Tag Archives: linear functions

Introduction to Linear Functions – Buying a Used Car

When our 3rd child was born, we decided to buy a used Honda Odyssey as 3 young kids were not fitting into a sedan. Being the stats geek I am (master’s in statistics at the University of South Carolina – total geek) I collected mileage and price data for all the used Odysseys for sale on dealer sites throughout South Carolina. I then created a the scatterplot shown below. I went to a dealer, showed an agent my graph, and he immediately exclaimed “Where did you get that? We create graphs like that every week!”

It was this experience that led me to the idea of using used car data to introduce linear functions. Shopping for a used car has proven to be a relevant, real life activity the students enjoy.

Here is a link to a comprehensive activity that walks students through various components I use for introducing students to linear function topics.

  • Used car shopping to collect data on 10 used cars of a single make and model.
  • Creating a scatterplot for price vs mileage of the used car of choice.
  • Creating a line of best fit (regression line) to model the data.
  • Creating a linear bi-variate equation (regression equation) to model the data.

The activity is presented on a WORD document (feel free to revise). It shows screenshots to walk student through the Carmax website (subject to Carmax revising their website). The screenshots make it easy for the student to navigate, which increases independence. (NOTE: there is an ample number of Youtube videos on using Google Sheets for this activity.)

The end product looks like this. Note the importance of using 1000s of miles as the slope is more meaningful, -$140.64 per thousand miles, as opposed to 14 cents per mile. I would start with the scatterplot alone to unpack the variables, the relationship between the variables, and the ordered pairs. Then the line and equation can be introduced to show a meaningful use of the line and the equation. The y-intercept has meaning with “0 miles” equating to a new car (I do not explain that new cars have miles already accumulated until we unpack the math).

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Linear Functions with Comic Book Context

intro to linear functions comics

This is a follow-up to a previous post about using comics to engage a student with autism. In the photo above the comics are on sale for $2 each which is a situation modelled by a linear function. The student finished this assignment independently, quickly and accurately (aside from the bars on the graph). (Note that he did not need the table at the top that shows the different number of comics.) In another previous post I explained the different levels of representation (CRA) with the equation being the most abstract. In this handout the equation was the last item addressed and was computed using the graphing calculator (Linreg function).

The following photo is from a warm up given prior to the assignment above. It addressed prerequisite skills for the intro to linear functions assignment. This student confused the x and y axes (you can see some of the points from his initial effort) and I used color coding to clear this up.Do no intro to linear functions comicsThe following photo is the student’s effort on a follow-up problem, which he completed correctly (and again did not need the table at the top).

intro to linear functions independent practice

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