Make an equilateral triangle by folding paper and use it to make patterns of your own.

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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

Turn through bigger angles and draw stars with Logo.

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

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

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

Make some celtic knot patterns using tiling techniques

Make a clinometer and use it to help you estimate the heights of tall objects.

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

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

Learn about Pen Up and Pen Down in Logo

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

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

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

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

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

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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

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.

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

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 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.

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?

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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?

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?

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

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

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?

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?

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

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?

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

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

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

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

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