Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
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?
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 most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
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?
Explore the triangles that can be made with seven sticks of the same length.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
How many triangles can you make on the 3 by 3 pegboard?
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 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?
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?
You'll need a collection of cups for this activity.
These practical challenges are all about making a 'tray' and covering it with paper.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
An activity making various patterns with 2 x 1 rectangular tiles.
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 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?
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.
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?
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
What shapes can you make by folding an A4 piece of paper?
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?
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.
Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.
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?
Can you create more models that follow these rules?
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?
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?
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?
Can you make the birds from the egg tangram?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
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 these people?
Can you fit the tangram pieces into the outline of this telephone?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Can you fit the tangram pieces into the outlines of these clocks?
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
Can you fit the tangram pieces into the outline of this junk?
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?