Multiple Representations Fixed Perimeter Problems

There is a lot for students to think about on this warm-up. To frame their work time, I tell them: "The big idea here is to think about multiple representations of the same information and equivalent expressions that show the same formula." When students get stuck with computations or algebra, I redirect them back to this big idea and ask them to try to figure out the details using these connections. The more they think about the big ideas to develop their methods for solving the problems, the more sense their methods will make to them.

Students can work on this warm-up for 30-40 minutes, with you circulating to ask them questions and trying to understand how their are thinking about the problems.

The end-of-week check out gives students the chance to reflect on all of the big ideas of the week. I tend to rush the check-outs towards the end of class, but I find check-outs like these to be more worthwhile if students have a bit more time to think. This check-out, for instance, is best done with 5-7 completely silent minutes. This gives students a chance to think, and helps them know if they are learning the big ideas. 

There is no need for a share-out with this one, because we as teachers can read and process the information on our own time to decide which of these big ideas need more emphasis for the upcoming week.