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Can you split each of the shapes below in half so that the two parts are exactly the same?

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What is the greatest number of squares you can make by overlapping three squares?

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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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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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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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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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Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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Can you make the birds from the egg tangram?

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

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

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Can you describe a piece of paper clearly enough for your partner to know which piece it is?

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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?

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

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A game in which players take it in turns to choose a number. Can you block your opponent?

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

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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?

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We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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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?

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Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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You have a set of the digits from 0 â€“ 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

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Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

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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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Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

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These pictures show squares split into halves. Can you find other ways?

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

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

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

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

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Can you each work out what shape you have part of on your card? What will the rest of it look like?

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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.

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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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Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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Can you put these shapes in order of size? Start with the smallest.

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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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Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

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You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

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Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

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Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

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Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?