16% Time Revised: Scaling it back

Hi there. Been a while hasn't it? Well I'm back baby!

I'm now on my second term of the 16% time experiment, and I've made a few minor changes. There were two big problems with my first attempt; we didn't have time (only 3 or 4 hours per term) to really get in to some of the more impressive sounding projects I (or they) suggested and many pupils had no idea how to start answering some of the questions posed. This is a top-set group and yet I repeatedly had to suggest googling a maths word they didn't yet know!

I still think that these big projects are within their grasp, but I think we started too big and students who have not done anything like this before just got lost.

Scaling it back

• Project suggestions are now reasonably 'completable' in 1-2 hours.
• They come with minor prompts and questions, to scaffold the directions they could take.
• There is a difficulty rating on each project.
• If they want to do a different project, I have a form for them to work through that gets them to write their own criteria for success and scaffold the project themselves.

We've had one lesson in this style and it was a lot more purposeful an environment and more accessible to the lower end of the class. I'm not sure if this will be quite as inspiring as before though. I'll let you know how it goes.

Here are my new suggested projects so far:
Revision  Complex Numbers  Arithmetic Proofs  Euclid  Different bases  Estimation and Large Numbers  Magic

16.6666666666% Time

I have some very bright and very highly motivated pupils in my top-set year 10 class this year and I feel like my classes are a bit wasted on them. The topics we go through need to be practiced and there is always extension material for them, but they just breeze through it. Last week I completely failed at tried to create a 3D-Graph, following this excellent post by Ashli. Basically I botched the explanation and expected too much to get done in a single lesson. Anyway, it was motivating to some, but others just felt it was another standard maths lesson.

Inspired by Shawn Cornally's Inquiry style of teaching and the idea I first heard from Google of 20% Time for employees, I decided to try out our own version of 20% Time in class:

In a recent survey I did with the pupils, most were happy with the pace of our classes, about 6 felt it was too slow and a couple felt it was too fast. I didn't want to leave that majority out of this, which is why I give them the option to revise topics. I will provide materials for this and it should hopefully help those less confident students.
To start with, my guess is that pupils will not have any idea where to go with this, so I have a few suggested project ideas:

Though I'm dangling these in front of them in the hope that someone will bite, I made it clear that they can really choose any topic they want. There are only two constraints:

• It must be mathematical and include maths which is currently beyond their knowledge/ability.
• Success or failure in the project is not so important, but you must aim for the project to be awesome (no powerpoints based heavily on wikipedia, etc. I want outrageous 6ft models and flashing, dancing lights!)

When they have picked a project and started working on it, I will drop a few words like 'game theory' as hints to the directions they could go, and vet their projects for mathematical content and awesomeness. Apart from that though, I hope to sit back and let them explore.

What do you reckon? Do you have any other intriguing/inspiring project ideas I could offer up as bait?

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