Resource Shout-Out: Modelling Epidemics and an Investigation that Leads to a Proof of Pythagoras'

For the start of this term I have been asked to make a couple investigation lessons for each year group. Nothing too difficult, but just something that pupils could get on with after being talked at about syllabus, expectations, homework policy, etc.

Here are a couple of GREAT activities that I just adapted slightly for our classes:

• Investigating Epidemics from nrich.maths.org I just removed the 'counter plague' to spend more time letting groups try to improve the model and try it out on the class.

• Sloping Squares by noycefdn.org (pdf file)I really like how you end this investigation with a² + b², on the cusp of proving Pythagoras' Theorem. There seemed to be too big a leap for me between question one and the algebra in question two, so I added a middle question: 

  "What sizes of square is it possible to make (below 25)?"

When you look at the possible areas, you can see how they can all be made by adding two squares together and hopefully this will help bridge that leap in to the general case.

  Possible areas: 2, 5, 8, 10, 13, 17, 18, 20, 25