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

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

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

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

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

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

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

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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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Make a mobius band and investigate its properties.

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

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

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

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

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Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

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

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

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

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