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 builds off of the problem solving strategies in the Mission Impossible series. "Mission Possible" and the 5 lessons that follow - although unrelated in content - should find the students with a much higher confidence level and a broader skill set for attacking a non-routine problem.

Please see the attached Video Narrative for this section.

The 5 Different Entry Documents have also been provided with the intent for differentiation between groups. Each group receives only one problem. (This also makes for a great presentation day at the business meeting, because the class doesn't have to hear the same problem discussed over and over again!)

The math practice standards and Common Core content standards are spread out throughout this lesson series. MP3 is particularly prevalent throughout: on a in intra-group basis in the problem solving stage AND on an inter-group basis in the problem presentation stage.

20 minutes

Following constructing Know’s/N2K’s with their partner, see the attached Know's/N2K's Protocol I next put the groups together who share similar problems. Since there are 5 problems in the class, there will be 5 different meetings taking place. Because the problem is so in-depth and overwhelming at first, the students will need time to figure out what Know’s/N2K’s they have in common, as well as any that they have overlooked. This is a great way to have the students construct arguments and critique the reasoning of others AT THE ENTRY LEVEL of the problem. So many times in mathematics we do this with a process, or an answer, but we rarely take time to do this at the onset of a new problem. This is the perfect opportunity!

During this process the students will also motivate the need for a common vocabulary and search for words like “constraints” and/or “functions of _____________”.

*Putting students in situations where they have to talk about the problem when they seemingly are overwhelmed or "do not have an answer" is important to help build a classroom culture! We don't want the students to view collaboration as simply "Well, do our final answers match?"*

10 minutes

The previous lesson concluded by challenging the students to express the distances the aircraft in the “Mission Impossible” problem traveled as functions of time. One of the biggest hurdles the students faced during the activity is rescaling the axis of their grid to suit the needs of the problem.

In taking time to discuss this task with the students, we motivate, revisit, and push-the-limits of their understanding of finding solutions. What is a solution? How do we know it is a solution graphically? Will we always have a solution, or will some “missions” really be “impossible”? This is a great way to lead them into their current problem (little do they know) which will actually have MULTIPLE solutions.

To efficiently display a few student work samples, I use my IPAD to take pictures of the graphs of their functions (while having the students share with the people around them for 1-2 minutes). This is much faster than having multiple students redraw their graph on the board!