Visualising and representing

problem
Differential equation matcher

Age

16 to 18

Challenge level

Match the descriptions of physical processes to these differential equations.
problem
Negatively triangular

Age

14 to 16

Challenge level

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
problem
Swimming pool

Age

5 to 11

Challenge level

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?
problem
The perforated cube

Age

14 to 16

Challenge level

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?
problem
One out one under

Age

14 to 16

Challenge level

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
problem
Making tracks

Age

14 to 16

Challenge level

A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?
problem
Drilling many cubes

Age

7 to 14

Challenge level

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
problem
Start cube drilling

Age

5 to 7

Challenge level

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
problem
More building with cubes

Age

7 to 11

Challenge level

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!
problem
Building with cubes

Age

5 to 7

Challenge level

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?