Quick thoughts: Exponents

I teach Advanced Algebra at a High School.  Last year I taught Algebra and Intermediate Algebra to accelerated 7th graders.  During both years, when I started teaching a unit on exponents I searched the MTBoS for ideas.  (I love this search engine or I search twitter and click on ‘from people you follow’ in the ‘options’ menu)  I quickly came across 2 posts that added great tweaks to how I had taught this topic in the past.

#1.  My first tweak to teaching exponents was to focus on some error analysis.  I got this idea from Andrew Stadel’s blog post here and a 2nd part here.  Click and read it before you proceed.  Andrew has 3 great resources you can print and use with students at the end of the post.  I used all 3.  Love.  Each worksheet examining errors lead to great student discourse.

#2. I have a few favorite math bloggers and one in my top 3 is Michael Fenton.  He gave me my 2nd tweak, a tweak to my language.  After reading the first part of this blog post (read it now through to the ‘TWO MINUTE TIME WARP’).  I loved how he asked his students to talk about the meaning of exponents.  Instead of saying 10^ 4 is ‘4 10’s multiplied together’ he instead worked on students stating the meaning of 10^4 as ‘4 factors of 10’.

b factors of a

This small shift in language with my students has lead to a much better understanding of rational exponents (see #3 below).  In the past if I showed my students the meaning of 100^(1/2) they would struggle.  Not sure what I am hoping to hear?  Keep reading.

#3.  Also from Michael Fenton’s blog, Reason and Wonder, I found a great post on Rational Exponents that gave me my 3rd tweak.  I highly recommend you read it here.  In the past I’ve been super excited if my students could fluently transfer from a rational exponent expression to something with a radical.  After reading Michael’s post and using the insight I gained in #2 above, I tweaked my language this year and asked things like ‘what is 2/3 factors of 8?’.  Read his blog.  It makes more sense than I can do quickly here.  What I loved about today’s class, was seeing so many of my student’s faces have ‘a-ha’ moments light across them.  Love.

2 THIRDS FACTOR OF 8

BONUS Idea:  If you are teaching scientific notation and powers of 10, I highly recommend you check out these fun videos and links.  The first is an oldie from the 70’s – you would think my 7th graders would have found it boring, but they were intrigued and asked tons of questions.   The 2nd is a version of the video the Simpsons did to mimic the 70’s video.  I did not show this one, but it sets the cultural context of the first video.  The last is a website a teenager created to visualize powers of 10.  Zoom in and out and be sure to click on everything you see.  Amazing.  Enjoy.

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