One of my favourite resources when looking at aspects of mathematical modelling is the Desmos Penny Circle activity. Originally posed as a problem as part of Dan Meyers ‘3 act math‘, the team at desmos have made great use of technology to support a truly interactive and collaborative approach to problem solving. If you just want to dive straight in then go to https://teacher.desmos.com/pennycircle, create an account and create the activity, for a little bit more guidance then read on!
How it works
The main aim of the activity is to create a model to estimate how many pennies fit inside a circle.  Students work through interactive questions and as they do their answers and responses are collected together and where useful made available to the teacher and the rest of the class. Key skills of prediction, collection, modelling, extrapolation and analysis are all utilised.
Step 1 – create a new activity
You can click the link on https://teacher.desmos.com/pennycircle. You will need to create a new account (it’s all free and totally worthwhile). You might also want to have a quick look through the overview presented on the page if you want more info
Step 2 – share your custom link with the class
You’ll be given a custom code that will assign students together (and to your own class) when they visit the site. No extra work required 🙂
Simply tell students to visit class.desmos.com and input the code
Step 3 – have a great lesson!
All the guidance should be fairly self-explanatory. You will also be given your own page where you can see how students are getting on and what they’ve answered.
I really love this activity for a few reasons. Firstly because it’s one of the first times I’ve seen technology used in such a neat way to make use of the fact that pupils are still in a classroom despite having technology. Real-time collaboration allows them to crowd-source information and develop their own models in real-time.
Secondly because it shows great collaboration between teachers and techies – as well as being pedagogically rich things just work and are extremely easy to use. There are a number of activities that have been built by this team (and still growing), I can really recommend most of them (my next favourites are function carnival and central park) and recently they’ve also  been working on a platform so that teachers can design their own lessons.
