## General Teaching – Rules of Exponents

Today in my elementary algebra class we covered exponent rules. I taught it a little differently than I normally do, and it seemed to go really well. Here’s how the class went.

I often begin this lecture by writing the 6 rules on the left side of the board. I then follow with two or three examples of each rule before moving on to more rigorous examples combining 2 or more rules. Pretty traditional & pretty boring.

Today I began by writing the example , and I asked my students what the “answer” was. A studdent told me it was x to the 7th power, so I told her she was correct and wrote that on the board.
I then asked another student to tell me how she got that result, and he told me that she added the exponents.
At that point I wrote the left hand side of our first rule, , on the board and asked the class to tell me what to write on the right side. After they told me  I wrote it on the board.
I followed up by asking my students “Why do we add the exponents?” I proceeded to explain that  was the same as  and  was the same as , so if we multiply we get  or .

At this point I felt that my students understood the rule, and felt more ownership because they were involved in deriving the rule. I proceeded to develop the other 5 rules in a similar fashion

, , , ,

I felt that my students had a solid conceptual understanding of the rules, rather than trying to memorize the rules.

I then put the expression  on the board, and asked my class to give me an expression that would simplify to be  using one of our rules.
One student said , which was good.
I then asked for another student to give me another expression that would work, using a different rule. Another student said .
We did it again, and I got a third student to say .

At this point I moved on to several problems on the board for students to work through, but the next time I teach this I will include more of these “backward” examples – I think they really develop conceptual understanding.

Do you have any tricks for presenting this topic? I’d love to hear about them. Post your ideas as a comment, or email suggestions through the contact page on my website.

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. I blog about general teaching ideas every Wednesday. Let me know if there are other topics you’d like me to cover. You can email suggestions through the contact page on my website.

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• 1. Andy Hynds  |  March 25, 2010 at 6:46 am

I taught the same concept this week, and went over the rule in a similar way. When going over the concept of division, I like to write out the exponents as x * x * x * x… in the numerator and denominator, and show how pairs of x’s cancel out. Often by this point, they already know that subtraction will take place, since they see the connection between multiplication and adding exponents.

• 2. georgewoodbury  |  March 25, 2010 at 6:54 am

Thanks Andy. This approach also helps them to understand the concept of negative exponents (which we’ll talk about today).

• 3. Diane  |  March 25, 2010 at 6:49 am

Good ideas! I hate teaching the sections that are mainly rules. I usually start by showing them a really complicated exponent problem and start the rules with the simple problems. When they see that complicated one – they have a little motivation to do the shorter, easier problems.

• 4. georgewoodbury  |  March 25, 2010 at 6:53 am

Thanks for the comment Diane. I owe you an email – I’ll be in touch soon.
George