2. N.E. LINCS. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2005

3. N.E. LINCS. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2005 How to use the presentation Each question is presented twice. Slides with a red square in the top right corner are the tasks to be performed and are printable for child use. Click to select the duplicate slide to display the answer. A mouse will appear on the slide - click once The slide will then process the answer automatically and where appropriate present a strategy for solving the problem. When the process is complete a green arrow will appear. Click the green arrow and the slide will move to the next problem.

4. Printing slides for children’s use. Select the numbers of slides to be printed Select Ctrl P. Type slide numbers in the appropriate box. Suggest select: Pure black and white Frame slides Scale to fit paper Select print what: Highlight number of slides per page, (handouts 2 slides per page) works well. Select number of copies. Click OK.

5. Which number will make this number sentence correct? 5 x 4 x ? = 140

6. Which number will make this number sentence correct? 5 x 4 x ? = 140 5 x 4 x 7 = 140 Answer

7. Which numbers complete this sequence? -133192735

8. Which numbers complete this sequence? -133192735-511 The sequence is - add 8 to the previous number. To discover the sequence you may have to work backwards and subtract 8. Answer

9. What decimal fraction of this shape is shaded red?

10. Ans. 0.25 As a vulgar (ordinary) fraction the answer would be two- eighths or ¼. This is then changed into a decimal. Answer

11. Emily has three regular hexagons like the one below. Each side is 5cm long. She joins them to make a new shape. What is the perimeter of her new shape?

12. Emily has three regular hexagons like the one below. Each side is 5cm long. She joins them to make a new shape. What is the perimeter of her new shape? 70 cm The answer may be found by counting round each line of the shape in 5cm blocks. OR Each hexagon has a perimeter of 30cm. This makes 90 cm altogether. When they are joined 10cm of perimeter is hidden. They are joined twice, 90cm - 20cm = 70cm. 10 cm hidden here Answer

13. Each shape stands for a number. Use the information to work out the value of each shape. = = = x - ÷ 8 2 36

14. Each shape stands for a number. Use the information to work out the value of each shape. = = = x - ÷ 8 2 36 66 6 48 50 Answer

15. Find the four shapes hidden in the word search CYLINDERKITESPHERERHOMBUS R H R R E K P V T E H H M I F G Y L D O Z E I T N U M N J T H C O M B S I L Y C T F S P V L G D H O M B U S Y J L H R Y M L Y C S H KQ S K P H H O E P R X EI C Y L I N D E R K I T SPHERE H O M B U S

16. Find the four shapes hidden in the word search CYLINDERKITESPHERERHOMBUS R H R R E K P V T E H H M I F G Y L D O Z E I T N U M N J T H C O M B S I L Y C T F S P V L G D H O M B U S Y J L H R Y M L Y C S H KQ S K P H H O E P R X EI C Y L I N D E R K I T SPHERE H O M B U S Answer

17. Which of the blue shapes below has the same area as the shape on the grid? A C D B E

18. A C D B E 18 D Answer

19. Which five consecutive even numbers add up to 30?

20. 2, 4, 6, 8, 10 Answer

21. Estimate the size if this angle. N.b.this is a sketch of the original and may not be exact size if reproduced.

22. Estimate the size of this angle. 90 0 25 0 115 0 Leeway 110 0 to 120 0 Answer

23. The recipe makes 6 Yorkshire puddings. Adjust it for 8 Yorkshire puddings 240 g Flour 3 Eggs 360 ml Water 120 ml Milk

24. The recipe makes 6 Yorkshire puddings. Adjust it for 8 Yorkshire puddings 240 g Flour 3 Eggs 360 ml Water 120 ml Milk 320 g Flour 4 Eggs 480 ml Water 160 ml Milk Answer Two extra people is one third of six people. Find one third of each item and add it to the original amount.

25. ACalculate half of a quarter of 48. BA train leaves the station at 12:35. It arrives after travelling for 100 minutes. What time does it arrive. Answer in 24 hour clock. CJack receives £3.70 change from £10. He buys 2 items. One cost 50p. What did the other item cost?

26. ACalculate half of a quarter of 48. BA train leaves the station at 12:35. It arrives after travelling for 100 minutes. What time does it arrive. Answer in 24 hour clock. CJack receives £3.70 change from £10. He buys 2 items. One cost 50p. What did the other item cost? 6 14:15 £5.80 Answer

27. Each cube weighs the same. The cylinder weighs 0.6 Kg. What is the weight of 1 cube? 2Kg6Kg

28. Each cube weighs the same. The cylinder weighs 0.6 Kg. What is the weight of 1 cube? 2Kg6Kg 800 grams Total weight is 3Kg or 3000 g (on scale) Cylinder weighs 600g (0.6 Kg) Three cubes weigh 3 000g - 600g = 2 400 g altogether. One cube weighs 800g One cube weighs 2 400 g ÷ 3 800 grams Answer

29. TRUE OR FALSE? All odd numbers are prime numbers. All rectangles are quadrilaterals. A litre of water weighs 1 Kilogram. All 3-digit numbers are divisible by three without a remainder.

30. TRUE OR FALSE? All odd numbers are prime numbers. All rectangles are quadrilaterals. A litre of water weighs 1 Kilogram. All 3-digit numbers are divisible by three without a remainder. FALSE TRUE FALSE TRUE Answer

31. Jack multiplies 24 by 15 on his calculator. He presses the wrong digits and gets the answer 495 on the display. What is the difference between the correct answer and the one Jack sees on the calculator display?

32. 495 - 360 = 135 24 x 15 = 360 Answer

33. Use the information given to put the heights of the five children in order starting with the smallest child. Tom is 8 cm smaller than Jack. Jack is 2 cm taller than Ben. Ben is 1.5 m tall. Jack is 4 cm smaller than Emily. Amy is 10 cm smaller than Ben.

34. Use the information given to put the heights of the five children in order starting with the smallest child. Tom is 8 cm smaller than Jack. Jack is 2 cm taller than Ben. Ben is 1.5 m tall. Jack is 4 cm smaller than Emily. Amy is 10 cm smaller than Ben. AMY 140 cm TOM 144 cm BEN 150 cm JACK 152 cm EMILY 156 cm Answer HINT: Work in cm.

35. Both shapes are regular and have the same perimeter. How long is one side of the triangle? 12 cm

36. Both shapes are regular and have the same perimeter. How long is one side of the triangle? 12 cm Perimeter of equilateral triangle is 60 cm. 1 side is 60 ÷ 3 = 20 cm. Perimeter of regular pentagon is 5 x 12 cm = 60cm Answer

37. The numbers in the pyramid are calculated by adding the two numbers immediately below. Complete the pyramid. 2311 16

38. The numbers in the pyramid are calculated by adding the two numbers immediately below. Complete the pyramid. 2311 16 13 1514 3130 61 Answer

39. Each cube has a surface area of 6 square units. The shape below is made from similar cubes What is the total surface area of the new shape?

40. 18 square units. Total surface area is 6 x 4 = 24. Each join takes away 2 faces or 2 square units. There are three joins so the new area is 24 - 6 = 18 square units 2 square units hidden here and here Answer Or you could just count

41. It takes 3 of the middle container to fill the large one. It takes six of the small one to fill the middle one. How many millilitres does the small container hold? 450 ml

42. It takes 3 of the middle container to fill the large one. It takes six of the small one to fill the middle one. How many millilitres does the small container hold? 450 ml ÷3 ÷6 150 ml 25 ml Answer

43. Each line in the drawing adds up to 1000. Complete the boxes to make the target total for each line. 550 375250 150

44. Each line in the drawing adds up to 1000. Complete the boxes to make the target total for each line. 550 375250 150 375 475 75 Answer

45. Amy makes rectangular shapes by linking three similar rectangles. How many rectangles can you count altogether in Amy’s drawing?

46. 11 3 2 2 4 Answer

47. Below is an EQUATION 3n + 9 = 30 What does n equal?

48. 3n = 30 - 9 3n = 21 n = 7 Answer

49. A house is bought for £175 000. A year later the house is sold for 10% more than it cost originally. What is the new price?

50. 10% 0f £175 000 is £17 500. Add together £175 000 and £17 500. New price £192 500. Answer

51. The box is as wide as it is tall. What is the volume of the box? 12 cm 5 cm

52. The box is as wide as it is tall. What is the volume of the box? 12 cm 5 cm Volume = l x b x h 12cm x 5cm x 5cm = 300cm 3 Answer

53. Ben says that a x a x a = a 3 a 3 = 125 What does a equal?

54. a = 5 5 x 5 x 5 = 125 Answer

55. The number completing this number sentence is the same for each box. Which number completes the sentence? 175 = + 45 + 40 + +

56. The number completing this number sentence is the same for each box. Which number completes the sentence? 175 = + 45 + 40 + + 30 Another 90 needs to be added to 45 + 40 to make 175. As each box is the same amount the answer is 30 Answer

57. BONUS ROUND All three questions must be answered correctly to score bonus points A.Six similar sweets cost a total of £2.40. How much does 1 sweet cost? B.Two boxes weigh 100 g altogether. One weighs 10 g more than the other. How much does each box weigh? C. How many minutes are there between 9:25 a.m. and 11:15 a.m.?

58. BONUS ROUND All three questions must be answered correctly to score bonus points A.Six similar sweets cost a total of £2.40. How much does 1 sweet cost? B.Two boxes weigh 100 g altogether. One weighs 10 g more than the other. How much does each box weigh? C. How many minutes are there between 9:25 a.m. and 11:15 a.m.? 0.40p 55 g & 45 g 110 min. Answer

59. Amy has some jumbled mathematical shapes. Can you sort them out? A.LY IN RED C B.GO ON ACT C.RING A TEL

60. Amy has some jumbled mathematical shapes. Can you sort them out? A.LY IN RED C B.GO ON ACT C.RING A TEL CYLINDER OCTAGON TRIANGLE Answer

61. Draw any two lines of symmetry on the shape below

62. Answer

63. What percentage of this shape is not shaded red?

64. 15 squares out of 20 are not red. This is ¾ of the shape = 75% 25% of the squares are red. 100% - 25% = 75% not red Answer

65. Estimate the length of a given curved line in mm. [There is a leeway for the answer]

66. A line of this configuration was given. The answer was between 140 and 160 mm. Answer

67. Which two decimal fractions are shown on the number line? 2.0 4.0 A B

68. Which two decimal fractions are shown on the number line? 2.0 4.0 A B A = 1.7 B = 3.4 Answer

69. How many cubes are needed to build this shape? (Look and think carefully)

70. 14 cubes The arrows show where hidden cubes must be placed to make the shape stand up. Answer

71. Emily uses five digit cards. She makes the smallest 3-digit odd number and makes a note of it. She then makes the largest 3-digit even number. She subtracts her two answers. What is her result? 98374

72. 98374 374 984 SMALLEST 3- DIGIT ODD NUMBER LARGEST 3- DIGIT EVEN NUMBER 984 374 - 376 Answer

73. The coins show Jack’s change from £10. Which item did he buy? £5.45£4.45 £6.45 £4.55 £4.65

74. The coins show Jack’s change from £10. Which item did he buy? £5.45£4.45 £6.45 £4.55 £4.65 The money totals £5.45. The plant at £4.55 added to the change gives Jack’s original total of £10 Answer

75. The vertical lines of the square pass through the centres of the circles. The radius of each circle is 5.5 cm. What is the perimeter of the square?

76. The radius of the circle is 5.5 cm The diameter of the circle is 11 cm The sides of the square and the diameter are the same length = 11 cm 11 cm 4 x 11 cm = 44 cm Answer

77. The advert shows holiday prices to Costa Packet. COSTA PACKET The ideal family holiday 14 Nights at the Hotel Fawlty Half board Under 16’s 50% reduction. Under fives go for £20 £240pp Mr. and Mrs. Smith take grandma, baby Jake [3 years old] and Lucy [15 years old] on holiday. How much does the holiday cost altogether?

78. The advert shows holiday prices to Costa Packet. COSTA PACKET The ideal family holiday 14 Nights at the Hotel Fawlty Half board Under 16’s 50% reduction. Under fives go for £20 £240pp Mr. and Mrs. Smith take grandma, baby Jake [3 years old] and Lucy [15 years old] on holiday. How much does the holiday cost altogether? £890 Answer

79. The graph shows how a number of children travel to school 2 CHILDREN A. How many more children walked than came by bus? B. 60 children took part in the survey. How many came to school on a bicycle? WALK CAR BICYCLE TAXI BUS

80. The graph shows how a number of children travel to school 2 CHILDREN A. How many more children walked than came by bus? B. 60 children took part in the survey. How many came to school on a bicycle? WALK CAR BICYCLE TAXI BUS 21 8 21 - 8 = 13 60 - 47 = 13 15 3 Answer

81. 40% 0f a number is 60. What is the number?

82. If 40% is 60 then 10% of the number is 60 ÷ 4 = 15. 100% is 10 x 15 = 150 100% is [2 x 40%] + 20%. 2 x 40% = 120 20% of the number is 30 The number is 120 + 30 = 150 Answer

83. a BONUS ROUND - All three questions must be answered correctly. The triangle is equilateral. Calculate angle a Each square on the grid represents 1cm 2. What is the area of the shape drawn on the grid? The area of the large square is 36cm 2. What is the area of the blue square?

84. a BONUS ROUND - All three questions must be answered correctly. The triangle is equilateral. Calculate angle a Each square on the grid represents 1cm 2. What is the area of the shape drawn on the grid? The area of the large square is 36cm 2. What is the area of the blue square? 14cm 2 9cm 2 180 o - 60 o = 120 0 Answer

85. Jack’s parents’ car weighs 1.2 tonnes Jack’s bicycle weighs 24 000 grams. What is the weight of the car and bicycle altogether in Kilograms?

86. Jack’s parents’ car weighs 1.2 tonnes. Jack’s bicycle weighs 24 000 grams. What is the weight of the car and bicycle altogether in Kilograms? 1 200 Kg 24 Kg 1 2 24 Kg Answer

87. Ben thinks of two numbers. Their total is 5000. Number A is 1200 smaller than number B. What is the value of each number?

88. Number A is 1900 number B is 3100 Answer

89. Both shapes below are regular and have the same perimeter. The length of one side of shape B is 120 cm. What is the length of one side of shape A? AB

90. AB 480 cm ÷ 5 = 96 cm Perimeter 480cm ( 4 x 120cm) Answer

91. The chart shows the cost of making telephone call. Listeners Telephone Co. Charges Standing Charge £25 Local calls 5p per minute National calls 20p per minute

92. The chart shows the cost of making telephone call. Listeners Telephone Co. Charges Standing Charge £25 Local calls 5p per minute National calls 20p per minute 120 minutes Answer

93. King’s Park Rovers win a home football match 2-1. What are the possible half-time scores at the game?

94. 0-0 1-0 2-0 2-1 1-1 0-1 Answer

95. Emily earns 50p one day. The next day she earns £1. Her wages double each day from the day before. How much does she earn altogether in eight consecutive days?

96. Day 1 50p Day 2 £ 1 Day 3 £ 2 Day 4 £ 4 Day 5 £ 8 Day 6 £16 Day 7 £32 Day 8 £64 £127.50 Answer

97. AB 55 cm

98. AB 185 cm Answer 30cm45cm 55cm

100. N.E. LINCS PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2005

101. N.E. LINCS. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2005 How to use the presentation Each question is presented twice. Slides with a red square in the top right corner are the tasks to be performed and are printable for child use. Click to the duplicate slide to display the answer. A mouse will appear on the slide - click once The slide will then process the answer automatically and where appropriate present a strategy for solving the problem. When the process is complete a green arrow will appear. Click the green arrow and the slide will move to the next problem.

102. Printing slides for children’s use. Select the numbers of slides to be printed Select Ctrl P. Type slide numbers in the appropriate box. Suggest select: Pure black and white Frame slides Scale to fit paper Select print what: Highlight number of slides per page, (handouts 2 slides per page) works well. Select number of copies. Click OK.

103. Which three numbers from this list make 200 when added together? 99 61 80 21 39 Which three numbers from this list make 200 when added together? 99 61 80 21 39

104. Which three numbers from this list make 200 when added together? 99 61 80 21 39 Which three numbers from this list make 200 when added together? 99 61 80 21 39 Answer

105. The local zoo receives a delivery of tropical spiders and snakes. They are all in the same box. The zoo keeper counts 64 legs and 23 heads. How many snakes are there?

106. The local zoo receives a delivery of tropical spiders and snakes. They are all in the same box. The zoo keeper counts 64 legs and 23 heads. How many snakes are there? 15 SNAKES [23 - 8 = 15] [The 64 legs belong to 8 spiders because it is very difficult to count snakes ‘legs’] Answer

107. A B C D E

108. A B C D E

109. x30 600 530 Complete the grid and write the answer to the calculation

110. x30 600 530 6 120 150 20 Complete the grid and write the answer to the calculation 36 x 25 = 900 Answer

112. 165p or £1.65 9 2 1250 mm Answer -3 -4 -5 -6 -7

113. 1Kg3Kg A C 1200 g

114. 1Kg3Kg A C 1200 g 800g1600g Answer

116. 23rd in line Answer

118. 595 m 345m250m Answer

120. 16 Answer

121. ABCDEF

122. ABCDEFE

123. 9184 122315 167116 1820510

124. 9184 122315 167116 1820510 5, 6, 8, 9, 14, 1 Answer

126. Perimeter = 33 cm 11 cm Answer

127. 15 cm 45 cm

128. 15 cm 45 cm 215 cm Answer

129. 0 100 200 300 The graph shows the number of tyres sold at a garage over six days. MonTueWedThurs Fri Sat A. How many more tyres were sold on Monday than Tuesday? B. On Wednesday, Thursday and Friday 475 tyres were sold altogether. How many tyres were sold on Thursday? C. A tyre costs on average £40. What was the value of tyres sold on Friday altogether?

130. 0 100 200 300 The graph shows the number of tyres sold at a garage over six days. MonTueWedThurs Fri Sat A. How many more tyres were sold on Monday than Tuesday? B. On Wednesday, Thursday and Friday 475 tyres were sold altogether. How many tyres were sold on Thursday? C. A tyre costs on average £40. What was the value of tyres sold on Friday altogether? 50 125 £4 000 Answer

131. D I A G O N A L P A R A L L E L F R A C T I O N

132. D I A G O N A L P A R A L L E L F R A C T I O N D I A G O N A L P A R A L L E L F R A C T I O N Answer

134. 49 books Answer

135. Petrol in litres 60 L0 L EF

136. Petrol in litres 60 L0 L EF A journey of 76Km use 9.5 Litres of fuel. ¾ of the tank is 45 Litres of fuel 45 L - 9.5L = 35.5L Answer

137. CCCCC C CCCCCC

138. CCCCC C CCCCCC Ben eats 8 pieces, Amy eats 6 pieces, Jack eats 10 pieces Answer

139. 451 374 344 1399 489 401 349 466 351 3420 333 2400 444 501 299

140. 451 374 344 1399 489 401 349 466 351 3420 333 2400 444 501 299 Answer

144. 5 ÷ 8 = 0.625 Answer

146. 10% of £12 800 = £1 280 5% of £12 800 = £640 15% of £12 800 = £1 920 Selling price = £12 800 - £1 920 = £10 880 Answer

148. 24 x 60 = 1 440 min [24 hours] 1440 x 10 = 14 440 min [240 hours] Answer

149. 3628 52 29

150. 3628 52 29 13 5120 Answer

152. Square Answer

153. 1223 8

154. 1223 8 246 24 192 Answer

155. 14

156. 14 1 3 4545 1515 1 4545 3 1515 += 5

158. Emily spends £20 - £8.45 = £11.55 Answer

160. Any 6 x 3 rectangle [oblong] in any orientation 18units 2 Perimeter 18 units Answer

162. 15, 24, 33, 42, 51, 60 Answer

163. 62 4

164. 62 4 3 15

166. Complete one vertical and horizontal line to help you The grid is 5 x 9 She can cut 45 squares from one sheet. From 15 sheets she will cut 45 x 15 = 675 squares Answer

168. 348m - [163m + 119m + 8m] 348m - 290m = 58m Answer

170. £2 625 45 bars 180 0 - 85 0 = 95 0 Answer

172. Two programmes last 180min. - 75min. = 105min. The second programme lasts 105min - 50min, = 55min. Answer

174. 271, 273, 281, 283 Answer

176. The outer squares are double the area of the one inside 3cm 2 6cm 2 12cm 2 24cm 2 48cm 2 Answer

177. Number of squares Number of circles 13 25 37

178. Number of squares Number of circles 13 25 37 The pattern is - number of squares equals the number of circles subtract one then halve your answer. 25 - 1 = 24 Half of 24 is 12 squares Answer

179. 112926141823 8242615221322 11912236247

180. 112926141823 8242615221322 11912236247 PYRAMID SCALENE PRODUCT Answer

182. The square and rectangle have a common side 5cm long The area of the square is 5cm x 5cm = 25cm 2 5cm Answer

184. One number is 800 ÷ 4 = 200. The other number is 350 more than this number. The two numbers are 550 and 200 Answer

185. Book A 852.259 Book B 825.955 Book C 582.529 Book D 852.529 Book E 825.928 Book F 851.016

186. Book A 852.259 Book B 825.955 Book C 582.529 Book D 852.529 Book E 825.928 Book F 851.016 C E B F A D Book C 582.529 Book E 825.928 Book B 825.955 Book F 851.016 Book A 852.259 Book D 852.529 Answer

187. Amy and Jack are both saving for a digital camera costing £175. Amy has saved £97 and Ben has saved £108. How much more do they each have to save? £175

188. Amy and Jack are both saving for a digital camera costing £175. Amy has saved £97 and Ben has saved £108. How much more do they each have to save? £175 Amy needs £175 - £97 = £78 Ben needs £175 - £108 = £67 Answer

192. 5n = 66 - 6 5n = 60 n = 60 ÷ 5 = 12 Answer

194. The smallest number is 45.9 less than 98.4. 98.4 - 45.9 = 52.5 52.5 98.4 Answer

196. One-eighth Two-sixteenths = one eighth Answer

197. 42 0 ARSENAL MAN. UTD. EVERTON CHELSEA LIVERPOOL The chart shows how many children support the top 5 Premiership football teams 2005 15 children supported Arsenal. How many supported Chelsea?

198. 42 0 ARSENAL MAN. UTD. EVERTON CHELSEA LIVERPOOL The chart shows how many children support the top 5 Premiership football teams 2005 15 children supported Arsenal. How many supported Chelsea? 7 children 15 children = 90 0 1 child = 6 0 So 42 0 = 7 children Answer