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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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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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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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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?

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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 greatest number of squares you can make by overlapping three squares?

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This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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

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

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

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Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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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 outlines of the people?

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

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Can you fit the tangram pieces into the outline of Mah Ling?

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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

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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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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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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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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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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 telephone?

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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 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 brazier for roasting chestnuts?

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

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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 Wai Ping, Wu Ming and Chi Wing?

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

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A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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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 Granma T?

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

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Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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