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 cut up a square in the way shown and make the pieces into a triangle?
What is the greatest number of squares you can make by overlapping three squares?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Reasoning about the number of matches needed to build squares that share their sides.
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Exploring and predicting folding, cutting and punching holes and making spirals.
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?
Here's a simple way to make a Tangram without any measuring or ruling lines.
Can you fit the tangram pieces into the outline of Mai Ling?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Make a cube out of straws and have a go at this practical challenge.
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
Can you fit the tangram pieces into the outline of the rocket?
Which of the following cubes can be made from these nets?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of this telephone?
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 outlines of the chairs?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this plaque design?
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 outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
How can you make an angle of 60 degrees by folding a sheet of paper twice?