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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

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The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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Can you make square numbers by adding two prime numbers together?

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Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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This game can replace standard practice exercises on finding factors and multiples.

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Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

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Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?