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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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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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Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

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

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

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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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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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If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.

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What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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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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Reasoning about the number of matches needed to build squares that share their sides.

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

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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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Move just three of the circles so that the triangle faces in the opposite direction.

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How many different triangles can you make on a circular pegboard that has nine pegs?

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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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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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In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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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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Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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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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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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Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

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What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

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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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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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Can you find ways of joining cubes together so that 28 faces are visible?

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

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Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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Find your way through the grid starting at 2 and following these operations. What number do you end on?

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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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Why do you think that the red player chose that particular dot in this game of Seeing Squares?

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Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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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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A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?