## Reflection: The Music Shop Model, Day 1 of 2 - Section 3: Building the Model

By the end of the 45 minutes period, the class had just begun graphing the system of inequalities!  The homework assignment was to complete the graph; tomorrow we’ll work out what the solutions set is and what it means.  It’s only the 2nd day, and I’m already behind!

For the graph, I’ve found it is very helpful for many students to make two simplifications.  First, replace B and G with y and x, since students are more familiar with these variables.  Second, replace the inequality with an equality.  This allows students to identify individual points to graph and helps them to see the boundary line of the solution set.  After the boundary line has been graphed, reassert the inequality and determine which side of the line represents the solution set.  Finally, reinterpret this solutions set in terms of B and G to make sure that it makes sense of the given constraint.  This is a longer process, but I found that many of my students were simply stumped by an inequality like B + G < 50.

In the final analysis, the primary struggle my students faced was keeping track of the meaning of the symbols being used (see Student Work).  Many students would interpret something like “17 guitars” as “17G” rather than “G = 17”.  They were thinking of the symbol G as a unit label, like "cm" or "sec", rather than as a variable standing in place of a number.  They also had trouble choosing the operation that correctly captured the scenario.  For instance, the total number of instruments might be written as a product rather than a sum.  In this case, I say, "Suppose Jake bought 12 guitars and 18 basses, how would you use your equation in this case?"  As they began to explain to me what they would do, it usually became clear that multiplying didn't make sense.

Taking it Slowly

# The Music Shop Model, Day 1 of 2

Unit 1: Modeling with Algebra
Lesson 2 of 15

## 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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Standards:
45 minutes

### Jacob Nazeck

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