Conjecturing and generalising
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Can they be equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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Generating triples
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
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Number pyramids
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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Odds, evens and more evens
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
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Round and round the circle
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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Have you got it?
Can you explain the strategy for winning this game with any target?
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Two primes make one square
Can you make square numbers by adding two prime numbers together?
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Mind reading
Think of a number, add one, double it, take away 3, add the number
you first thought of, add 7, divide by 3 and take away the number
you first thought of. You should now be left with 2. How do I know?
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Break it up!
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?