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.

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?

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.

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?

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

Make some celtic knot patterns using tiling techniques

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?

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

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?

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

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

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

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

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.

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?

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

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.

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

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

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

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 birds from the egg tangram?

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.

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?

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

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

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?

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

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.

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?

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?

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

Delight your friends with this cunning trick! Can you explain how it works?

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

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

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

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.

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?