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Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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

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Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

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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 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?

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

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

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

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Can you fit the tangram pieces into the outlines of the people?

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An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

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Can you fit the tangram pieces into the outline of the clock?

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Can you fit the tangram pieces into the outlines of the convex shapes?

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Can you fit the tangram pieces into the outline of the playing piece?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

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A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

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Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?

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

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Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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

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Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

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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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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 fit the tangram pieces into the outline of Mah Ling?

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Can you fit the tangram pieces into the outline of the plaque design?

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Can you fit the tangram pieces into the silhouette of the junk?

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Can you fit the tangram pieces into the outline of Granma T?

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Can you fit the tangram pieces into the outlines of the numbers?

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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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Can you fit the tangram pieces into the outlines of Little Ming and Little Fung dancing?

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Can you fit the tangram pieces into the outline of Little Ming?

Explore our selection of interactive tangrams. Can you use the tangram pieces to re-create each picture?

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Can you fit the tangram pieces into the outline of Little Fung at the table?

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Can you fit the tangram pieces into the outlines of the telescope and microscope?

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Can you fit the tangram pieces into the outline of the sports car?

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Can you fit the tangram pieces into the outline of the telephone?

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Can you fit the tangram pieces into the outline of the candle?

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Can you fit the tangram pieces into the outline of the butterfly?