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Try out these calculations. Are you surprised by the results?
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Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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Can you find rectangles where the value of the area is the same as the value of the perimeter?
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A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
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Invent a scoring system for a 'guess the weight' competition.
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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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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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Which of these pocket money systems would you rather have?
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Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: ×2 and -5. What do you think?
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There are lots of ideas to explore in these sequences of ordered fractions.
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Can you work out what step size to take to ensure you visit all the dots on the circle?
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Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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Which countries have the most naturally athletic populations?
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Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
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How well can you estimate 10 seconds? Investigate with our timing tool.
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Use properties of numbers to work out whether you can satisfy all these statements at the same time.
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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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Sequences of multiples keep cropping up...
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The number in the square is the mean of the four numbers surrounding it. Can you find the missing numbers?
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If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
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What's the largest volume of box you can make from a square of paper?
