Challenge Level

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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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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Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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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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Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

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How many different colours of paint would be needed to paint these pictures by numbers?

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Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

Challenge Level

Which of these triangular jigsaws are impossible to finish?