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

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

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

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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

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

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

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

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

Turn through bigger angles and draw stars with Logo.

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

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

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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?

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

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

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

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

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

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

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

What happens when a procedure calls itself?

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

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

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

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

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

Learn about Pen Up and Pen Down in 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.

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?

If you'd like to know more about Primary Maths Masterclasses, this is the package to read! Find out about current groups in your region or how to set up your own.

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.

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

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

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

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

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?