SWBAT create equations and inequalities to solve problems.
SWBAT represent relationships between quantitates and constraints graphically.
SWBAT interpret solutions as viable or non-viable options through the context of the mathematical model.

Students will work in small teams to solve a real world problem and present their findings in a whole-class business meeting!

15 minutes

*This lesson is DAY #2 of a problem solving series - a "unit inside of a unit" if you will. *

I begin class with an opening workshop about what I observed in **day #1**. A workshop, as I define it in my particular class, is nothing more than a student-requested lesson. Although it is really nothing more than a change in terminology, I choose not to call this a "lecture" or a "lesson" because these words (whether true or untrue) traditionally imply a passive student roll - or that I am delivering it to them without a choice. Calling them "workshops" is nothing more than a creative way to frame the delivery so that it is student requested. In summary, a workshop really is nothing more than a lecture or lesson, but I try to frame it as if the students actually asked for it!

(Framing it this way is a little bit of an art sometimes... especially in a math class. Please see the attached video narrative that explains how I attempt to do it for this particular lesson.)

The overarching theme of the workshop is for the students to share and brainstorm an effective problem solving process on their way to the "3 Tips and Tricks" activity in the next section of the lesson.

Please see the attached video narrative for further commentary on this section.

10 minutes

In this activity, I probe the students to reflect on their personal problem solving strategies (building off of the start of class workshop). To understand where the students are at, and to get them to where they need to go, it is VERY helpful to have them talk about what their tendencies are when attacking a word problem. Although most students have not had significant experience with in-depth problem solving, especially since the CCSS are so fresh and new, the students do likely have a series of assumptions and tendencies that resonate with them as they attempt to make sense of the complex task. To pull these things out of the students, I ask them to make a list of three suggestions that they have for someone else who is attempting to solve an overwhelming math problem. You will be surprised at the quality of things that they come up with! I first ask if anyone would like to volunteer to share their lists, and then ask several students who did not volunteer to share out as well. Small activities like these go a long way to creating a strong culture in a math classroom.

To culminate the activity, I ask the students to come to a consensus on what they think the three most important things that were mentioned should be. I make a note of these three things, post them on our wall, and am sure to highlight when I see positive instances of these things throughout the next several days.

At this time, I circulate the Exit Ticket to the students. I share with them that I would like for these questions to be answered by the end of the class period, and to use the great problem solving strategies that we just revealed in the workshop/discussion to accomplish the task. The Exit Ticket is not due until the end of class, and will take the students some time to complete.

10 minutes

After all of this problem solving talk, the students are likely ready to get going! With the help of the opening workshop, they will likely now be ready to re-read their problem and highlight any significant information that they initially overlooked. While I let them get started, I rotate the room and answer any questions that they have KEEPING IN MIND that it is often best to answer a question with a question – we don’t want to reveal too much to the students! Math teachers, including myself, often water down mathematics so much that it is unbearable, and merely becomes a series of steps. Also, it is in our teaching DNA to want to help kids, but unfortunately we do this too much, or not in the best way!

10 minutes

To wrap up this lesson, I ask the students to complete the attached exit slip with their partner. This data will help me identify which groups may need additional support in understanding the initial breakdown of their problem. I believe it to be an accurate template for assessing progress in the problem.