Grow your Yellow 2 The wee Maths Book of Big Brain Growth Measure, Symmetry, coordinates and Angles. 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.
Tips for Parents #2(a) Talk to you child on a regular basis about being a resilient and reflective learner 1. Reflective learners try to learn from mistakes Ask your child to give you examples of where they learned from a mistake they had made. 2. An assessment are not an end point, it is part of the learning process. Your child will sit a Mathematics assessment soon. After the assessment encourage him/her to celebrate what they achieved, but more importantly to identify mistakes which he/she will work hard to learn from. Page 2
Measure (3-17b) M1s I can read scales given in Whole Number graduation 1. Jamie has made a mistake while constructing his number line (a) Copy the line and renumber it the way you think it should be? (b) What advice could you give Jamie for the next time he draws a number line, so that he can learn from this mistake? 2. Can you spot the mistake in these each number line? (a) (b) Page 3
3. Draw a number line that satisfies each of the following conditions (a) The number line starts at zero. (b) The number line goes up in twos. (c) Starting at zero, only write each second number on your number line. (d) The last number on your number line should be 20. 4. Draw another number line that satisfies each of the following conditions (a) The number line starts at 100. (b) The number line goes up in fives. (c) Starting at 100, write each fourth number on your number line. (d) The last number on your number line should be 200. 5. Draw your last number line so that satisfies each of the following conditions (a) The number line starts at 20. (b) The number line goes up in fours. (c) Starting at 20, write each second number on your number line. (d) The last number on your number line should be 60. Page 4
6. What numbers are located at positions a) to i) on the number lines below? 7. Two rulers are shown below. (a) Write down the length of the crayon (b) Write down the length of the pencil Page 5
8. For each protractor, write down the size of the angle shown. (a) (b) (c) Page 6
9. 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? 10. David realised he was driving in a 60 miles per hour zone. He looked at his speedometer. Should he change his speed? Justify your answer Page 7
11. Some water had been added to the measuring jars below. How much water is needed to fill each jar to the top mark? (a) (b) (c) 150ml 75ml 300ml 100ml 50ml 200ml 50ml 25ml 100ml 12. John 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 Page 8
M2s I can read scales given in graduations to one decimal place 1. What numbers are located at a) to h) on these number lines 2. What number is each arrow pointing to? (a) (b) Page 9
3. Write down each of the number being pointed to by the arrows (a) (b) (c) (d) (e) (f) Page 10
4. Write down the length of each object in millimetres and centimetres. (a) (b) (c) (d) (e) Page 11
5. Eva has a model car shown below. Eva has a box which is 65 mm long. Should her model car fit in the box? Justify your answer. 6. The line in the diagram has to be extended to be 9 5cm. By what length must the line be extended? Show your working Page 12
7. Ben is doing a sponsored weight loss. Ben s weight in kilograms (kg) at the start is shown on the bathroom scale. What was Ben s weight at the start of his sponsored weight loss? 8. (a) Do you think the ruler shown measures centimetres? (b) What is the length of the leaf in whatever units are represented? 9. 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 13
M3t I can use a ruler and a protractor to measure and draw accurate lines and angles 1. Using a ruler to help find the perimeter of each of these shapes in centimetres. (a) (b) 2. Using a ruler to help find the perimeter of each of these shapes in millimetres. (a) (b) Page 14
3. Use a protractor to measure the angles below. (a) (b) (c) (d) 4. Draw angles which are of the following sizes: (a) 43º (b) 127º (c) 53º (d) 151º Page 15
5. Below are four sketches of angles. Make and accurate drawing of each of the sketches. 6. The sketch below shows the dimensions of a mobile phone s screen. Make an accurate drawing of the phone s outline. Page 16
7. 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 17
9. 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 18
10. 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 19
M4t I the context of measure, I understand that the first two digits after the decimal point represent tenths and hundredths respectively. The rulers below measure centimetres. Write down, in centimetres and millimetres, the measurements indicated by the arrows. 1. (a) (b) (c) 2. (a) (b) (c) 3. (a) (b) (c) Page 20
4. The three stopwatches below measure time intervals to the nearest hundredth of a second. (i) (ii) (iii) (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. 5. Ski Sunday is a program which show a variety of snow sports. The result of the men s downhill is shown below. 1. M Kane 1min 32 21 secs 2. D Marsden 1min 32 23 secs 3. S Crichton 1min 32.53 secs The commentator made the following comments. This was a tight race, only 2 tenths of a second between first and second. Then 3 tenths of a second between second and third Can you spot a mistake? Justify your answer Page 21
6. Match the numbers in Bubble A, with the equivalent value in Bubble B. 0 01 0 03 0 11 Bubble A 0 1 0 3 Bubble B 7 100 11 100 1 100 10 0 07 100 0 7 30 100 7 10 3 100 7. Match the numbers in Bubble C, with the equivalent value in Bubble D. 0 23 0 2 0 04 Bubble C 0 4 0 8 Bubble D 8 10 23 0 02 100 0 5 2 10 4 100 2 100 5 10 40 100 Page 22
Tips for Parents #2(b) Talk about your child s progress in a way which emphasises their own ability to influence a positive and successful future. 1. Focus you child s attention on the questions they did not manage to successfully complete. Don t concentrate too much on class averages. Focus on what they have mastered and the areas they meet to put in more effort in order to make improvements. 2. Relate grades to honest and realistic estimation of how well your child prepared. Preparation includes classroom application, at all times, and home study/revision. A way to visualize this is to consider a result of 40% meaning the meed to improve revision/study/preparation by 60%. Page 23
Symmetry (2-19a, 3-19a) S1s I can recognise, draw and complete simple symmetrical figures using line symmetry Complete Symmetry Worksheet 1. S2t I can illustrate the lines of symmetry for a range of 2D shapes and complete more complex symmetrical pictures and patterns Complete Symmetry Worksheet 2 and 3. S3t I can create or copy a tiling using a shape template Complete Tiling worksheet 1. Page 24
Coordinates (2-18a, 3-18a) S4s I can read coordinates from a grid and plot points on a grid For questions 1 to 3 write the coordinates of each point. 1. 2. 3. 4 Using a ruler draw a neat 10 square by 10 square coordinate diagram (correctly numbered and labelled) and plot the following points. Write the letter beside each point A(3, 0) B(0,5) C(2, 7) D(7, 3) E(2, 4) F(0, 9) G(6, 7) H(4, 4) I(8, 0) J(9, 8) K(4,9) L(0, 0) Page 25
Page 26 5. Write down the coordinate of the points A to I shown on the coordinate diagram shown. 6. Write down the coordinates of the vertices of the rectangle shown in the coordinate diagram. y x 0 2 4 6 8 10 2 4 6 8 10 A B C D E F G H I y x 0 2 4 6 8 10 2 4 6 8 10 R E F S
7. Write down the coordinates of the vertices of the rhombus shown in the coordinate diagram. y 10 8 S 6 4 V T 2 0 U 2 4 6 8 10 x 8. Write down the coordinates of the vertices of the parallelogram shown in the coordinate diagram. y 10 8 6 4 2 0 C B T A 2 4 6 8 10 x Page 27
S5s I have successfully made a picture by plotting points on a coordinate grid, joining them up 1. Draw an x-axis from 0-18 and a y-axis from 0 20 like the grid shown. 2. Plot the co-ordinates below on your grid. Join up the co-ordinates in order as you plot them. (6,1) (6,3) (4,1) (3,3) (4,4) (4,3) (6,4) (6,5) (7,15) (9,18) (10,19) (13,19) (14, 18) (16, 15) (17, 5) (16, 4) (16, 3) (17, 4) (17, 1) Page 28
3. Now on the same diagram plot the next set of coordinates below (a) (8, 13) (8, 15) (10, 15) (10, 13) (8, 13) Put a separate cross at (9, 14) (b) (13, 13) (13, 15) (15, 15) (15, 13) (13, 13) Put a separate cross at (14, 14) (c) (7, 15) (8, 16) (10, 16) (11, 15) (12, 15) (13, 16) (15, 16) (16, 15) (16, 13) (15, 12) (13, 12) (12, 13) (11, 13) (10, 12) (8, 12) (7, 13) (7, 15) (d) (8, 9) (16, 9) (15, 7) (13, 6) (11, 6) (9, 7) (8, 9) (e) (6, 7) (8, 5) (15, 5) (17, 7) (17, 6) (16, 5) (16, 0) (7, 0) (7, 5) (6, 6) (f) (11, 3) (12, 3) (11, 2) (10, 3) (11, 4) (g) (5, 7) (5, 6) (4, 4) (2, 2) (1, 2) (5, 6) (h) (i) (8, 17) and (8, 18) (ii) (9, 18) and (10, 18) (iii) (10, 19) and (10, 20) (iv) (11, 19) and (11, 20) (v) (12, 19) and (12, 20) (vii) (13, 19) and (13, 20) (viii) (14, 18) and (14, 19) (ix) (15, 17) and (15, 18) Page 29
S6t I can read and plot points in four quadrants. 1. Write down the coordinates of each points A to L A y K C J -5 D 5 F B 0 5 L E -5 I H G x Page 30
2. Look at the Cartesian Diagram below. List the coordinates of the points P, Q, R, S, T and U. y 10 Q X P X 5 X R 10 5 5 10 T X x U X 5 X S 10 3. Copy the axes above then plot and label the points A(-2, 6), B(5, 9), C(-7, -3) and D(6, -8). Page 31
S7t I can identify the x-coordinate and the y-coordinate of a point 1. Use the diagram below to answer the following questions. (a) Write the x-coordinate of: (i) W (ii) T (iii) Z (b) Write the y-coordinate of: (i) U (ii) S (iii) V (c) Which two points have the same: (i) x-coordinate (ii) y-coordinate (d) Which point has the same x-coordinate and y-coordinate? (e) The point K has the same x -coordinate as U and the same y - coordinate as S. Write the coordinates of K Page 32
2. Look at the coordinate map below Write down all of the places on the map with (a) a x-coordinate of 5. (b) a y-coordinate of 4 or more. (c) a x-coordinate of 2. (d) a y-coordinate of -3 or less. (e) a x-coordinate of -3. (f) a y-coordinate of between -3 and 4. (g) a x-coordinate of -5. Page 33
Angle (MTH 2-16a, MTH 2-17a, MTH 2-17b, MTH 2-16a, MTH 3-17a) S8s I can classify angles by size (right, acute, obtuse, straight and reflex) 1. Write each letter in your jotter and the type of angle beside it. b a c e d j o n m h f l k i g Page 34
2. Copy the table into you jotter. Acute Right Obtuse Straight Reflex Put these angles into the correct column 90, 180, 127, 35, 270, 97, 88, 249, 177, 23, 310. 3. Write down each of the angles, shown in Charlotte s web, in your jotter. Then beside each angle, write down the type (acute, right, obtuse, straight or reflex). 89 158 90 180 58 19 135 160 Page 35
S9t I can use letters to name vertices, lines, angles and shapes. 1. Some pupils are taking part in a tresure hunt. D X (Finish) Z V (Start) A K S (a) Write down the name of each of the acute angles. (b) Write down the names of the obtuse angles. (c) Write down the name of the right angle. Page 36
2. ABCD is a quadrilateral. (a) What is the name of the vertex at the 132 angle? A 42 3 2 cm B 102 (b) What is the name of the 3 2cm side? (c) What is the size of angle BCD? D 132 84 C 3. PQRST is a pentagon. (a) What is the name of the vertex at the 72 angle? Q 72 R 132 103 S (b) What is the name of the 5 6cm side? 139 (c) What is the size of angle QRS? P 5 6 cm 94 T 4. In the diagram shown: Y Z (a) What is the name of the vertex at the acute angle? (b) What are the names of the right angles? (c) What is the name of the longest side? W (d) What is the name of the obtuse angle? X Page 37
S10t I can carry out calculations and deduce the size of missing angles using supplementary, complementary sum of the angles in a triangle and vertically opposite 1. For each diagram, (i) Construct an equation with the information given (ii) Solve the equation to find the size of the missing angle. (a) (b) b 44 65 a 28 (c) (d) d 135 145 c Page 38
2. For each diagram, (i) Construct an equation with the information given (ii) Solve the equation to find the size of the missing angle. (a) (b) 243 p q 52 (c) (d) r s 132 44 28 Page 39
3. The pizza below has been cut into 8 slices. The mathematical name for the shape of each slice is a sector. A pizza is cut into 8 equal slices, or sectors. x (i) Let x be the angle at the point of the sector. Write down an equation in x. (ii) Solve the equation to find x. 4. Repeat question 3 with a pizzas cut into (a) Six slices. (c) Ten slices. (b) Four slices. (d) Five slices. Page 40
5. For each diagram, (i) Construct an equation with the information given (ii) Solve the equation to find the size of the missing angle. (a) t (b) s s t t 30 (c) (d) 70 70 u 56 u 87 Page 41
6. For each diagram find the size of the missing angles. Clearly show how you arrive at your answer. (a) (b) c 38 a b 82 43 (c) (d) 43 82 f 38 d e Page 42
7. In the diagram below find the size of the shaded angle. Clearly show all the steps to the answer. 63 77 32 8. In the diagram shown find the size of the shaded angle. Clearly show all the steps to the answer. 32 59 29 Page 43
9. The diagram below shows a pylon for carrying powerlines a b 120 d 100 c Find the size of all the angles marked by letters. How to get the correct answer might not be obvious at first as there are many ways to do this problem You have to be prepared to experiment and you might make mistakes. If you make a mistake don t get upset learn from it. Page 44