A group of children are discussing the height of a tall tree. How would you go about finding out its height?
These pictures show squares split into halves. Can you find other ways?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
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 this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
Can you lay out the pictures of the drinks in the way described by the clue cards?
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
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?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Here is a version of the game 'Happy Families' for you to make and play.
Can you make the birds from the egg tangram?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
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.
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Can you create more models that follow these rules?
Explore the triangles that can be made with seven sticks of the same length.
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?
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?
This practical activity involves measuring length/distance.
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
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 outline of this junk?
These practical challenges are all about making a 'tray' and covering it with paper.
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
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?
For this activity which explores capacity, you will need to collect some bottles and jars.
In this activity focusing on capacity, you will need a collection of different jars and bottles.
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
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?
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 fit the tangram pieces into the outline of this telephone?
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 these clocks?
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 outline of this shape. How would you describe it?
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?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
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 Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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?
Ideas for practical ways of representing data such as Venn and Carroll diagrams.