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.

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

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

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. . . .

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

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

Turn through bigger angles and draw stars with Logo.

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 some celtic knot patterns using tiling techniques

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

A game to make and play based on the number line.

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.

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

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

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

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.

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

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?

Learn about Pen Up and Pen Down in Logo

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

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

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

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?

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

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

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

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?

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?

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.

Can you make the birds from the egg tangram?

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?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

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

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

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

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

What happens when a procedure calls itself?

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.

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.