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A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

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The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

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Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .

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Surprising numerical patterns can be explained using algebra and diagrams...

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Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

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Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

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Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

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A task which depends on members of the group noticing the needs of others and responding.

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Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

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A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?

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Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.

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Can you explain why a sequence of operations always gives you perfect squares?

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Can you explain what is going on in these puzzling number tricks?

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Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

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Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

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A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

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Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

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Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

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If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

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The sums of the squares of three related numbers is also a perfect square - can you explain why?

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Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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Can you find rectangles where the value of the area is the same as the value of the perimeter?

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

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The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

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Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

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If you know the perimeter of a right angled triangle, what can you say about the area?

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A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

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There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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The Number Jumbler can always work out your chosen symbol. Can you work out how?

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How many winning lines can you make in a three-dimensional version of noughts and crosses?

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What is special about the difference between squares of numbers adjacent to multiples of three?

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A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .

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Where should you start, if you want to finish back where you started?

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There are unexpected discoveries to be made about square numbers...

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The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

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32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

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Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

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Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.

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A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

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How good are you at finding the formula for a number pattern ?

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Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.