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

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

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

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.

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

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?

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

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?

Make some celtic knot patterns using tiling techniques

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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?

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

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Here is a version of the game 'Happy Families' for you to make and play.

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.

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

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.

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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.

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?

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

Can you make the birds from the egg tangram?

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

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?

Learn about Pen Up and Pen Down in Logo

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

How many models can you find which obey these rules?

This activity investigates how you might make squares and pentominoes from Polydron.

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