'Discover Pythagoras's theorem by investigating the areas of these Skewey Squares'
This is a fantastic investigation full of surprises that really help to understand how mathematical phenomena can be discovered by just playing with ideas. Using cm2 paper, can you draw a square with an area of 4cm2? What about 5cm2? In fact what whole number areas can be made with squares? This seems obvious at first, but a bit of lateral thought is required to answer this question fully!
There is a series of student worksheets to go with this activity that can be given out separately or all at once. Start with Skewey Squares and the the Hint Sheet. This can be followed by Skewey Squares to Pythagoras Theorem.
The following screen cast uses dynamic geometry just to quickly demonstrate how squares can be drawn at different angles to find areas other than square numbers.
Here follows an outline of what the task is.
- Try to draw squares with integer values from 1 to 30 and consider which are possible and which are not.
- Also with the numbers from 1 to 30, try to express as many as possible as the sum of two squares.
- Consider the common ground between the two previous investigations and what can be concluded from two sides of a right angled triangle.
- Work towards an expression of Pythagoras's theorem and practise it in the context of this investigation.