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How many different symmetrical shapes can you make by shading triangles or squares?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
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.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
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?
A game for 2 or more people, based on the traditional card game Rummy.
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
Can you find the area of a parallelogram defined by two vectors?
Why not challenge a friend to play this transformation game?
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
Where should runners start the 200m race so that they have all run the same distance by the finish?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Can you make sense of the three methods to work out what fraction of the total area is shaded?
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
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 rhombus.