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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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A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
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Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
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Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.
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A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?
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Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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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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Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
