2. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Pinocchio's nose is 5cm long. Each time he tells a lie his nose doubles. How long is his nose after telling 9 lies? Click mouse to start answer sequences Start Lie 1 Lie 2 Lie 3 Lie 4 Lie 5 Lie 6 Lie 7 Lie 8 Lie 9 5cm 10cm 20cm 40cm 80cm 160cm 320cm 640cm 1280cm 2560cm 2560 cm or 25.6 metres

3. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 How many triangles can you find in the drawing? Click mouse to start answer sequences 9 6 7 8 9

4. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 E AB C D Steve is snookered on all the reds by the yellow. He plays the cue ball (white) along the line shown. The ball rebounds at right angles at all times. Which red is he most likely to hit? Click mouse to start answer sequences C

5. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 1 st 2 nd 3 rd Sam continues this pattern of discs. How many discs will there be in the 4 th pattern? Click mouse to start answer sequences 4 th 32

6. 10 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 05- 5 The triangle is translated to a new position. One line of the new position has been drawn for you. What are the new co-ordinates of the triangle after translation? Click mouse to start answer sequences (1,5) (2,1) (-3,4) (1,5)(2,1)(-3,4)

7. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The two red triangles are both the same size and are equilateral The three blue squares are the same size The total area of the three squares is 75cm 2 What is the total perimeter of both the triangles when added together? Click mouse to start answer sequences The area of one square is 75cm 2 ÷ 3 = 25cm 2 The length of one side of a square is 5cm The length of one side of a triangle is 5cm x 2 = 10cm The perimeter of a triangle is 10cm x 3 = 30cm The perimeter of two triangles is 30cm x 2 = 60cm 60cm

8. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Joe adds 0.25 to the red decimals and subtracts 0.3 from the blue decimals in this list. He then writes his new decimals in order starting with the largest. 0.50.050.350.450.70.551.2 Write the new order in the boxes below Click mouse to start answer sequences 0.20.30.60.150.40.80.9 0.20.60.80.30.40.15

9. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The chart shows the results of Premier League Football matches and the attendance figures Arsenal 3 Wigan 1 52 655 Everton 2 Man. City 0 39 677 Spurs 0 Aston Villa 0 27 402 Ben rounds each attendance to the nearest thousand and uses this information to then find the average attendance. What is the average attendance for the three games? Click mouse to start answer sequences 40 000 53 000 40 000 27 000 120 000 ÷ 3 = 40 000 53 000 + 40 000 + 27 000 = 120 000

10. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Lucy has a six-sided spinner. Which of her statements below are true or false? 1 5 2 3 6 3 C. If I spin the spinner twice and add the outcomes together the total will always be three or more. B. I have a 1 in 3 chance of spinning an even number. A. I have a 50% chance of spinning a 3. Click mouse to start answer sequences F T F I have a 33% chance of spinning a 3. I have a 2 in 6 chance or a 1 in 3 chance of spinning an even number. I could spin a 1 twice, making a total of 2

11. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 On a digital clock the numbers are made up of a series of small bars. E.g. Basic designThe number 6 Jack converts the time 3:38 p.m. and records it on to a 24-hour digital clock. How many small bars will he fill in altogether to show the digital time? Click mouse to start answer sequences 3:38 is 15:38 on a 24 hour clock 19

12. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 In a standard set of 28 dominoes the largest number of spots on any domino is 12 ( the double six) Jade sorts out all the dominoes that have a four on them. She adds together all the spots on all of these dominoes. What is the total number of spots she counts? Click mouse to start answer sequences 4949 45678910

13. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 4 5 3 2 11 4 3 5 22 1 3 4 5 Put the numbers 1 2 3 4 and 5 in the drawing below so that each line totals 9 Click mouse to start answer sequences There are several different orientations of the answer. The key number is 3 in the middle. 1 2 3 5 45 4 3 1 24 1 3 2 5 Etc.

14. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 If you look directly down on this shape which of the plan views below will you see? ABCDE Click mouse to start answer sequences A

15. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 11332244 Each number in the boxes that make the pyramid is the sum of the two numbers immediately above What number goes in the grey box? 11332244 5566 99121 220 Click mouse to start answer sequences

16. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 To buy one pencil costs 30p Jack buys a total of 26 pencils. How much change does he receive from £10? Packs of four pencils £1 per pack Use the information on the page to the best advantage £3.40 Jack can buy 6 packs (24) of pencils for £6 He then buys 2 separate pencils for a cost of 60p £6 + 60p = £6.60 £10 - £6.60 = £3.40 Click mouse to start answer sequences

17. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The radius of each circle is 25mm. Each vertex of the hexagon lies at the centre of a circle. What is the perimeter of the hexagon in centimetres? 50mm 10 x 50 mm = 500 mm = 50cm 50c m Click mouse to start answer sequences

18. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Amy works out the two number problems below. She then subtracts one answer from the other. ( 5 x 14 ) - ( 13 + 27 ) = 100 - ( 3 x 6) + ( 8 x 4 ) = What are her two possible answers? ( 5 x 14 ) - ( 13 + 27 ) = 100 - ( 3 x 6) + ( 8 x 4 ) = 70 - 40 = 30 100 - 18 + 32 = 114 114 - 30 = 84 30 - 114 = - 84 84 and - 84 Click mouse to start answer sequences

19. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A school netball ball match is played in two halves and lasts a total of 20 minutes. Westside School score a goal on average every 2½ minutes throughout the match. Eastside school score a goal on average every 2 minutes in the first half and a goal every ten minutes in the second half. How many goals are scored altogether? Westside school score 8 goals Eastside school score 5 goals in the first half and 2 goals in the second half; a total of 7 goals 8 + 7 = 15 15 goals Click mouse to start answer sequences

20. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 To find the volume of a cube the length of the cube is multiplied by its width and height. length width height Tom arranges four cubes the same size as shown. The total volume of the shape is 108cm 3 What is the length of each edge of the cubes? 3cm One cube has a volume of 108cm 3 ÷ 4 = 27cm 3 Length x width x height = 27cm 3 so each edge is 3cm 3cm x 3cm x 3cm = 27cm 3 Click mouse to start answer sequences

21. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The average of the four corner numbers in the number square is 21 What number is missing from square A? 1714A 251630 202218 If the average is 21 then the total must be 21 x 4 = 84 The total for the three known squares is 17 + 20 + 18 = 55 Square A is 84 - 55 = 29 29 Click mouse to start answer sequences

22. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The drawing is reflected in the dotted mirror line. Write the letter of the shape that shows this reflection AB C DE F E Click mouse to start answer sequences

23. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Ben puts the numbers on the left into a function machine. His outcomes are on the right. What process did the function machine perform to change the numbers? ? 11 5 8 41 17 29 Multiply by 4 and subtract 3 5x 4 = 20 20 - 3 = 17 8 x 4 = 32 32 - 3 = 29 11 x 4 = 44 44 - 3 = 41 Click mouse to start answer sequences

24. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 All the hexagons are regular. The perimeter of the white hexagon is 90cm What is the outer perimeter of A the striped shape B the checked shape? The striped shape has 18 sides 15cm x 18 = 270cm Each side of the white hexagon is 90cm ÷ 6 = 15cm The checked shape has 30 sides 15cm x 30 = 450cm Click mouse to start answer sequences

25. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Lucy finds 1/3 of a number, Jack finds ¼ of Lucy’s number, Tom finds 1/12 of Lucy’s number and Amy finds 1/8 of Jack’s number. Lucy’s answer is 32. What numbers do Jack, Tom and Amy have? Lucy’s number is 32 x 3 = 96 Jack’s number is 96 ÷ 4 = 24 Tom’s number is 96 ÷ 12 = 8 Amy’s number is 24 ÷ 8 = 3 Click mouse to start answer sequences

26. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Five children each have five hats. Each hat has five badges. Each badge has 5 stars. Each star has five points. How many points are there altogether? 5 x 5 x 5 x 5 x 5 children hats badges stars points 3125 Click mouse to start answer sequences

27. PRINTABLE VERSION OF EACH SLIDE

28. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Pinocchio's nose is 5cm long. Each time he tells a lie his nose doubles. How long is his nose after telling 9 lies?

29. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 How many triangles can you find in the drawing?

30. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 E AB C D Steve is snookered on all the reds by the yellow. He plays the cue ball (white) along the line shown. The ball rebounds at right angles at all times. Which red is he most likely to hit?

31. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 1 st 2 nd 3 rd Sam continues this pattern of discs. How many discs will there be in the 4 th pattern?

32. 10 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 05- 5 The triangle is translated to a new position. One line of the new position has been drawn for you. What are the new co-ordinates of the shape after translation?

33. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The two grey triangles are both the same size and are equilateral The three squares are the same size The total area of the three squares is 75cm 2 What is the total perimeter of both the triangles when added together?

34. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Joe adds 0.25 to the red decimals and subtracts 0.3 from the blue decimals in this list. He then writes his new decimals in order starting with the largest. 0.50.050.350.450.70.551.2 Write the new order in the boxes below

35. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The chart shows the results of Premier League Football matches and the attendance figures Arsenal 3 Wigan 1 52 655 Everton 2 Man. City 0 39 677 Spurs 0 Aston Villa 0 27 402 Ben rounds each attendance to the nearest thousand and uses this information to then find the average attendance. What is the average attendance for the three games?

36. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Lucy has a six-sided spinner. Which of her statements below are true or false? 1 5 2 3 6 3 C. If I spin the spinner twice and add the outcomes together the total will always be three or more. B. I have a 1 in 3 chance of spinning an even number. A. I have a 50% chance of spinning a 3.

37. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 On a digital clock the numbers are made up of a series of small bars. E.g. Basic designThe number 6 Jack converts the time 3:38 p.m. and records it on to a 24-hour digital clock. How many small bars will he fill in altogether to show the digital time?

38. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 In a standard set of 28 dominoes the largest number of spots on any domino is 12 ( the double six) Jade sorts out all the dominoes that have a four on them. She adds up the spots on all of these dominoes. What is the total number of spots she counts?

39. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Put the numbers 1 2 3 4 and 5 in the drawing below so that each line totals 9

40. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 If you look directly down on this shape which of the plan views below will you see? ABCDE

41. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 11332244 Each number in the boxes that make the pyramid is the sum of the two numbers immediately above What number goes in the grey box?

42. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 To buy one pencil costs 30p Jack buys 26 pencils. How much change does he receive from £10? Packs of four pencils £1 per pack Use the information on the page to the best advantage

43. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The radius of each circle is 25mm. Each vertex of the hexagon lies at the centre of a circle. What is the perimeter of the hexagon in centimetres?

44. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Amy works out the two number problems below. She then subtracts one answer from the other. ( 5 x 14 ) - ( 13 + 27 ) = 100 - ( 3 x 6) + ( 8 x 4 ) = What are her two possible answers?

45. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A school netball ball match is played in two halves and lasts a total of 20 minutes. Westside School score a goal on average every 2½ minutes throughout the match. Eastside school score a goal on average every 2 minutes in the first half and a goal every ten minutes in the second half. How many goals are scored altogether?

46. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 To find the volume of a cube the length of the cube is multiplied by its width and height. length width height Tom arranges four cubes the same size as shown. The total volume of the shape is 108cm 3 What is the length of each edge of the cubes?

47. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The average of the four corner numbers in the number square is 21 What number is missing from square A? 1714A 251630 202218

48. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The drawing is reflected in the dotted mirror line. Write the letter of the shape that shows this reflection AB C DE F

49. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Ben puts the numbers on the left into a function machine. His outcomes are on the right. What process did the function machine perform to change the numbers? ? 11 5 8 41 17 29

50. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 All the hexagons are regular. The perimeter of the white hexagon is 90cm What is the outer perimeter of A the striped shape B the checked shape?

51. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Lucy finds 1/3 of a number, Jack finds ¼ of Lucy’s number, Tom finds 1/12 of Lucy’s number and Amy finds 1/8 of Jack’s number. Lucy’s answer is 32. What numbers do Jack, Tom and Amy have?

52. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Five children each have five hats. Each hat has five badges. Each badge has 5 stars. Each star has five points. How many points are there altogether?