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.

This is a screen shot from explorelearning’s Gizmos. This site has various simulations related to science and math. This one shows multiple reprsentations for a system of equations. The site has 5 minute test trials which can be used to present a topic in class. I used the one for photosynthesis for a 7th grader with asperger’s who was collecting data for his science fair project.

The photo shows a snippet of a handout I use as a discovery activity for solving systems by graphing. It shows the use of color coding as well. I start the lesson with a do now handout that reviews graphing, checking a solution for a system and previews a word problem modeled by a system.