Tilted Squares Activity (Chapter 10 page 11 of part 2)
This activity is to be used in key stage four to reintroduce Pythagoras' Theorem. Opportunity to bring in many mathematical topics.
Begin by asking how we can calcuate the length of the vector (4¦3) Discuss the difference between calculate and measure. Explore the link between the area of a square and the length of a side of a square. Explore different methods for finding the area of a tilted square. Emphasise that a clear description of the method of finding the area of the square is what is required.
At this point begin the tilted square activity. The aim is to re-enforce that Pythagoras' Theorem is as much to about areas of squares as it is about right-angled triangles.
Extension (p. 153 of book, p 15 of the pdf) Q5 area of isosceles triangle, Q7 proof using Pythagors' theorem, Q8 Is Pythagors' Theorem still valid for non right-angles triangles?
Further exension (Page 155) Does Pythagoras Rule work with other shapes other than squares e.g semi-circles?