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

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

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

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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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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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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 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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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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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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Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

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

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

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

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

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

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

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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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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 greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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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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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 convex shapes?

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Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

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

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

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

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A shape and space game for 2, 3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board.

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

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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 outlines of the camel and giraffe?

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

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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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Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?