Book 2. The wee Maths Book. Growth. Grow your brain. N4 Numeracy. of Big Brain. Guaranteed to make your brain grow, just add some effort and hard work

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1 Grow your brain N4 Numeracy Book 2 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. Length, Volume and Percentages

2 D Length and Volume D1 I am aware of the different metric units in which length is measured and can decide which unit is most appropriate in a given context. Complete this exercise without the aid of a calculator 1. Change these measurements into millimetres (a) 7cm (b) 12cm (c) 8 6cm (d) 3cm 4mm (e) 59 1cm (f) 702cm 2. Change these measurements to centimetres (a) 60mm (b) 400mm (c) 250mm (d) 3mm (e) 4m (f) 0 5m (g) 17m (h) 8m 90cm (i) 9m 8cm (j) 3 6m (k) 0 02m (l) 1 75m 3. Convert these measurements into metres (a) 300cm (b) 5000cm (c) 1400cm (d) 590cm (e) 60cm (f) 71cm 4. Convert these measurements into kilometres (a) 19300m (b) 8650m (c) 450m (d) cm (e) 20000cm (f) 1400cm Page 2

3 5. Change the units of the following measurements as indicated (a) 2 4 cm into mm (c) 180 cm into m (e) 760 m into km (g) 5 6 cm into mm (i) cm into m (k) 501 m into km (b) 3 2 km into m (d) 1060 mm into cm (f) 0 03 m into cm (h) 0 72 km into m (j) mm into cm (l) 1 94 m into cm 6. Change the units of the following measurements as indicated (a) 31 3 cm into mm (c) m into cm (e) 34 m into km (g) cm into mm (i) 0 02 cm into m (k) m into km (b) km into m (d) 43 mm into cm (f) cm into m (h) 1 5 km into m (j) mm into cm (l) 43 m into cm 7. Change the units of the following measurements as indicated (a) 0 71 cm into mm (c) 89 4 m into cm (e) 231 m into km (g) cm into mm (i) 27 cm into m (k) m into km (b) 7 8 km into m (d) 6 67 mm into cm (f) 9 08 cm into m (h) 1 05 km into m (j) 9 34 mm into cm (l) 202 m into cm Page 3

4 8. Elle is building some raised beds for growing vegetables. She needs pieces of wood that are 1 45 metres long. When Elle goes to purchase the wood, she finds all the measurements are in millimetres. What length of wood does Elle need to order? 9. The heights of all of the members of One Direction are listed below. Name Niall Harry Louis Liam Height 171cm 1780mm 1 74m 177cm What is the mean (average) height of the band? 10. Calculate the perimeter of the rectangle below. 32cm 1 05m Page 4

5 11. Shaun uses a trundle wheel to measure the perimeter of the school s fence; he finds that it is 879 metres long. How many complete laps of the school will Shaun need to run to ensure he covers 5 kilometres? 12. The distance from the Earth to the Moon is approximately kilometres. The Samsung Wind turbine in Fife is 200 metres tall. How many of these wind turbines would fit end-to-end between the Earth and the Moon.? 13. Baked beans come in cylindrical tins 11 centimetres high and with diameter 7 centimetres. The tins are packed into boxes measuring 420 mm by 280 mm by 350 mm. 7cm 280mm 11cm 350mm (tin and box not to scale) 420mm (a) One layer of cans is placed (upright) into the bottom of the box above. How many cans will fit into the bottom layer? (b) How many tins can be packed into the box altogether? Page 5

6 D2 I can solve problems which involve perimeter and can include inconsistent units 14. The diagram shows the dimensions of a swing park. 3 m 250cm 525cm 9 m (a) Find the perimeter of the swing park in metres. (b) Is 22 metres of fencing enough to fence the swing park. Justify your answer with a calculation. 15. Another swing park is shown. Will 42 metres of fencing be enough to fence this swing park? 450cm 5 m 12 m Justify your answer with a calculation. 150cm Page 6

7 16. The following two shapes have the same perimeter. 4cm 5cm 20mm 110mm 10mm 70mm x 5cm Find the missing length of the triangle. 17. Lucy wants to decorate her kite with new ribbon around the perimeter. 150mm 30cm She bought a one metre roll of ribbon. Will this be enough ribbon to decorate around her kite? Page 7

8 18. The diagram shows the room dimensions of Tammy s bedroom. 520cm 4 7m Tammy wants to put new skirting boards round her bedroom. (a) The door entrance is 60cm wide and will not require any skirting. Calculate the amount of skirting board required. (b) Skirting board costs 2 50 per metre. Tammy has 45 will this be enough to buy the new skirting boards? Page 8

9 D3 I can comfortably convert between litres, millilitres and cubic centimetres 19. Write the volume of each of the following items in litres. (a) (b) (c) 2000 cm cm cm 3 (d) (e) (f) 5 ml 568 cm ml (g) (h) (i) Page 9

10 500 ml 750 ml 3500 cm 3 (j) (k) (l) cm cm ml 20. Write the volume of each of the following items in millilitres. (a) 160 litres (b) 50 litres (c) 2 litres (d) litres (e) 4 litres (f) 0 5 litres (g) litres (h) 0 75 litres (i) 0 05 litres 21. For each of your answers in Q2, give an example of a container which would normally contain that volume. Page 10

11 22. I have 1 litre of water in a jug to be used in an experiment. On the way to my table I spill some. I have 780ml left. How much have I lost? 23. I have 1 litre of Sprite. I give 300ml to William, 200ml to Paul and 250ml to Mia. How much do I have left? 24. Mr Hart has to have a fluid intake of at least 2 litres. He has drunk two 275ml of tea, one 300ml of coffee, 200ml of orange juice and 180ml of water. How much more fluid does Mr Hart require? 25. Clare is having a party and has bought three 2 litre bottles of fizzy pop. She has 30 party cups and decides to share the fizzy pop evenly. How many millilitres will go in a cup? 26. Sarah needs litres of vegetable stock for making lentil soup. She decides to use OXO vegetable stock cubes and on the box it says: For a tasty stock dissolve one cube in 190 ml of boiling water. How many stock cubes will Sarah need for making her stock? Page 11

12 27. Drew is looking at the materials needed for the Fizzing and Foaming experiment. For this experiment you will need: 15 cm 3 (1 tablespoon) of baking soda (sodium bicarbonate) 15 cm 3 (1 tablespoon) of laundry detergent about 180 millilitres (3/4 cup) of water about 60 millilitres (1/4 cup) of vinegar several drops of food colouring (optional) a 400-milliliter (12-ounce) drinking glass a waterproof (plastic or metal) tray a teaspoon (a) How many millilitres does a tablespoon hold? (b) How many tablespoons of water are required? (c) Drew has a 1 litre bottle of vinegar, how many Fizzing and Foaming experiments can he complete with this bottle? 28. For the Mentos Geyser Experiment it is advised to have one Mentos sweet per 250 ml of Diet Coke. (a) Kate has a 1.75 litre bottle of Diet Coke, how many Mentos sweets does she need? (b) Craig has a 3 litre bottle of Diet Coke, how many Mentos sweets does he need? Page 12

13 E Percentages E1 I can convert comfortably between (common) fractions, decimals fractions and percentages in order to compare quantities given in different formats. 1. Write each of the following as a fraction and as a decimal fraction (a) 13% (b) 24% (c) 99% (d) 56% (e) 25% (f) 83% (g) 10% (h) 180% (i) 75% (j) 116% (k) 5% (l) 103% (m) 7.2% (n) 35% (o) 1% 2. Change each fraction into a percentage (calculator), (a) (b) 4 5 (c) 7 10 (d) (e) (f) 1 4 (g) (h) 5 8 (i) (j) 6 75 (k) 12 8 (l) Write down the percentage which is equivalent to each of the following fractions (without a calculator) (a) 1 2 (b) 3 4 (c) 1 10 (d) 2 3 (e) 1 5 (f) 3 10 Page 13

14 4. Work out the percentage which is equivalent to each of the following fractions. Give your answer to 2 significant figures and how your working clearly. (a) 9 11 (d) 1 3 (g) 5 8 (b) 7 13 (e) (h) (c) (f) (i) Write down the fraction which is equivalent to each of the following percentages (without a calculator). (a) 25% (b) 1% (c) 20% (d) 12½% (e) 10% (f) 30% (g) 90% (h) 5% (i) 15% 6. Write each of the following percentages as a fraction in its simplest form. Show your working clearly. (a) 30% (b) 4% (c) 85% (d) 7 5% (e) 9 4% (f) 0 3% (g) 65 5% (h) 8 02% (i) 0 12% (j) 5 55% (k) 0 05% (l) 0 64% Page 14

15 E2 I can find a percentage of a quantity involving at most 4 digits (Non Calculator and Calculator). Without a calculator 7. At a comedy show 9% of the audience buy a programme. If 1500 attend the show, how many buy a programme? 8. A travel firm offers a discount of 40% off the full price of package holiday. The full price of the package holiday is 760. How much is the discount? 9. A salesperson is paid commission of 15% of her weekly sales. How much will her commission be in a week when her sales total 800? 10. A bottle of iodine solution contains 7% iodine by volume. What volume of iodine is there in a 500ml bottle? 11. A metal alloy contains 60% pure gold. How much gold is there in 270g of the alloy? 12. A hotel in Glasgow offers 30% off the full price of a weekend break. How much is this saving if the full price of a weekend break is 700. Page 15

16 E3 I can calculate percentage increase and decrease. 13. A new luxury villa in Florida is valued at $ It is expected to rise in value by 15% during its first year. What will the value of the villa be at the end of the first year? 14. Mrs Dodds buys a new for It depreciates in value by 12% during its first year. How much will Mrs Dodds car be worth at the end of the first year? 15. Jorge buys a new house for The value of the house depreciates by 8% in the first year. How much would his house be worth at the end of the first year? 16. Company shares worth 1,200 depreciate in value over a month by 12%. How much were the shares worth at the end of the month? 17. The Pollards bought a bungalow for 110,000. It appreciated in value by 8% in first year. How much was the bungalow worth at the end of the first year? Page 16

17 E4 I can express one quantity as a percentage of another and work out a percentage increase or decrease using the original value and final value. 18. Alan scored 28 out of 40 in a Maths test. What was his percentage score? 19. The Head of First Year knows there are 300 pupils in the year group. 160 of them are girls. What percentage are boys? 20. Jamie bought a new car for in 2009 and sold it for 8000 three years later. Calculate the depreciation, and express it as a percentage of the cost when new? Give your answer to 1 decimal place. 21. In the season Lionel Messi scored 73 of the 190 goals scored by Barcelona. What percentage of Barcelona s total goals Lionel Messi score? Give your answer to 1 decimal place. 22. Last year Sally was paid 20 per hour. This year she gets per hour. Calculate her percentage increase in pay. Page 17