Visualising and representing

There are 575 NRICH Mathematical resources connected to Visualising and representing
Picture Story
problem
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Picture story

Age
14 to 16
Challenge level
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Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
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?

Seven Squares - Group-worthy Task
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Seven squares - group-worthy task

Age
11 to 14
Challenge level
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Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
On the Edge
problem
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On the edge

Age
11 to 14
Challenge level
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If you move the tiles around, can you make squares with different coloured edges?
Isosceles Triangles
problem
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Isosceles triangles

Age
11 to 14
Challenge level
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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
How far does it move?
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How far does it move?

Age
11 to 14
Challenge level
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

Back fitter
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Back fitter

Age
14 to 18
Challenge level
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10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Which solids can we make?
problem
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Which solids can we make?

Age
11 to 14
Challenge level
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Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Catrina's Cards
problem
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Catrina's cards

Age
5 to 7
Challenge level
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How would you find out how many football cards Catrina has collected?
Nine Colours
problem
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Nine colours

Age
11 to 16
Challenge level
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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?