## Reflection: The Music Shop Model, Day 2 of 2 - Section 2: Individual Time

Students began by working individually, but while many students correctly converted the cost equation to an inequality, only one graphed it with the rest of the system without being explicitly prompted to do so.  Many students were simply staring at the new inequality wondering what to do.

I pointed out to one group after another that "900B + 750G < 36,000" was structurally similar to "B + G < 50"; they should be able to include this new inequality as part of their system.  This was all the help some groups needed, but others weren’t sure how to go about drawing the graph since the inequality wasn’t in a slope-intercept form. With these groups, I again suggested exchanging B and G for y and x and then converting the inequality to an equality in slope-intercept form.  This was enough for all but one group of students.

Fortunately, once a student had been called to the board to explain how the inequality became a graph, it seemed that everyone understood how to interpret the graph and what its implications were for the feasible region.  Class ended before anyone had a chance to investigate the maximum feasible cost, although several students intuitively reasoned that it should be one of the vertices furthest from the origin.  (To this, yesterday's "fuming" student responded that he had identified all of the feasible solutions, and that vertex wasn't one of them because it didn't have integer coordinates.)

For homework, I asked everyone to repeat what we had just done for a minimum cost of \$38,000.  I want to see if everyone is able to write the inequality, graph it, and identify the new feasible region.  This assignment should also draw out the fact that the cost lines are always parallel and move outward as the cost is increased.

Making Changes on the Fly
Making Changes on the Fly

# The Music Shop Model, Day 2 of 2

Unit 1: Modeling with Algebra
Lesson 3 of 15

## 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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45 minutes

### Jacob Nazeck

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