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

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

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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

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

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

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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

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?

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

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

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

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

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?

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

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?

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

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?

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

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

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

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?

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

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

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?

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

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

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

In this activity focusing on capacity, you will need a collection of different jars and bottles.

For this activity which explores capacity, you will need to collect some bottles and jars.

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?

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

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

Here's a simple way to make a Tangram without any measuring or ruling lines.

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

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

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

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?

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

Can you fit the tangram pieces into the outline of this junk?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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?

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?

Can you make the birds from the egg tangram?