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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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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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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 models can you find which obey these rules?

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

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

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Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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

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

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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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Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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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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Surprise your friends with this magic square trick.

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

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

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These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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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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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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Can you make the birds from the egg tangram?

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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.

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

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

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

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

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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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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?