Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Pick's Theorem
problem
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Pick's theorem

Age
14 to 16
Challenge level
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Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Odd Squares
problem
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Odd squares

Age
7 to 11
Challenge level
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Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

Hundred Square
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Hundred square

Age
5 to 11
Challenge level
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A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Fractional Wall
problem
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Fractional wall

Age
7 to 11
Challenge level
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Using the picture of the fraction wall, can you find equivalent fractions?

Route to infinity
problem
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Route to infinity

Age
11 to 14
Challenge level
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Can you describe this route to infinity? Where will the arrows take you next?
Holes
problem
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Holes

Age
5 to 11
Challenge level
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I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

Counting Cogs
problem
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Counting cogs

Age
7 to 14
Challenge level
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Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Sitting round the party tables
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Sitting round the party tables

Age
5 to 11
Challenge level
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Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Seeing Squares
problem
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Seeing squares

Age
5 to 11
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.

Bracelets
problem
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Bracelets

Age
7 to 11
Challenge level
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Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?