I begin this lesson with a story problem projected on my front board. This helps set the tone for the whole unit by connecting to prior knowledge from Algebra I and also by demonstrating the value of creating with algebra.
The number of calories (C) a person burns performing an activity varies directly with the time (t) spent performing the activity. If a 140 lb person can burn 95 Calories by dancing for 20 minutes. How long should that person dance to burn at least 650 Calories?
As my students come in, I listen to their discussion of how to solve the problem. It's interesting to observe which students try to figure it out by making a chart or table, which grab paper and pencil to start calculating, and which ones reach for their calculators. I let them work on this for a few minutes until either someone has an answer or the activity slows. (MP1) I ask selected students to share their work on the board. (My video addresses how/why I select these students) When the work is all posted I ask my students to all review what they see and offer suggestions and/or critiques of the work. (MP3) After everyone has had an opportunity to comment, I ask them to consider which method they would recommend if I said we needed to find the answers for several more Calorie amounts or times. I expect them to recognize that the equation is necessary to graphing and is much faster than a table or chart for larger numbers.
You will need copies of the Story Problems Challenge for this section. I tell my students that now they get to work in teams create story problems that can be solved using linear or quadratic equations, then swap equations with other teams to compare/critique. I distribute the Story Problems Challenge and tell my students they will be working with their left-shoulder partner. I ask everyone to review the directions and answer any questions that arise. While my students are working I walk around offering encouragement and redirection as needed. After about 15 minutes I tell my students to finish the question they're on and get ready to pass their problems to another team. (MP2, MP4)
I tell them to pass their problems in a counter-clockwise direction. I then tell them that their new challenge is to attempt to solve the problems they've just received on a separate piece of paper. I ask them to make explain any difficulties they encounter and also any problems they find particularly interesting. I circulate again while they're working. (MP1)
When everyone is done, I have them return the problems to the teams who authored them. I tell each team to review the answers they received as well as any comments. I then say that there will be a five minute open discussion time for teams to talk about the answer, comments, and any clarifications they want to make.
As the last step to this creation process and to close this lesson, I tell my students that I would like to use some of their problems for my lessons and ask them to make sure that they've made them all as good as possible. I explain that I need linear or quadratic story problems that are interesting and unambiguous for the reader. During this final few minutes I try to focus on those teams that are still struggling to write well. Each of my classes has a separate folder for work to be turned in, so students place their papers in the folder as they complete the assignment or on their way out the door.