Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Make 37 Poster
problem
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Make 37

Age
5 to 11
Challenge level
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Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

More Number Pyramids
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More number pyramids

Age
11 to 14
Challenge level
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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Square It
problem
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Square it

Age
11 to 16
Challenge level
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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Harmonic Triangle
problem
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Harmonic triangle

Age
14 to 16
Challenge level
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Can you see how to build a harmonic triangle? Can you work out the next two rows?
Clapping Times
problem
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Clapping times

Age
5 to 7
Challenge level
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If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
Interactive Spinners
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Interactive spinners

Age
11 to 14
Challenge level
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This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
circles in quadrilaterals
problem
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Circles in quadrilaterals

Age
14 to 16
Challenge level
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Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

What shape?
problem
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What shape?

Age
7 to 14
Challenge level
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This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
Area and perimeter
problem
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Area and perimeter

Age
7 to 11
Challenge level
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What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Carroll Diagrams
problem
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Carroll diagrams

Age
5 to 11
Challenge level
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Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?