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**Problem Solving Starter - 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?

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**Gurmit paid £2, £4, £6, £1, and £8 for the five presents.**

Solution – Presents Gurmit paid £2, £4, £6, £1, and £8 for the five presents.

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**Problem Solving Starter – Three Digits**

Don’t forget you can only have up to 9 beads on each stick! Imagine you have 25 beads. You have to make a three-digit number on an abacus. You must use all 25 beds for each number you make. How many different three-digit numbers can you make? Write them in order.

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**You can make six different numbers.**

Solution – Three digits You can make six different numbers. In order, the numbers are: 799, 889, 898, 979, 988, 997.

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**Problem Solving Starter – Make Five Numbers**

Take 10 cards numbered 0 to 9. Each time use all ten cards. Arrange the cards to make: Five numbers that are multiples of 3 Five numbers that are multiples of 7 Five prime numbers Make up more problems to use all ten cards to make five special numbers.

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**Solution – Make Five Numbers**

12, 39, 45, 60, 78 7, 42, 63, 98, 105 5, 23, 67, 89, 401 There are other solutions.

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**Problem Solving Starter – Maze**

Start with zero. Find a route from ‘start’ to ‘end’ that totals 100 Which route has the highest total? Which has the lowest total? Now try some different starting numbers. Start + 6 X 9 ÷ 2 + 9 X 7 ÷ 3 X 5 X 5 - 6 X 3 - 5 ÷ 3 X 7 - 8 End

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Solution – Maze There are two routes that total 100 exactly: +6 x7 -6 x3 -8 =100 +9 x7 ÷3 x5 -5 =100 The route giving the highest total is: +9 x7 -6 x7 -8 =391 The route giving the lowest total is: +6 x7 ÷3 x3 -8 =34

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**Problem Solving Starter – Eggs**

Mrs Choy spent exactly £10 on 100 eggs for her shop. Large eggs cost her 50p each. Medium eggs cost her 10p each. Small eggs cost her 5p each. For two of the sizes, she bought the same number of eggs. How many of each size did she buy?

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Solution – Eggs Mrs Choy bought: 10 large eggs at 50p each 10 medium eggs at 10p each 80 small eggs at 5p each.

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**Problem Solving Starter – Flash Harry**

In April Flash Harry bought a saddle for £100. In May he sold it for £200. In June he was sorry he had sold it. So he bought it back for £300. In July he got tired of it. So he sold it for £400. Overall, did Flash Harry make or lose money? How much did he make or lose?

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Solution – Flash Harry Flash Harry’s bank balance looked like this: April - £100 May + £100 June - £200 July + £200 So Harry made £200 overall.

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**Problem Solving Starter – Age old Problems**

My age this year is a multiple of 8. Next year it will be a multiple of 7. How old am I? 2. Last year my age was a square number. Next year it will be a cube number. How long must I wait until my age is both a square number and a cube? My mum was 27 when I was born. * years ago she was twice as old as I shall be in 5 years’ time. How old am I now?

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**Solution – Age old Problems**

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. I am 9 years old now.

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**Problem Solving Starter – 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? What if Zids have 5 spots, Zods have 7 spots, and there are 140 spots together? Find as many solutions as you can.

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**Problem Solving Solution – Zids and Zods**

There are 3 Zids with 4 spots and 4 Zods with 9 spots. If Zids have 5 spots and Zods have 7 spots, the possible ways of making 140 are: 28 Zids; 21 Zids and 5 Zods; 14 Zids and 10 Zods; 1 Zids and 15 Zods; 20 Zods.

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