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Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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Reverse to Order

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

Tilted Squares

Stage: 3 Challenge Level: Challenge Level:1

Two standard methods for working out the areas of shapes may help.

Boxing in the tilted squares, working out the area of the box and subtracting the areas of the unwanted right-angled triangles: 

 boxing in method


Splitting the tilted squares into right-angled triangles and squares and adding the areas of the different parts:

Diagram of tilted square split up into 4 right angled triangles and a square, with their corresponding areas.