Problem Solving with Polynomials

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SWBAT to apply polynomial factoring in a real world context. SWBAT to present mathematical concepts to Algebra I students.

Big Idea

Real world applications of polynomials in factored form. Communicating mathematical concepts so that Algebra 1 students can learn.

Roll Out

10 minutes

This lesson involves collaboration with an Algebra I class in your building.  If you are unable to collaborate, an alternative version of the lesson can be found in the last section.  

Prior to class, I have my students put into pairs* (MP4).  I team like ability students together since I have differentiated the problems already and of course aim to have kids work together who are going to get along. To make the most efficient use of class time, as the students enter the classroom, I have the groups displayed on the projector, and I ask the students to sit with partners.  

Once the bell rings, I tell the students they will be involved in solving a unique problem solving task (MP1/MP4).  I encourage students right from the start to explore different ways to solve the problem, but that I would like for them to highlight the significance of POLYNOMIALS in their solutions.  As I explain this to the students, I am passing out the entry documents.  There are 5 different problems, and each group gets one.  I have differentiated the problems (1 is the easiest, 5 is the hardest).  You do not need to share this information with your students, in fact, I would recommend keeping it to yourself. The students emphasis on POLYNOMIALS is important since they will be sharing their results in a short informal presentation to an Algebra I class.  This is an incentive for my students to "step up their game" because they'll want to look very competent in front of the freshman and it also helps freshman buy into what they are learning about in Algebra I.  It is a WIN-WIN for all!

 Look for exemplary student work to be coming soon!  Showing students this work is a good idea, especially on a non-routine task.  I plan to create and implement a "6th problem" that way the students don't get any answers from the student work sample.

*If your students are not accustomed to groups it is a good idea to make a note somewhere on the screen or a poster: Here are your groups!  Please remain professional as we roll out this new problem.  My students know "professional" means their attitude towards partners.  I do not want feelings to be hurt because someone makes an off-hand comment.  My students know my expectations on this because I we have the "professionalism" conversation early in the school year.  


5 minutes

At this time, I have the students run a brief Knows/Need 2 Knows session and compare their lists with those of other teams with the same problem (MP3).   This is a launching process I use regularly in my classroom to generate opening discussion about a new problem.  If we don't understand what we are working with, or what the problem is asking, then we will never be able to solve it!

Work Time

25 minutes

Workshop Request Sign Up

5 minutes

Although it is usually relatively easy to see where each group's progress is as you rotate the room, I typically end a class session such as this one by posting an OPTIONAL WORKSHOP REQUEST sheet and allowing the students to sign up for topics/concepts that they need help with.  Due to the fact that the problem is due by the middle of the class period tomorrow, I want to make sure that every student has an opportunity to have their questions answered.  From time to time, a student has an quick question about how to type a symbol in equation editor, etc.  On the next day, I be sure to give start-of-class-priority to these questions.  (It also helps me document students who are taking ownership over their own learning.  I regularly give these students shout-outs at our grade level assemblies.)


Lesson Alternative: If you do not have an Algebra I class collaboration.

1 minutes