SWBAT use equations and inequalities to model a situation and solve for unknown values.

Use linear models to help Jack make an exercise plan that will help him lose one pound each week.

25 minutes

At the start of today's class, I organize my students into groups of 2-3. I give students only the first page of The Exercise Plan, as I plan to provide them with an overview of the question being asked. The task today involves both design and modeling elements, so our work flow will be a little different than normal.

In their groups, students will start to think about how to answer the question. I will encourage students to begin to construct an initial plan that will help Jack to lose weight by exercising regularly.

I provide each group a piece of large chart paper where they can make a plan for Jack that will help him to lose 1 pound per week. I explain to students that they should record all of their ideas on the chart paper. An important part of teaching this activity takes place as I observe how students try different plans and evaluate the effectiveness of each exercise plan. So, I ask students **NOT TO ERASE **anything. The Chart Paper is a record of their designs. Like an engineering notebook, it is important for them to keep track of what has been tried and how well it worked. Students should make note of things that do not work, but, erasing or crossing out unsuccessful attempts simply erases valuable information.

As groups work I circulate around the room to monitor the different approaches that are under development. I try not to be too helpful! An important element of today's activity is the opportunity to persevere and continue to seek better and better results (**MP1**). In Part II of this lesson, students will be asked to approach the same problem with more direct guidance. Part I gives students an opportunity to use their own reasoning and problem solving to make sense of the situation.

I find that this is one of those activities in my course that requires students to apply many of the mathematical practices. In particular, focus will be on solving problems (**MP1**), reasoning abstractly and quantitatively (**MP2**), allowing students to construct viable arguments (**MP3**), using mathematics to model (**MP4**) and using tools strategically (**MP5**). Here, the use of tools is meant to refer to the table that students will decipher and use as part of their solution.

10 minutes

Next, I assign each group a section of wall space to hang their chart paper with all of their work from the Investigation. Here's how our Gallery Walk will work:

- Each group should assign one member of the group to stay behind to answer questions about their Investigations and what they have come up with so far.
- The other members of the group will circulate and visit the other team's posters to learn about different approaches that were taken in the design of the Exercise Plan.
- I ask each group to move around the room in a certain direction (e.g. clockwise).
- I ask the students who are moving to bring a notepad to write down at least one idea from each group they visit.
- I typically keep my students moving on a schedule so that they stay on task.

During the Gallery Walk I encourage my students to ask questions about the approaches that they are seeing. I also try to help the students who have stayed behind answer the questions clearly. I find this to be a good opportunity to support students with respect to MP3.

Before setting the students off, I make a final plea to students. I say, "Pay attention to what didn't work, as well as what did work. And, to try to gather as many interesting ideas as possible as you visit the other groups around the room."

5 minutes

After the Gallery Walk students rejoin their original groups to discuss what they learned from the other groups' efforts. Each team should then create a list of good approaches to solving this problem (MP4). If the team has already come up with a solution, they should try to think of how they could refine their approach, or, they should consider whether or not a different approach might be better than their current plan.

At the end of the lesson, I will ask each group to share one or two goals that they have for their work during tomorrow's lesson.