Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
What happens to the area and volume of 2D and 3D shapes when you
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?
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
Jo made a cube from some smaller cubes, painted some of the faces
of the large cube, and then took it apart again. 45 small cubes had
no paint on them at all. How many small cubes did Jo use?
Drawing a triangle is not always as easy as you might think!
Rajeev sent us a great description of his exploration of different
Go to last month's problems to see more solutions.
Many NRICH tasks have been designed with group work in mind. Read about Jo Boaler's research on the benefits of collaborative work and watch a clip of a teacher working in this way.
Group work depends on effective team work. This article describes
attributes of effective team work and links to "Team Building"
problems that can be used to develop learners' team working skills.
A game in which players take it in turns to turn up two cards. If
they can draw a triangle which satisfies both properties they win
the pair of cards. And a few challenging questions to follow...
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?