Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Largest product
problem
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Largest product

Age
11 to 14
Challenge level
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Which set of numbers that add to 100 have the largest product?
Multiplication square
problem
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Multiplication square

Age
14 to 16
Challenge level
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Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Real Statistics
problem
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Real statistics

Age
7 to 11
Challenge level
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Have a look at this table of how children travel to school. How does it compare with children in your class?

More Twisting and Turning
problem
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More twisting and turning

Age
11 to 16
Challenge level
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It would be nice to have a strategy for disentangling any tangled ropes...
Power mad!
problem
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Power mad!

Age
11 to 14
Challenge level
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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.

Diminishing Returns
problem
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Diminishing returns

Age
11 to 14
Challenge level
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How much of the square is coloured blue? How will the pattern continue?
Follow the numbers
problem
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Follow the numbers

Age
7 to 11
Challenge level
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What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Largest Even
problem
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Largest even

Age
5 to 11
Challenge level
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How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
Consecutive Numbers
problem
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Consecutive numbers

Age
7 to 14
Challenge level
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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Of all the areas
problem
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Of all the areas

Age
14 to 16
Challenge level
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Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?