Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Can you make a 3x3 cube with these shapes made from small cubes?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Can you cut up a square in the way shown and make the pieces into a triangle?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
Can you find ways of joining cubes together so that 28 faces are visible?
Which of the following cubes can be made from these nets?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
Exploring and predicting folding, cutting and punching holes and making spirals.
What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?
An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.
Reasoning about the number of matches needed to build squares that share their sides.
Make a cube out of straws and have a go at this practical challenge.
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?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the chairs?
On which of these shapes can you trace a path along all of its edges, without going over any edge twice?
Can you fit the tangram pieces into the outline of this telephone?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of the rocket?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Can you fit the tangram pieces into the outline of Granma T?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Can you fit the tangram pieces into the outline of Little Ming?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.