Well Geoff and Michael have been bugging me, and I  was also really inspired by Stadel's recent post on exponents that I wanted to quickly share my little intro to exponent rules for my grade eights this year. They (and I) really enjoyed it, and I think it touches a bit on what Dan Meyer is trying to get at with Tiny Math games.  In Grade 8 students do not need to know exponents, but our school wants them to be familiar with them, before grade nine, so I concocted this little activity.

The Setup

Nothing too fancy here, but basically I printed out this sheet multiple times
exponent_explorations.docx
File Size: 15 kb
File Type: docx
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exponent_explorations.pdf
File Size: 63 kb
File Type: pdf
Download File

I sliced each section, and put them in envelopes at the front of the board titled "Product Rule," "Quotient Rule," "Power Rule," and a^0=?  I told students a few simple directions
  1. Follow the directions on the first slip of paper.
  2. Complete all directions on your large whiteboard.
  3. When you think you have it figured have me come and take a picture.
  4. Practice that rule with some basic worksheets.
  5. Move to the next rule.

The Inspirations

If you can't tell or don't recognize the questions, I was inspired by Exeter.  Reading their problems I realise they have a knack for assessing, and teaching within the context of a clear and concise question.  The question itself pushes students to work through the problem solving in a natural way (even if it is pure math not applied). I worked on these questions for awhile, to make sure that they put the students through the algebraic clarity but they also had a chance to play and punch numbers in their calculator.

(aside) This in my mind is also a less rigorous version of David Cox's fantastic lesson.

The Context

Students had a concept of repeated multiplication.  They knew how to evaluate exponents within whole numbers and could hit the "equals" button on their calculator a repeated number of times.  They were not instructed how to find the exponential form of a number (for example they can find 2^3=8 but they had never tried 8=2^3).

The Payoffs

Since this only needed to be an overview, and we just needed to touch on these concepts I felt that I didn't need to make sure that everyone learned every rule.  Most students were very proficient with the product rule and quotient rule, and figured that the power rule would somehow involve multiplication of the exponents.

What students LOVED is that they could work through it "at their own pace" (KA buzzwords I KNOW, but still!).  Students struggled through it, but it was set up in a way that was just out of their intuitive reach!  The students who arrived at a^0=1 were very easily convinced of that fact, and because of that, I knew I had a winner.

The Drawbacks

Sure they know the rules, and that is fine and dandy, but do they know the reasons behind the rules?  I do not teach associative property in grade eight, and therefore reasoning through WHY these concepts work (at this stage, rather than because my teacher said so, it is kind of because my calculator said so), but I think this is only a small drawback, because students are convinced of these rules, and they feel they are natural because they found them.  The rigour can come later.

Conclusion

I will do this again with students, especially as review.  I think it puts them in a state of problem solving that is not to laborious, but also not rote procedural notes.  Tell me what y'all think!
Picture
The MONEY shot!
 


Comments

04/16/2013 10:30pm

Good work here Timon. I love how you're pushing your students beyond the bare minimum.
One thing about the handout. Can you make it a pdf file? Not all of the equations in your Word document are friendly.
Thanks for sharing.

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05/15/2013 7:34am

Actually, the exponents in your Word doc were friendly to me. A little TOO friendly, in fact. One of them was rubbing my leg.

This is nice. I like how open-ended it is and how it encourages student-led deep understanding.

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