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A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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

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

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Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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How much of the square is coloured blue? How will the pattern continue?

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A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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What is the best way to shunt these carriages so that each train can continue its journey?

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Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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Can you fit the tangram pieces into the outline of this teacup?

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

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An activity centred around observations of dots and how we visualise number arrangement patterns.

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Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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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 house?

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

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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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How many different symmetrical shapes can you make by shading triangles or squares?

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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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These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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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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Which of these dice are right-handed and which are left-handed?

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

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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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Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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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 find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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 outline of Mah Ling?

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

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How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

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Design an arrangement of display boards in the school hall which fits the requirements of different people.

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

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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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Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

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Can you fit the tangram pieces into the outlines of the camel and giraffe?

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Can you logically construct these silhouettes using the tangram pieces?

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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 outlines of the chairs?

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

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Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?

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