Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Here is a version of the game 'Happy Families' for you to make and play.
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
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?
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 the child walking home from school?
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 this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of these rabbits?
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?
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 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 the chairs?
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 this telephone?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of this junk?
These pictures show squares split into halves. Can you find other ways?
Can you split each of the shapes below in half so that the two parts are exactly the same?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you create more models that follow these rules?
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Can you make the birds from the egg tangram?
An activity making various patterns with 2 x 1 rectangular tiles.