Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
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
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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
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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?
Abundant Numbers
problem
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Abundant numbers

Age
7 to 11
Challenge level
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48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Which is quicker?
problem
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Which is quicker?

Age
7 to 11
Challenge level
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Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Partitioning revisited
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Partitioning revisited

Age
11 to 14
Challenge level
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We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
At right angles
problem
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At right angles

Age
14 to 16
Challenge level
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Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
Mystic Rose
problem
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Mystic rose

Age
14 to 16
Challenge level
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Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.