Reflection: Letters & Postcards, Day 2 of 2 - Section 2: What is Linear Programming?

 

I decided in class that the students needed a bit more practice, so we carefully walked through yet another example of linear programming, paying special attention to the process of interpreting the graphical solution.  The biggest challenge seems to be using a movable line to identify the optimum solution. (see the whiteboard) Most students are satisfied instead to determine intuitively the neighborhood of the optimum solution and then to test all the points in that neighborhood.  Once I get over my frustration at their rejection of the method I'm teaching, I can accept this.  Honestly, it’s a good way to solve the problem, it shows that they clearly understand the meaning of the solution set, and it doesn’t take them much longer than the alternative.  In fact, many students can pin down the optimum solution this way in less time than it would take them to write the linear equation.

I’ve decided to focus my attention, then, on interpretation of the graphical solution, rather than on mastery of the technique of linear programming.  If students can model the situation and then use that model to find the optimum solution, what more could I want?  That's the definition of success in this case!

  What more could I ask for?
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Letters & Postcards, Day 2 of 2

Unit 1: Modeling with Algebra
Lesson 5 of 15

Objective: SWBAT write a system of linear inequalities and use the system to answer questions about balancing time and cost in a real world context. SWBAT explain their solutions to a modeling problem to their peers and respond to the explanations given by others.

Big Idea: Systems are useful mathematical models for situations with a several of constraints. Time is money!

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