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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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Can you explain the strategy for winning this game with any target?

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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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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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We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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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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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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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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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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A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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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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Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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

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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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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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The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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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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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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Here is a chance to play a fractions version of the classic Countdown Game.

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

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Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

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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 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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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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A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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 problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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

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

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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

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

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Use Excel to explore multiplication of fractions.

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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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An Excel spreadsheet with an investigation.

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A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.