Grow your Yellow 4 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 Length (including circumference) and Area Calculations 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.
Tips for Parents #4 Talk about your child's brain power improving, through hard work, and not being something that is fixed 1. Discuss brain growth with your child Make your child aware hard work, and persistent effort, can actually change their brain, making physical connection between neutrons which in turn will make their brain grow fitter and stronger. 2. Define smart as a process not an attribute Say things like: "It was smart to try those five questions, check the answer and to learn from all your mistakes" Page 2
Length (MNU 2-11a, 2-11b, 2-11c, 3-17c) M5s I can use my knowledge of familiar objects and journeys to assist me when making an estimate of length The height of the door handle on the classroom door is 1 metre. Use this to estimate the following lengths. 1. The height of the door? 2. The length and breadth of the classroom? 3. The length of the maths corridor? 4. The length of the football pitch? The breadth of your finger nail is about 1 centimetre. Use this to estimate the following lengths. 5. The length and breadth of your jotter? 6. The length and breadth of your desk? 7. The length of your pencil? 8. The length of a calculator? Page 3
M6s I have experience of choosing appropriate measuring devices and units to measure the length of various everyday objects and distances between places The answers to Questions 1 to 6 should be chosen from the following list. ruler trundle wheel measuring tape 1. What would be the most appropriate measuring devices to measure the length of the street? 2. What would be the most appropriate measuring device to measure the width of your desk? 3. What would be the most appropriate measuring device to measure the length of a classroom? 4. What would be the most appropriate measuring device to measure the length of one of your fingers? 5. What would be the most appropriate measuring device to measure the width of your jotter? 6. What would be the most appropriate measuring device to measure the length of the maths corridor? Page 4
M7s I can measure length to a required degree of accuracy 1. Measure the length and breadth of the street. 2. Measure the length of the Maths corridor. 3. Measure the perimeter of the football park. 4. Measure the length and breadth of this booklet. 5. Measure the perimeter of your desk. 6. Measure the length and breadth of your classroom. 7. Measure the perimeter of the Maths Quadrangle (don t include the stairs). Page 5
M8s I can use the common units of measure to convert mm to cm, cm to m and m to km 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) 900000cm (e) 20000cm (f) 1400cm Page 6
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) 69 35 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) 34256 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) 0 00503 m into cm (e) 34 m into km (g) 0 062 cm into mm (i) 0 02 cm into m (k) 0 089 m into km (b) 0 201 km into m (d) 43 mm into cm (f) 846 81 cm into m (h) 1 5 km into m (j) 342 67 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) 0 802 cm into mm (i) 27 cm into m (k) 0 9091 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 7
M9s 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. The answers to Questions 1 to 5 should be chosen from the following list. Millimetres Centimetres Metres Kilometres 1. What would be the most appropriate unit to measure the length of a football pitch? 2. What would be the most appropriate unit to measure the width of your fingernail? 3. What would be the most appropriate unit to measure the distance from Calderglen to Glasgow? 4. What would be the most appropriate unit to measure the length of a golf hole? 5. What would be the most appropriate unit to measure the width of your desk? Page 8
M10s I can calculate the perimeter of various 2D shapes Find the perimeter of the following shapes. 1. 2. 15 cm 15 cm 15 cm 3 cm 3 cm 15 cm 15 cm 3 cm 3 cm 15 cm 15 cm 15 cm 3. 4. 1 2 m 1 2 m 1 2 m 24 mm 24 mm 1 2 m 1 2 m 24 mm 24 mm 1 2 m 24 mm Page 9
5 3 cm 5. 28 mm 32 mm 28 mm 5 3 cm 6. 4 2 cm 1 8 cm 62 mm 62 mm 1 8 cm 5 5 cm 5 5 cm 7. 97 mm 5 5 cm 55 mm 7 3 cm Page 10
M11s I can solve problems which involve perimeter and include inconsistent units 1. The diagram show 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. 2. 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 11
3. The following two shapes have the same perimeter. 4cm 5cm 20mm 110mm 10mm 70mm x 5cm Find the missing length of the triangle. 4. 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 12
5. The diagram, which is not drawn to scale, shows the room dimensions of Tammy s bedroom. 420cm 3 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? (c) Tammy s bed is 2100 millimetres in length. When the door is fully open, as shown in the diagram, there is a gap between the door and the bed. How big is this gap? Page 13
M12t I can use a simple scale to make enlargements and reductions. 1. Use a scale of 1cm to 5km to make an accurate scale drawing of the sketch below. 2. Use a scale of 1cm to 2km to make an accurate scale drawing of the sketch below. Page 14
3. Use a scale of 1cm to 10km to make an accurate scale drawing of the sketch below. 4. Use a scale of 1cm to 10m to make an accurate scale drawing of the sketch below. All internal angles in the shape are right angles. Page 15
Area (MTH 2-11c, 3-11a, 3-11b) M13s I can find the area of figures by counting squares 1. If the squares on the grid below are all square centimetres, find the area of each shape. (a) (b) (c) (d) (e) (f) (g) 2. Draw, on square centimetre paper, as many rectangle as you can with an area of 36 square centimetres. Page 16
3. If the squares on the grid below are all square centimetres, find the area of each shape (a) (b) (c) (d) (e) (g) 4. Draw, on square centimetre paper, any shape with an area of (a) 20 square centimetres. (a) 24 square centimetres. (a) 32 square centimetres. Page 17
M14s I have investigated the relationship between lengths of sides of squares and rectangles to calculate area 1. Find the area of each shape using the appropriate formula and showing all of your working. Don t forget to include units in your answer. (a) 5 cm (b) 20 cm 12 cm 150 mm (c) 2 m (d) 8 m 2 m 2 m 20 m 2 m Page 18
2. Alan gets a driveway company to give him a quote for the cost of mono-blocking his 4 5m by 6m rectangular driveway. The price quoted is 85 per square metre including all materials and labour. If Alan chooses this company, what would be the cost of monoblocking his driveway? 3. Susan wants to turf her rectangular back garden. She orders the turf from her local garden centre who charge 2 70 per square metre and a delivery charge of 15. 5 5m 9m How much would it cost Susan for the turf (including delivery)? Page 19
M15t I can use a formula to calculate the area of a rectangle. I 1 can use the formula A 2 bh to calculate the area of a triangle. 1. Find the area of each shape using the appropriate formula and showing all of your working. Don t forget to include units in your answer. (a) (b) 200 mm 150 mm 6 cm (c) (d) 18 m 16 cm 30 m 15 cm Page 20
(e) 8 m (f) 9 m 5 cm 4 cm 3 cm 2. The side view of a wooden door wedge shows the height is 4cm and the length is 16 5cm. 4cm 16 5cm Calculate the area of the shaded part of the wedge. 3. The white sail of the yacht Ocean Voyager is in the shape of a right angled triangle with dimensions shown. 5 5m Calculate its area in m². 4 6m Page 21
Circle (MTH 2-16a) S11s I can identify the radius, diameter and circumference of a circle 1. Copy the diagram below into your jotter 2. The London Eye, is a giant Ferris Wheel in London. It is 120 metres if measured from one end through the middle to the other. The distance around the outside is 377 metres and passengers are always 60 metres from the centre of the wheel. Write down the sizes of the circumference, diameter and radius of the London Eye. Page 22
3. A bike has a wheel 65 centimetres from one side to the other through the middle. The rim of the wheel is always 32 5 centimetres from the centre of the wheel and the wheel travels 204 centimetres in one complete turn. 65 cm Write down the sizes of the radius, the diameter and the circumference of the wheel. 4. A roulette wheel turns through 250 centimetres in one complete turn. The rim of the roulette wheel is always 40 centimetres from the centre and the distance across the roulette wheel is 80 centimetres. Write down the sizes of the radius, the diameter and the circumference of the roulette wheel. Page 23
S12t I have experience of drawing accurate circles using compasses and rulers 1. Draw accurate circles with the following sizes (a) A radius of 4 centimetres. (b) A radius of 36 millimetres. (c) A diameter of 9 centimetres. (d) A diameter of 60 millimetres. 2. Draw a pattern which is made up of five equally spaced concentric circles as shown below. You can decide on the size of your circles but it must fit into your jotter. Page 24
S13t I have worked with compasses to produce circle patterns 1. Use a set of compasses to draw the pattern below Your teacher will show you how to do it. 2. Use a set of compasses to draw the pattern below Your teacher will show you how to do it. Page 25
S14s I have investigated the relationship between the radius and diameter using everyday objects 1. The Olympic symbol consists of five identical circles. Part of the symbol is shown in the diagram below. the length of the symbol is 45 centimetres the circles are equally spaced the gap between the adjacent circles is 1 5 centimetres. Calculate the radius of a circle. 2. An ornamental fence is made from semi circles. Part of the ornamental fence, made from 12 touching semi-circles, is shown below. 295.2 centimetres Calculate the radius of one semi-circle. Page 26
S15s Given the circumference, I can work out the distance travelled in a number of rotations of a wheel. 1. A toy train travels 157 centimetres when it completes one lap of the track. How far would it travel in 100 laps of the track? 2. A bike has a wheel which has a circumference of 204 centimetres. How far does the wheel travel in 250 rotations? 3. An ant is walking around the rim of a circular plant pot. The circumference of the pot is 25 7 centimetres. (a) How far will the ant walk in 10 laps of the plant pot? (b) How far will the ant walk in 100 laps of the plant pot? Page 27
A well nurtured and emotionally healthy pupil will know that they can improve their brain power through regularly applying themselves to his/her studies in class and by completing all of the tasks in this booklet. He/she will feel more included, respected and will develop greater levels of responsibility if you regularly discuss with them their progress, both progress in class and progress through this booklet. You will encourage him/her to be a passive learner and intellectually lazy if you show them how to attempt every question. Encourage them to think for themselves. Your child will achieve more if they actively experiment with the questions in this booklet, safe in the knowledge that they can learn from any mistakes made. Tips for Parents 1. Talk to your child on a regular basis about the work they are attempting in Mathematics. 2. Give praise for appropriate effort and resilience, and avoid praise which uses the words clever or smart. 3. Talk about your child's brain power improving through hard work and not being something that is fixed. 4. Mistakes are part of the learning process. Your child should be able to experiment with Maths safe in the knowledge that they can learn from their mistakes. 5. Talk about your child s progress in a way which emphasises their own ability to influence a positive and successful future. This will encourage them to become more resilient and equipped to meet the challenges of the course. Page 28