## Introducing Systems of Equations: A Tasty Learning Experience

11/12/2012

The "after-math" of introducing systems of equations. Delicious pun, huh?
Introducing systems of equations about the same time of year as Halloween candy flows freely can be dangerous. I tried to use students' sugar cravings to introduce the topic in class though.

I have a sweet spot for Little Debbie's Oatmeal Creme Pies and noticed a peculiar pricing setup betwixt their Single Decker and Double Decker snacks.

At a budget-friendly price, I was able to bring snacks for my students to help solidify their work on the example we posed to introduce systems of linear equations.

Gimmicky, I know, but it definitely grabbed their attention, wondering why I brought snacks that day.

The rest of the example relied heavily on the photo at left, which showed two different "recipes" of Oatmeal Creme Pies available at our local convenience store, one the traditional Single-Layer-O'-Creme and the other the legendary Double Decker. This gave students a familiar context and placement of the example and led to a pretty casual conversation that was more engaging than cracking open the textbook, without a doubt.

We investigated several things about the snacks:
• Does the weight matter for the price (hinting at a use of direct variation which we had studied previously)?
• What are the things about the snacks we CAN change and which things are non-negotiable? (i.e. what are our variables and our constants in this scenario? I was proud they got this outlined so quickly.)
• Is there a more efficient way to solve for the cost per cookie layer and cost per creme layer?

So, with hook baited, we entered into the strategies for solving linear systems of equations, notably in this instance the substitution method. We set up the system of equations at the bottom of the graphic at left and solved, arriving at an astonishing revelation:

The creme layer costs ZERO cents!
(The cookie layer costs twenty-five cents, as we discovered.)

Students had a hard time wrapping their heads around this, thinking more of the context or production costs until another classmate emphasized that our goal was to figure out the PRICE for each cookie and creme layer, not the COST.

This was a decent introduction to the idea of a solution for a system of equations, because students emphasized to one another that zero cents for a creme layer did not make much sense on the surface, but the pricing structure we solved for WORKED with the label price of each snack (made a true statement). When I had to back up and give a concrete definition for what a solution to a system is, students had already seen it used in context and had a more concrete understanding of how it worked in the abstract sense of the topic.

I hope you enjoy this example as much as my students did. Without a doubt, timing during the school day was critical with this example. Oh, a side note: I did not use the Oatmeal Creme Pies as pictured; I bought 12-packs that were a bit smaller but still grabbed students' attention just as well.

For now, I need to run. Just reflecting on this lesson is making me hungry.

--Keltner--

## Scott Keltner

Math teacher and loving it. Tech-savvy because it's necessary. Husband and dad (only male in the house besides the dog).
Kansas, USA