Mathematical challenges for able pupils. Year 5 B Securing number facts, understanding shape
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1 Mathematical challenges for able pupils Year 5 B Securing number facts, understanding shape
2 Square it up You need six drinking straws each the same length. Cut two of them in half. You now have eight straws, four long and four short. You can make 2 squares from the eight straws. Arrange your eight straws to make 3 squares, all the same size. Visualise 2-D shapes.
3 For example: Solution to Square it up Visualise 2-D shapes.
4 A perfect match 1. A matchbox tray slides into its outer cover. In how many different ways can you do this? Visualise 2-D shapes.
5 A perfect match Imagine a cube and an open box just large enough to hold it. In how many different ways can you fit the cube into the box? Visualise 2-D shapes.
6 Solution for a perfect match 1. A matchbox tray fits into its outer cover in 4 different ways. 2. A cube will fit into a box with any one of its 6 faces uppermost. Each face can be rotated into any one of 4 different positions. So there are 6 x 4 = 24 ways of fitting the cube in the box. Visualise 2-D shapes.
7 Spot the shapes 1. How many triangles can you count? Visualise 2-D shapes. Explain methods and reasoning.
8 Spot the shapes 2. How many squares can you count? Visualise 2-D shapes. Explain methods and reasoning.
9 Spot the shapes 3. Draw your own diagram to count triangles. Don t use too many lines! How many triangles can a friend find? Can you find more? Visualise 2-D shapes. Explain methods and reasoning.
10 Solution for Spot the shapes 1. There are 11 triangles. 2. There are 17 squares. Visualise 2-D shapes. Explain methods and reasoning.
11 Four by four You need some squared paper. This 4 by 4 grid is divided into two identical parts. Each part has the same area and the same shape. Find five more ways of dividing the grid into two identical parts by drawing along the lines of the grid. Rotations and reflections do not count as different! Visualise 2-D shapes. Find fractions of shapes.
12 Four by four Explore ways of dividing a 4 by 4 grid into two parts with equal areas but different shapes. Visualise 2-D shapes. Find fractions of shapes.
13 Solution to Four by four Did you find any more? Visualise 2-D shapes. Find fractions of shapes.
14 Make five numbers Take ten cards numbered 0 to 9. Each time use all ten cards. Arrange the cards to make: Five Make numbers prime up more numbers that problems are multiples to use of of all 3. 7 ten cards to make five special numbers. Know 3 and 7 times tables. Recognise prime numbers.
15 Solution to make five numbers For example: a. 12, 39, 45, 60, 78. b. 7, 42, 63, 98, 105. c. 5, 23, 67, 89, 401. There are other solutions. Know 3 and 7 times tables. Recognise prime numbers.
16 1. My age this year is a multiple of 8. Next year it will be a multiple of 7. How old am I? Age old problems Know multiplication facts to 10 x 10. Recognise square and cube numbers.
17 Age old problems 2. Last year my age was a square number. Next year it will be a cube number. How old am I? How long must I wait until my age is both a square number and a cube? Know multiplication facts to 10 x 10. Recognise square and cube numbers.
18 Age old problems 3. My Mum was 27 when I was born. 8 years ago she was twice as old as I shall be in 5 years time. How old am I now? Know multiplication facts to 10 x 10. Recognise square and cube numbers.
19 1. I am 48 years old (or possibly 104). 2. I am now 26 years old. In 38 years time, when I am 64, my age will be both a square number and a cube. 3. I am 9 years old now. Know multiplication facts to 10 x 10. Recognise square and cube numbers. Solution to age old problems
20 Zids and Zods Zids have 4 spots. Zods have 9 spots. Altogether some Zids and Zods have 48 spots. How many Zids are there? How many Zods? Know multiplication facts to 10 x 10. Add two-digit numbers mentally.
21 Zids and Zods What Sims have 5 spots and Sams have 7 spots and there are 140 spots altogether? Find as many solutions as you can. Know multiplication facts to 10 x 10. Add two-digit numbers mentally.
22 Solution to Zids and Zods 1. There are 3 Zids with 4 spots and 4 Zods with 9 spots. 2. If Sims have 5 spots and Sams have 7 spots, the possible ways of making 140 are: 28 Sims; 21 Sims and 5 Sams; 14 Sims and 10 Sams; 7 Sims and 15 Sams; 20 Sams. Know multiplication facts to 10 x 10. Add two-digit numbers mentally.
23 Money bags Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p, without opening any bag. How many pennies did Ram put in each bag? Explain methods and reasoning.
24 Solution to Money bags Ram put 1p, 2p, 4p and 8p in the four bags. Any sum from 1p to 15p can be made with these amounts. Explain methods and reasoning.
25 Join any four numbers. Find their total. Joins can go up, down or sideways, but not diagonally. The score shown is = 47. Find the highest possible score. Joins Find the lowest possible score. Add and subtract two-digit numbers mentally.
26 Try joining five numbers. Find their total. Joins can go up, down or sideways, but not diagonally. Find the highest possible score. Joins Find the lowest possible score. Add and subtract two-digit numbers mentally.
27 Try joining five numbers. Now try joining five numbers using only diagonal joins. Find the highest possible score. Find the lowest possible score. Joins Add and subtract two-digit numbers mentally.
28 Solution to Joins Using four numbers: the highest score is = 69, the lowest score is = 30. Using five numbers: the highest is = 86, the lowest is = 37. Using five numbers and diagonal joins: the highest is = 83, the lowest is = 47. Add and subtract two-digit numbers mentally.
29 Presents Gurmit paid 21 for five presents. For A and B he paid a total of 6. For B and C he paid a total of 10. For C and D he paid a total of 7. For D and E he paid a total of 9. How much did Gurmit pay for each present? Explain methods and reasoning.
30 Solution to Presents Gurmit paid 2, 4, 6, 1 and 8 for the five presents. Explain methods and reasoning.
31 Jack s book The pages of Jack s book are numbered from 1. The page numbers have a total of 555 digits. How many pages has the book? How many of the digits are a 5? Know what each digit represents.
32 Solution to Jack s book The book has 221 pages. 42 of the digits are a 5. Know what each digit represents.
33 The end,thank you!
34 References and additional resources. The questions from this PowerPoint came from: Mathematical challenges for able pupils in Key Stages 1 and 2 Corporate writer was Department for Education and Employment and it is produced under a Crown copyright 2000 Thank You PowerPoint template published by These Mental Maths challenges can be found as a PDF file at : Contains public sector information licensed under the Open Government Licence v3.0. ( All images used in this PowerPoint was found at the free Public Domain Clip Art site. ( These units were organised using advice given at:
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