Grow your brain Green Book 17 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 Enlargement and Reduction 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. Angles and the Circle
E Enlargement and Reduction E1 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 2
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 3
5. Use a scale of 1cm to 5m to make an accurate scale drawing of the sketch below. All internal angles in the shape are right angles. 6. Use a scale of 1cm to 2m to make an accurate scale drawing of the sketch below. All internal angles in the shape are right angles. Page 4
E2 I can use a fractional scale factor to enlarge or reduce a shape on a grid. 7. Copy each shape into your jotter and enlarge them using a scale factor of 3. (a) (b) 8. Copy each shape into your jotter and enlarge them using a scale factor of 3 2. (a) (b) Page 5
9. Copy the shape into your jotter and reduce it using a scale factor of 3 5. 10. Copy the shape into your jotter and reduce it using a scale factor of 2 7. Page 6
11. Copy the shape into your jotter and reduce it using a scale factor of 3 8. 12. Copy the shape into your jotter and reduce it using a scale factor of 2 3. Page 7
F Using parallel lines, symmetry and circle properties to calculate angles F1 I understand the terms Acute Angle, Right Angle, Obtuse Angle, Straight Angle and Reflex Angle and can apply this understanding in a variety of contexts. 1. Write each letter in your jotter and the type of angle beside it. b c a d e t g f r s h q p m K i o n l j Page 8
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 of angle (acute, right, obtuse, straight or reflex) it is. 89 158 90 180 58 19 135 160 Page 9
F2 I can use letters to name vertices, lines, angles and shapes. 4. 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 10
5. 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 6. 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 7. 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 11
F3 I can use angle facts to deduce the size of missing angles. 8. 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 12
9. 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 13
10. 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. 11. Repeat question 3 with a pizzas cut into (a) Six slices. (c) Ten slices. (b) Four slices. (d) Five slices. Page 14
12. For each diagram, (i) Construct an equation with the information given (ii) Solve the equation to find the size of the missing angle. (a) 108 (b) s s r 30 (c) (d) 100 t u u t 70 t Page 15
13. 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 d f e 38 Page 16
14. In the diagram below find the size of the shaded angle. Clearly show all the steps to the answer. 63 77 32 15. In the diagram shown find the size of the shaded angle. Clearly show all the steps to the answer. 32 59 29 Page 17
16. The diagram below shows a pylon for carrying powerlines a b 120 d 100 c Page 18 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.
17. For each diagram find the size of the missing angles. Clearly show how you arrive at your answer. (a) a (b) 52 c d 112 b (c) (d) e f 113 g 27 h (e) 135 (f) 24 i j Page 19
A 18. In the diagram, ABC is an isosceles triangle. 63 Angle ABC is equal to 90. Find the size of the shaded angle. B C 19. In the diagram, PQR is an isosceles triangle. 108 P R Find the size of the shaded angle. Q Page 20
20. In the diagram, EFG is an isosceles triangle. Find the size of the shaded angle. E 30 65 F G 21. In the diagram, ABCD is a parallelogram. Find the size of the shaded angle. A 27 B D 23 C Page 21
F4 I can apply facts about the circle (angle in a semicircle and tangents to a circle) to calculate missing angles 22. In the kite below PQ is the tangent to the circle at Q and PS is the tangent to the circle at S. Q R 63 P S If angle QPS is 63, find angle QRS. 23. In the diagram, with circle centre O, triangle AOB is isosceles AB is a tangent to the circle at C Angle CAO is 26. Calculate the size of the shaded angle COB. Page 22
24. A circle, centre O, is below. In the circle PB is a diameter CR is a tangent to the circle at point P Angle BCP is 48. Calculate the size of angle EPR. 25. AD is a diameter of a circle, centre O. B and C are points on the circumference of the circle. Angle CAD = 25. Angle BDA = 46. Calculate the size of angle BAC. 26. In the diagram opposite, O is the centre of the circle PQ is a diameter of the circle PQR is a straight line RS is a tangent to the circle at S Angle OPS is 28. Calculate the size of angle QRS. Page 23