Sunday, May 4, 2014

When will I use this? (Laws of exponents?)

The Question: 

I received the following email from my Mom the other day. (She's been a middle school teacher since the early '90s). She wrote:
Jon, I received The Question today from one of my 7th graders today: "When am I ever going to need to know how to do this???" He is working on zero and negative exponents and had to solve problems like this:

Write an equivalent expression for 
The answer was

He understands how to do the problems--just wants to know why he needs to know, why it's not a waste of his time.

My Response:

Good questions! I wrote a blog post about the matter... let me know what you tell him. I'd love to hear how he responds.

That Blog Post (AKA, This Blog Post):

My colleague answers that question this way:
I don't know when or if you will ever need this particular concept. It depends on what you do with your life and what technological advances are made in the future. But you know what you will need to be able to do, regardless? You will need to problem solve. You will need to think critically (reason and prove). You will need to be able to communicate quantitative thinking to others. You will need to use representations to support your thinking and share your thinking. And you will need to make connections in order to consolidate your understanding. Mathematics is a discipline that provides opportunities to practice and strengthen all of these skills. So, as we solve for x, I want you to monitor your thinking because that's what's really important.
(Read his full blog post at:

He's talking about the Process Standards from NCTM (2000), which are now reflected in CCSS Standards for Mathematical Practice:

But just in case that argument doesn't satisfy your young math skeptic, you might want to share the following list of websites with him (see below). It turns out rational exponents are at the heart of a great many useful scientific formulas, not to mention a lot of really cool (and really beautiful) mathematics!

Good luck!
- Jon

Seven applications of rational exponents:

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