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

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

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

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

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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 ...

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

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

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

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

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Can you cut up a square in the way shown and make the pieces into a triangle?

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

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You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

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

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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?

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

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

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

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Can you make the birds from the egg tangram?

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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?

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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?

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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?

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Follow these instructions to make a three-piece and/or seven-piece tangram.

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

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Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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Follow these instructions to make a five-pointed snowflake from a square of paper.

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

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It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

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These practical challenges are all about making a 'tray' and covering it with paper.

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

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Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

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Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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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?

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Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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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?

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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?

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

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How many models can you find which obey these rules?

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This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

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Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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How can you make a curve from straight strips of paper?

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In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

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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?

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Did you know mazes tell stories? Find out more about mazes and make one of your own.

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Can you make five differently sized squares from the interactive tangram pieces?