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

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Use an interactive Excel spreadsheet to explore number in this exciting game!

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Use Excel to investigate the effect of translations around a number grid.

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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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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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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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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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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Use an Excel spreadsheet to explore long multiplication.

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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

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

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

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

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Use Excel to explore multiplication of fractions.

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Use Excel to practise adding and subtracting fractions.

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Use an interactive Excel spreadsheet to investigate factors and multiples.

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An Excel spreadsheet with an investigation.

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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. . . .

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

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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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Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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

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Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

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

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

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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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In this game you are challenged to gain more columns of lily pads than your opponent.

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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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Can you find a strategy that ensures you get to take the last biscuit in this game?

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Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

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

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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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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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Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

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Can you find triangles on a 9-point circle? Can you work out their angles?

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