October 19, 2016

# Yes, You Will Use Algebra After You Graduate

### By Annie Pettit, High School Mathematics Teacher

Moving. I've done it quite a few times. It can bring a myriad of emotions, but there is always one constant--making a plethora of decisions. Last year, I moved to a new town to take a teaching job. When I researched moving trucks, Budget was \$31.96 per day plus \$.63 per mile while U-Haul was \$19.95 per day plus \$.79 per mile. Which was a better deal? Oh no! It sounds like an Algebra problem. And yes, in fact, it is. The answer to the question depends on how many total miles will be driven. Sometimes this can be harder to figure out than one might think as distance to the truck depot and the potential of multiple trips need to be factored in. Algebra teachers call this scenario a system of equations as there are two different equations that need to be written. I happily got out my paper and pencil and got to work to figure out which would be best for me.

This is not a unique scenario. People encounter the same concept when choosing between Internet companies, cell phone companies, etc. Suppose Internet company A charges \$34.95 per month versus company B who charges \$29.95 per month plus an extra \$100 for the modem purchase. As consumers, we like to know if we are getting the best deal. Sometimes the answer is company A, and sometimes it is company B. Figuring out when the costs will be the same amount and then estimating how long services are needed to aid the consumer in making the best decision for their budget.

When people first hear the world Algebra, solving for x comes to mind. While that is a part of Algebra, it is just the tip of the iceberg. Algebra is more than just a set of concepts. It is a way of thinking. Cathy Seeley, a former president of the National Council of Teachers of Mathematics (NCTM) said, "Algebraic thinking includes recognizing and analyzing patterns, studying and representing relationships, making generalizations, and analyzing how things change."  Algebra is helping the brain develop analytical skills that seek to interpret the world around us. For example, I do not take the same route to work as I do home from work. Why? Traffic and stoplight patterns make a difference. I drove several different routes to my new job, observed which was the fastest, and tried to figure out why. In other words, I tried to figure out the morning commute patterns and evening commute patterns in order to make a generalization of which were the best routes . Algebra and math, in general, is helping the brain develop logical thinking and creative problem solving. These are invaluable life skills that employers value.

Beyond the type of thinking that Algebra fosters, the concepts taught today in an Algebra classroom do show up in the real world. This list is not all inclusive but includes ones that I encounter on a regular basis.
• Proportions: Two Equal Ratios
These show up in cooking, construction, architecture, quilting, etc. A former student once told me, "I couldn't survive without proportions. They make life so much easier." I wholeheartedly agree. For me personally, I use them the most in quilting. As a quilter, you can save quite a bit of money if you can make quilts the exact size you want without buying the patterns. Being able to look at a picture and then scale it makes this possible.
• Exponential Functions: Growing/Decaying at a Multiplicative Rate
Albert Einstein is quoted as saying "compounding is the 8th wonder of the world." He is referring to compound interest that shows up in interest rates, loans, and debt. Exponential decay is even applied to depreciating car values. As a teacher, I like my students to explore credit card and car purchasing scenarios. They are always shocked to learn that there are situations people can get into in which they can never pay off their debt or that people can owe more on their car than what it is worth. These everyday scenarios are models of exponential growth and compound interest. When people learn how this works, it can help them avoid financial hardships. In addition, it can also help a person save for retirement because exponential growth starts slowly. Then as more money is added, the total amount of money grows quickly. By starting to save at a young age, a person can end up with a large sum of money at retirement, even if that person has a modest salary each year.
• Rate of Change and Slope: Change in a Vertical Distance Over the Change in a Horizontal Distance or Change in one Quantity Over the Change in Another Quantity.
We encounter these all the time in everyday language: mph (miles per hour), or RPMs (revolutions per minute). The slope is found in construction, from building the appropriate slant to your roof to constructing a ramp that is to code. A student once told me that he went to apply for a construction job, and his interviewer said he would not hire him unless he knew what slope was and how to calculate it.
There are many more examples that can be given, but I hope these start an investigation into all the ways Algebra is truly used in the real world. Oh, and in case you are wondering, the mileage where the cost is equal for U-Haul and Budget was about 75 miles. Anything less and U-Haul is the optimal choice. Anything more and Budget is your best deal. I will let you solve the Internet problem.