An activity making various patterns with 2 x 1 rectangular tiles.

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

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.

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

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?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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?

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?

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 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.

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

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Use the tangram pieces to make our pictures, or to design some of your own!

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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?

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?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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

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

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

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

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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

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?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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?

What shape is made when you fold using this crease pattern? Can you make a ring design?

Can you make the birds from the egg tangram?

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Make a flower design using the same shape made out of different sizes of paper.

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?

Can you visualise what shape this piece of paper will make when it is folded?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Make some celtic knot patterns using tiling techniques

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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

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?

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

How many models can you find which obey these rules?

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

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

Reasoning about the number of matches needed to build squares that share their sides.