## Reflection: Grappling with Complexity Hybrid Cars - Section 2: Activity

When finding an equation for each type of car, my students often need to struggle and persevere. There are several steps that they must think through:

• For operating cost, they must realize that the cost of gas (operating cost) for a whole year must be found.
• To calculate the operating cost, they must divide 12,000 by the number of miles the car gives per gallon, and then multiply by the price of a gallon of gas.

Example: For the hybrid car: 12,000mi/40 mpg = 300 gal. So 300 x \$3.45 yields \$1035 a year worth of gas.

I let students work in pairs so that they can help each other to overcome these challenges. Then, I try to be patient and let them come up the correct equation modeling the cost of owning each car.

My students are very good at trying to get the equation out of me, always asking "is this right?", "is this it?"  I am prepared for them and I only say that the equation must represent the cost of owning and operating the vehicle. After a while, if neither student comes up with the equation and time is running out on them, I give them hints about the two bullet points above.

Grappling with Complexity: Writing Equations in a Modeling Task

# Hybrid Cars

Unit 2: Solving Linear Equations
Lesson 10 of 10

## Big Idea: Can buying a Hybrid car actually save money? Students compare graphs to determine just when a Hybrid is best.

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Standards:
Subject(s):
Math, linear functions, Algebra, Linear and Nonlinear Equations, graphing calculators, modeling
60 minutes

### Mauricio Beltre

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