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Have a look at these photos of different fruit. How many do you see? How did you count?

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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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I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

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An activity centred around observations of dots and how we visualise number arrangement patterns.

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A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

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

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How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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This challenge asks you to imagine a snake coiling on itself.

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Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

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What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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Watch this animation. What do you see? Can you explain why this happens?

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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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Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

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Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

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A task which depends on members of the group working collaboratively to reach a single goal.

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This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

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We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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What can you see? What do you notice? What questions can you ask?