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.

Learn about Pen Up and Pen Down in Logo

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.

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?

Turn through bigger angles and draw stars with Logo.

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.

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

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

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.

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.

What happens when a procedure calls itself?

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

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

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

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

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. . . .

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

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

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

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

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

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?

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

Make some celtic knot patterns using tiling techniques

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

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

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

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

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?

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

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?

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?

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?

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.