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

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

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Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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

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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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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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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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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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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 butterfly?

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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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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 house?

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

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,. . . .

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

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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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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?

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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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I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

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

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

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

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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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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 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 outlines of Mah Ling and Chi Wing?

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Can you fit the tangram pieces into the outline of the child walking home from school?

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

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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 outline of Granma T?

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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 outlines of the chairs?

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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?