A jigsaw where pieces only go together if the fractions are equivalent.

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

What shape and size of drinks mat is best for flipping and catching?

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Build a scaffold out of drinking-straws to support a cup of water

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Learn about Pen Up and Pen Down in Logo

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

Make a cube out of straws and have a go at this practical challenge.

What happens when a procedure calls itself?

Write a Logo program, putting in variables, and see the effect when you change the variables.

More Logo for beginners. Now learn more about the REPEAT command.

Learn to write procedures and build them into Logo programs. Learn to use variables.

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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?

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

Exploring and predicting folding, cutting and punching holes and making spirals.

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

What do these two triangles have in common? How are they related?

Turn through bigger angles and draw stars with Logo.

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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?

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 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.

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

A description of how to make the five Platonic solids out of paper.

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

An activity making various patterns with 2 x 1 rectangular tiles.

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

Can you make the birds from the egg tangram?

Here's a simple way to make a Tangram without any measuring or ruling lines.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Can you visualise what shape this piece of paper will make when it is folded?