 8, 10, 12.. (c) 15, 24, 33, 42, 51.. (d) 5, 10, 15, 20, 25.. (e) 11, 19, 27, 35, 43.. (f) 3, 12, 21, 30, 39.. Page 14

15 N52t I can use a pattern to make a Mathematical Model in a real-life context 1. Draw the next two patterns in the sequence of dots below. Pattern 1 Pattern 2 Pattern 3 2. Draw the next two patterns in this sequence of dots. 3. Draw the next two patterns in the sequence of dots and squares below. Page 15

16 4. A pattern, using matchsticks to make triangle, is shown below. (a) Draw the next set of triangles in the sequence. (b) Copy and complete the table below: No. of Triangles No. of Matchsticks Look at the pattern of trapezium shaped tables and customers in a restaurant. (a) Draw the next set of tables in the sequence. (b) Copy and complete the table below: No. of Tables No. of customers Page 16

17 6. The diagrams below show the number of people sitting at desks. (a) Draw the next diagram in the sequence. (b) Copy and complete the table below for this pattern. Number of Desks (d) Number of People (p) 4 6 (c) Write down a formula connecting p and d. 7. A manufacturer makes necklaces in various sizes. 1 ring 4 beads 2 rings 7 beads (a) Draw the next size in the sequence. (b) Complete this table to show how the pattern is built up. Number of Rings (r) Number of Beads (b) 4 7 (c) Write down a formula connecting b and r. Page 17

18 8. These patterns are made with circles. Pattern 1 Pattern 2 Pattern 3 (a) Draw pattern 4. (b) Copy and complete the table below. Pattern Number (P) Number of Circles (c) 1 4 (c) Write down a formula connecting c and P. 9. A design consists of rectangles and triangles. The first three patterns are shown. (a) Draw the 4th Pattern. (b) Copy and complete the table below. Number of Rectangles (r) Number of Triangles (t) 6 8 Page 18 (c) Write down a formula connecting t and r.

19 N53s I can extend Square Number sequences, Triangular Number sequences and Fibonacci sequences Square Numbers 1. Write out a sequence of 10 Square Numbers starting at 25. Triangular Numbers 2. Write out a sequence of 6 triangular numbers starting at 21. Page 19

20 Fibonacci Numbers Write out the next 4 terms in the Fibonacci Sequence above. 4. Write out the next 8 terms in a Fibonacci Sequence which starts with 1 and A sequence has the following formula for the nth-term of the sequence. nth-term = 3n + 1 Write out the first 5 terms of this sequence. 6. A sequence has the following formula for the nth-term of the sequence. nth-term = 2n 1 (a) Write out the first 5 terms of this sequence. (b) What is another name for this sequence of numbers? Page 20

21 Finance (MNU 2-09a, MNU 2-09b, MNU 2-09c) N54s Money Calculations 1. Ben s mum gave him five pounds going to school and said she wanted at least 2 change back. It cost Ben 80p for his bus to school and 80p back. He also spent 1 80 on a school lunch. Will he have enough change for his mum? 2. Jamie needs 5 lightbulbs for his new house. He found the type he wanted on the internet costing 3 54 each plus 2 99 delivery charge. Is 20 enough to get 5 of these bulbs delivered? 3. Sandy is tiling his bathroom. He has estimated he will need at least 100 tiles. The tiles are sold in packs of 12 which cost (a) How many packs of tiles does Sandy require? (b) How much will the tiles cost? Page 21

22 4. Cara and her three friends have won the lottery. The prize is and they decide to split it equally. How much will they each get? 5. Jillian bought a 6 pack of cans of cola. The pack cost How much is this per can? 6. A youth club is organising a bowling tournament at the local ten pin bowling alley. Six teams of 4 people will take part. The costs involved in running the tournament are as follows: * Three lanes hired, with 4 games each lane, at a cost of 3 80 per game * A drink and a snack for each person at a cost of 2 10 per person * 8 prizes costing in total How much should the youth club charge each team member so that all the costs are covered? Page 22

23 N55s I have investigated the use of bank cards. 1. Investigate the differences between a credit and a debit card. Write down what you have found. 2. Cara is booking seats on a flight from Glasgow to Malaga online. At the payment page, she reviews the details of her booking which are shown. How much more expensive are the seats using a credit card? 3. Ben is in Birmingham and is planning a trip to Verona. The cost of the flight, which is shown, includes a payment fee for using a credit card. How much extra will it be for Ben to pay for the flights using a credit card? Page 23

24 N56s I can compare costs for a given budget and what is affordable. 1. Cara checked her purse and found she had the following notes and coins. (a) How much money does she have? (b) She wants to buy three new pens which are 1.99 each. Does she have enough money? 2. Callum saves 7 50 every week to buy a new pair of football boots. The boots cost Will Callum have enough to buy them after 12 weeks? 3. Eva has been saving 6 50 each week to pay for her gymnastics club trip to London. Eva has 28 weeks before the trip must be paid. Will she have enough if the trip costs 200. Page 24

25 4. Ben has been to the supermarket and part of his till receipt is shown below (a) How much does he have to pay? (b) He has the following money in his pocket. Is this enough to pay for his shopping? 5. Sandy earns 152 per week. His weekly expenses come to 83. He saves half of his surplus each week. Will he save enough over 10 weeks to pay for a holiday which costs 380? Page 25

26 N57s I can calculate Profit or Loss 1. A small business has an annual turnover of The total annual expenditure for the business (including staff wages) is (a) Calculate the profit for the year. (b) Calculate the weekly profit if the business operates a 50-week working year people attended this Race Night. (a) How much money was collected, in total, from the entrance fee? (b) The races collected 550 in bets but paid out 120 in prizes. How much profit was made from the races. (c) The cost of hiring the hall was 850. Did the Race Night make a profit? Page 26

27 3. The local rugby club are selling raffle tickets for 50 pence each. (a) The first and second prizes together cost the club 550 and the raffle tickets cost 40 to get printed. Calculate the total cost of running this raffle. (b) If the club sold 2000 raffle tickets, how much profit did they make. 4. At New Year, the Charities Committee staged a firework display. It cost them 640 for the fireworks, 70 for beefburgers, 30 for rolls and 65 for juice. 500 tickets, priced at 2 50 each, were sold. How much profit did they make for charity? Page 27

28 More non-calculator skills N58s I understand Place Value in number up to one million. 1. The highest attendance at a Scottish football match during the season was (a) Write the digit in the thousands column. (b) What value does the 6 represent in this number? (c) Write out this number in words. 2. There were cinema visits in the UK during (a) Write the digit in the tenthousands column. (b) What value does the 8 represent in this number? (c) Write out this number in words. 3. It was reported in the daily newspapers that Estonians drank litres of alcohol per head of population per year. This was the highest level of alcohol consumption in the world. (a) Write the digit in the tenths column. (b) What value does the 8 represent in this number? (c) Write out this number in words. Page 28

29 4. In 2011 the US had citizens in jail, the highest number of prisoners in the world. (a) Write the digit in the hundred-thousands column. (b) What value does the 8 represent in this number? (c) Write out this number in words. 5. Honduras is a dangerous place with 169 murders per year per of the population in (a) Write the digit in the units column of the murder rate. (b) What value does the 1 represent in the murder rate? (c) Write out the murder rate in words. 6. Scotland was the most dangerous place in Europe in 2016 with 1 74 homicides per per year. (d) Write the digit in the hundredths column of the homicide rate. (e) What value does the 7 represent in the homicide rate? (f) Write out the homicide rate in words. 7. The number of Facebook users in the US in 2012 was (a) Write the digit in the millions column. (b) What value does the 3 represent in this number? (c) Write out this number in words. Page 29

30 N59s Adding and subtracting whole numbers and decimals. Carry out the following calculations without using a calculator. 1. (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) Page 30

31 N60s Multiplying and dividing decimals by 10, 100 and Carry out the following calculations without using a calculator. 1. (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) (a) (b) (c) (d) Page 31

32 N61s Long Multiplication. Carry out the following calculations without using a calculator Page 32