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.