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Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?

How can we help students make sense of addition and subtraction of negative numbers?

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Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

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A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.

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Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

This article suggests some ways of making sense of calculations involving positive and negative numbers.

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Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Different combinations of the weights available allow you to make different totals. Which totals can you make?

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Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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Play this game to learn about adding and subtracting positive and negative numbers

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In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

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If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

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How many ways can you find to put in operation signs (+ - x Ã·) to make 100?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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Here is a chance to play a fractions version of the classic Countdown Game.

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Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

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Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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Here is a chance to play a version of the classic Countdown Game.

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There are nasty versions of this dice game but we'll start with the nice ones...

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If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

This article for teachers suggests ideas for activities built around 10 and 2010.

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Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

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By selecting digits for an addition grid, what targets can you make?

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Got It game for an adult and child. How can you play so that you know you will always win?

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Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

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Try out some calculations. Are you surprised by the results?

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What happens when you add a three digit number to its reverse?

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Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

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Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

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A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

Find out about Magic Squares in this article written for students. Why are they magic?!

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There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .

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This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

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When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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Find the values of the nine letters in the sum: FOOT + BALL = GAME

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In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

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The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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How many solutions can you find to this sum? Each of the different letters stands for a different number.

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What is the sum of all the digits in all the integers from one to one million?

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Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

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This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.