4

# Quick Thoughts: Logarithms

### Teaching Logarithms – “Standing on the shoulders of giants”

‘Standing on the shoulders of giants’ – A metaphor of dwarfs standing on the shoulders of giants expresses the meaning of “discovering truth by building on previous discoveries“.  I find the Math Twitter Blog o’Sphere (MTBoS) a place where in my classroom I am standing on the shoulders of so many phenomenal math teachers from around the world.  I read their blogs and steal their stuff to use in my classroom.
A week or two ago I wrote about what I learned from the blog world that helped me introduce and teach exponents.  You can read that post here.
Since that post I have stood on the shoulders of many.  My students and I have been having fun with LOGARITHMS.  Here are a few posts I found particularly useful in helping me frame this topic with my students.
1. DO THIS!  From the amazing GIANT Kate Nowak’s webisite I found her post on Introducing Logarithms.  You need to read this.  Introducing logarithms the first time using the word ‘power’ in place of log was revolutionary.  Here is what the slides I used with students looked  like: In the words of giant Kate Nowak “And then let them in on the dirty little trick that in math we insist on calling it a logarithm instead of a power when we write it like that-To answer the inevitable “What the hell?“”  If you go to Kate’s site, you can even see her full notes for the lesson.  I totally believe introducing logs this way has allowed most students to have connected  logarithms to exponents in their brains.  Here are the word doc’s of my slides above (some of which I had students glue in their notebook).
2. AND THIS! This is a small tweak, but a good one.  Amy Gruen talks about using a big loop with logarithms.Amy Gruen talks about using a big loop with logarithms.  Here
is her a picture from her blog and then how it played out in my room.
I loved this because I have always seen this invisible loop in my head when I work with logs – though no one necessarily told me about it.  I loved being intentional with it.
3. AND FOR SURE, FOR SURE THIS! MiMi’s blog ‘I hope this old train breaks down…‘ has a provocative title “What just MIGHT be (for me) the Secret of Teaching Logarithms” I used her stuff on Day 1 along wit Kate’s stuff.  I HIGHLY recommend you do the say.  I drew thought bubbles with every logarithm we looked at for the first everal days (and had my students draw them too.  At the end of the unit – almost all students could look at any logarithm and say something like “What power of ____ that gives a value of _______ ?”.  Loved it.
4. AND THIS! Kate Nowak had a 2nd post on having students Discover the Exponent Properties.   I adapted her handout here: Log investigation and daily practice 3s  I loved the first 2 parts, but I need to rethink the third part before using it next year.  Read her post though.  This was good stuff.
5. Here is a copy of the exponent rules the teachers at my site gave students.  We matched up the properties of exponents with the related property of logarithms.  It is a work in progress.  There are a few tweaks I will make in the future.Exponent and Logarithm Rules
6. I used Kate Nowak’s Add ‘Em Up review task to review solving with logarithms.  Here are 2 sets of 4 cards I used in her task. Add em up Logarithm Review  Read her post here first though.
7. EXTRA’s
1. From the ‘Agree or Disagree?’ website, check out this cool task.agree_or_disagree_logarithm_statements
2. You must play Kate Nowak’s Logarithm War   The cards for this are here: logarithm war cards
3. Meg Craig is so generous in sharing her entire units.  Check out her resources here (scroll down for the logarithm unit.
4. I saw this too late to use it, but Julie at I Speak MathJulie at I Speak Math has a task for why we need logarithms using ZOMBIES.  Next year.
5. At my school we did a huge project in this unit on college loans (this is another whole post I should do sometime) – It is super powerful.  We are working hard to make sure our students don’t graduate from college with huge debt.  Good stuf.
6. I love using visuals that trigger students brains to connect 2 topics.  One crazy thing I did to do this with logarithms was to show a visual of what I called an Exponent Tree (and a
log) – asking students to notice what was happening to the branches in the tree and looking at how many little branches there were at the endpoints of the trees…then I used this visual…and the finally this one….Silly I know.
##### Sara VanDerWerf

I am Sara Van Der Werf, a 24-year mathematics teacher in Minneapolis Public Schools. I have taught math in grades 7-12 as well as spent several years leading mathematics at the district office. I currently teach Advanced Algebra at South High School and I'm also the current President of the Minnesota Council of Teachers of Mathematics (MCTM). I am passionate about encouraging and connecting with mathematics teachers. I'd love to connect via twitter.  Join the community.  Tweet me @saravdwerf.