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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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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

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Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.

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Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

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Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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Stop the Clock game for an adult and child. How can you make sure you always win this game?

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A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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What shaped overlaps can you make with two circles which are the same size?

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A game in which players take it in turns to choose a number. Can you block your opponent?

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Calculate the fractional amounts of money to match pairs of cards with the same value.

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Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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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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Train game for an adult and child. Who will be the first to make the train?

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A train building game for two players. Can you be the one to complete the train?

The 2012 primary advent calendar features twenty-four of our posters, one for each day in the run-up to Christmas.

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

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A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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Practise your number bonds whilst improving your memory in this matching pairs game.

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This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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Sort the houses in my street into different groups. Can you do it in any other ways?

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Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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Practise your tables skills and try to beat your previous best score in this interactive game.

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Can you complete this jigsaw of the multiplication square?

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Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.