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

 

I've attached a fairly typical sample of student work so you can see what students are turning in when they're all done.  This student made a nice graph showing two different "cost lines", one for a minimum of $36,000 and the other for a minimum of $38,000.  Based on our class discussion, she was able to convert the equations into slope-intercept form and replace the variables B and G with x and y.  Presumably, this made it easier for her to draw the graphs.  Her graph clearly shows the parallel nature of these two lines, and slope-intercept form of the inequality confirms this nicely.

Also notice that her initial answer for the point of maximum cost actually lay outside the feasible region.  During our class discussion, a student suggested this solution (perhaps it was this very student?), but others pointed out the fact that it didn't satisfy the second condition since 2*17 is more than 33.  I like the fact that she noted the problem with her initial answer, and then recorded the correct solution that we determined as a class.

  Student Solutions
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The Music Shop Model, Day 2 of 2

Unit 1: Modeling with Algebra
Lesson 3 of 15

Objective: SWBAT interpret a system of inequalities to identify optimum solutions in the context of a small music shop.

Big Idea: Students discover how a mathematical model can help them make sense of the complex problem of opening a small business.

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