Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Board Block Challenge
problem
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Board block challenge

Age
7 to 11
Challenge level
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Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Tangled Trig Graphs
problem
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Tangled trig graphs

Age
16 to 18
Challenge level
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Can you work out the equations of the trig graphs I used to make my pattern?

Times Tables Shifts
problem
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Times tables shifts

Age
7 to 11
Challenge level
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In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Your number was...
problem
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Your number was...

Age
11 to 14
Challenge level
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Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
This Pied Piper of Hamelin
problem
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This pied piper of hamelin

Age
7 to 11
Challenge level
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Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Doplication
problem
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Doplication

Age
7 to 11
Challenge level
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We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Expenses
problem
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Expenses

Age
14 to 16
Challenge level
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What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Amy's Dominoes
problem
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Amy's dominoes

Age
7 to 11
Challenge level
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Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
Take Three From Five
problem
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Take three from five

Age
11 to 16
Challenge level
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Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?