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

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

This article for students gives some instructions about how to make some different braids.

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

What shape would fit your pens and pencils best? How can you make it?

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

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

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

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

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

Turn through bigger angles and draw stars with Logo.

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

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Learn about Pen Up and Pen Down in Logo

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

What happens when a procedure calls itself?

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

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

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.

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.

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

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

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

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?

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

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.

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

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

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

Make some celtic knot patterns using tiling techniques

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

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

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?

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

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

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

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

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.

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?