1. Tools for Teaching Collaboration
Drawing on the work of Elizabeth Cohen, Ilana Horn, and others, we know the importance of "complex instruction" in creating an environment that seriously attends to "status" issues, norms/structures for equitable group work, and both recognizing and valuing multiple abilities. Part of that is creating and maintaining norms for interaction. Many people do activities to establish this at the beginning of the year, but it can be very important to revisit these periodically throughout the year as well (maybe every time you form new groups?).
Here are some resources for activities that will help with that:
In addition to setting up norms for interaction, it is important to have students reflect on their own group's interaction, pointing out strengths and weaknesses and making suggestions for future interactions. Here is a video that shows some students engaging in that type of reflection (see the 2nd video):
2. Mathematical Modeling
I've been intrigued by the SIAM M3 Challenge for some time. It is a mathematical modeling challenge for students that tackles important, meaningful questions.
Here is their website:
...along with some of the problems they have used for the competition...
...and some "entry level" problems that you could use with your class.
In addition, they have recently published a handbook on mathematical modeling that is really amazing. And, even better, they offer a FREE PDF download. Go check it out: