Reflection: The Music Shop Model, Day 1 of 2 - Section 4: Discussing the Model


As I mentioned, my class didn't get to this part of the lesson until the next day.

Students are much more confused by the graphing of the system than I thought they’d be.  (One young lady approached me privately before class to admit that she was totally lost. “Remember,” she said, “there’s a reason I’m only taking Geometry and Algebra 2 my senior year.”  I guess she meant that I shouldn't expect too much from her, but we'll see about that!)  So when class began, we carefully discussed how to turn a verbal expression into an algebraic one, using the sentence, "the number of guitars is at least twice the number of basses", as our example.  This was student-directed in the sense that I asked students to explain the strategies they used or the ways they thought about the process.  It took about 10 minutes, but I think it was helpful for very many students.

I found that when students came to the final problem (identifying feasible options for Jake) many were not making use of the graph.  Instead of identifying points inside the feasible region and then interpreting them in context, they were guessing at solutions and then checking them by hand against each constraint.  I called for everyone’s attention to point out the usefulness of the graphical solution.  By study hall, I found that one student who was struggling previously seemed to have made very clear sense of this “feasible region” and was able to recognize the point of least cost without prompting (see Student Work C).  This is progress!

  Taking it Slowly, Part 2
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The Music Shop Model, Day 1 of 2

Unit 1: Modeling with Algebra
Lesson 2 of 15

Objective: In the context of a small business, SWBAT represent constraints as a system of inequalities and identify viable solutions.

Big Idea: A system of inequalities is used to model a business situation that requires students to balance various cost constraints.

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