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

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

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

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

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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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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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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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Can you lay out the pictures of the drinks in the way described by the clue cards?

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

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

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

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

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

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Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

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

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

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

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

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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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This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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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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Explore the triangles that can be made with seven sticks of the same length.

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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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We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

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

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