Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Abundant Numbers
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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?
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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
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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
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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.
Ip Dip
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Ip dip

Age
5 to 11
Challenge level
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"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Circles, Circles
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Circles, circles

Age
5 to 11
Challenge level
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Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Tumbling Down
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Tumbling down

Age
7 to 11
Challenge level
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Watch this animation. What do you see? Can you explain why this happens?

Subtraction Surprise
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Subtraction surprise

Age
7 to 14
Challenge level
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Try out some calculations. Are you surprised by the results?
Same Answer
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Same answer

Age
11 to 14
Challenge level
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Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?