Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Explore the triangles that can be made with seven sticks of the same length.
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
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?
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?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
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?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
These pictures show squares split into halves. Can you find other ways?
Move four sticks so there are exactly four triangles.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
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?
Here is a version of the game 'Happy Families' for you to make and play.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
How many triangles can you make on the 3 by 3 pegboard?
Can you create more models that follow these rules?
We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?
What shapes can you make by folding an A4 piece of paper?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Can you make five differently sized squares from the tangram pieces?
Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.
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?
We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
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?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this junk?
You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
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?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
Can you fit the tangram pieces into the outline of this telephone?
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?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of these people?