Tag Archives: buying a car

Intro to Systems of Equations: Camry vs Mustang Depreciation

The scatterplot above is an approach I use to introduce systems of equations. Here is the process I use. (Note: I have found that students like math associated with buying a car – relevant, real life application for them.)

  • In my class, students would have seen a scatterplot with mileage and price for a single car. I explain that we will now compare two cars.
  • To review, in a do now or initiation at the start of class I would have one group generate a scatterplot for the Toyota Camry data and the other groups, Mustang (Excel sheet for all of this note: this data is old). Then they would share with each other
  • We would revisit the relationship shown and revisit the idea of depreciation.
  • I show a Camry and Mustang and ask two questions: Which car do you think costs more brand new? Which do you think depreciates faster and why?
  • Then I show them the scatterplot above and ask which car has higher dots at the far left? Explain what this means (Mustangs start off with a higher price). Then I ask about the dots at the far right.
  • The students are then asked to estimate when the cars have approximately the same value.
  • Then I present scatterplot below, with lines of best fit (trend lines) and they are asked the same question. We estimate the specific mileage and price and write as an ordered pair.
  • Finally, I explain that this is known as a system of equations and the ordered pair is the THE solution. The entire unit will focus on finding an ordered pair as a solution.

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Scaffolding for solving equations

 

 

 

Solving equations can be very abstract and¬†inaccessible¬†for students. The photo below shows a scaffolded handout that introduces students to solving two-step linear equations. The students are introduced to buying a car: down payment and monthly payment. This provides meaning for the variable (x is the monthly payment), for the constant (down payment) and coefficient (12 months – fabricated situation). This approach introduces the concept of having two steps and for which to choose. Take note of the little “PEMDAS” on the left side. I explain that solving involves using PEMDAS in reverse

 

scaffolding 2 step equations with buying a car

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