SWBAT create and interpret exponential functions. SWBAT paraphrase complex arguments as evidenced by writing a summary statement explaining their group's project and reasoning.

Students collaborate to identify, develop, and promote ways to use exponential functions to understand the world around us through mathematical modeling!

15 minutes

For this entry ticket, I have students start to brainstorm lists of different events and phenomena that can be modeled using exponential functions. The entry ticket is meant to initiate student thinking for the group project that they will work on during today's lesson. To minimize shifts and off-task time, I have students work in the same pairs during the entry ticket that they will work on for the project.

After a few minutes I ask each pair of students to share at least one context/scenario that can be modeled with an exponential function and get feedback from the class if they agree and any other constructive comments about the ideas. Sharing out in pairs provides a balance of allowing students to communicate in front of the whole class but not without some lead time to think, talk and write about the ideas they will share in a paired setting.

15 minutes

In this section I lay out the expectations and grading components for the Marketing Exponential Functions Performance Task/Project. I hand out a copy of the **Rubric and Performance Checklist: Marketing Functions Performance Assessment** to each student and give students a few minutes to silently review the assignment before discussing it.

I then go through the overall intent of the project as well as the different components. I also review logistics (materials and where they are in the classroom, expectations around positive behavior during group work, etc..).

Time for questions is then provided and students dive into working on the project! It also is a good idea to explicitly remind students that they already have made excellent headway with the project through the work they did on their entry ticket in today's class.

This project is geared to give students an opportunity to further develop the Math Practice standards **MP3 **and** MP4**. Students have time to create arguments and critique the perspective of their peers in a setting that encourages students to make connections of how exponential functions can be used to model situations and better understand real-world phenomena.

50 minutes

The remainder of the class time is spent working on the projects. As students work in small groups, I rotate among the pairs. At the beginning my goal is to be sure every group has made a decision about the scenario they are going to model. I think of myself as an external organizer providing various levels of support depending on the diverse needs of each pair of students. More information on **Executive Functions, **and how to promote these skills in the classroom, can be found in my strategy folder.

I make a point to ask each group of students what each person is working on. This sets the expectation that everyone should be working on a part of the project during the class. I want to promote division of tasks, as well as the interpersonal skills that are valued in workplace collaboration. If students are not able to identify a role for each person, I make suggestions. I provide help with an immediate tasks and a followup task, for after completing the task-at-hand.

The end result of this project will be a written narrative (preferably typed) as well as visual representations of the students' exponential functions. I encourage my students to be creative and utilize their artistic talent and creativity. I ask the students to think about how they will depict the function and its inverse. I suggest planning caefully for creating both a graph and a table. I inform students that at the end of the project, I will display the work of all groups in the classroom so that their peers can learn from them.

**Teaching Notes**:

- This project also lends itself to a display in the hallway and sets a nice expectation of valuing student work and creativity right at the beginning of the school year.
**Technology Integration:**As an extension to this project, technology such as laptops and tablets/ipads can be used to document student work as well as the process. Students could create videos on a site like Educreation presenting their exponential function and work. Ipads can be used to take pictures and/or video of the work as another means of expression.This use of technology is a great example of how assessments can be made more flexible in terms of how student's demonstrate their understanding of falls in line with**Universal Design for Learning**principle of**Multiple Means of Expression**.

10 minutes

To conclude the lesson, I spend a few minutes recapping the intent of the task as well as expectations and where students can find them (**Rubric and Performance Checklist: Marketing Functions Performance Assessment**).

For homework, each group of students needs to complete the project outside of class. As an Exit Ticket, I have each group of students reflect on the following prompts:

- What did your group do well on?
- What can your group improve upon for next time? What concrete suggestions do you have for how your group can make those improvements a reality?

Before ending class, I ask each group to tell me what their plan is to complete the project. This closing activity helps students break down the steps needed to complete the project. I push them to articulate a plan for completing the project and monitoring their progress as they do so. My goal here is to promote a skill that is important as they continue with their secondary and post-secondary education.

Next class, when students turn in their projects, I will take the time to display all of the presentations and wonderful work that students have created. I also try to invite school administrators and other teachers to see the work and, again, start the year on a positive note of high expectations, challenge with just the right balance of support.