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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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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.

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

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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.

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

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A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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

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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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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?

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

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

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How many models can you find which obey these rules?

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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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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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Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

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

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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?

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

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

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

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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.

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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.

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

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

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

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Here are some ideas to try in the classroom for using counters to investigate number patterns.

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

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

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

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