Sunday, October 28, 2012

Converting between Exponential and Logarithmic Expressions - The Snail Method

The last unit in trigonometry was Exponential and Logarithmic Functions. One of the early learning targets of the unit was converting between exponential and logarithmic expressions. Now this topic can be taught a variety of ways and initially, I had asked the kids to look at the patterns and what usually was happening. I then had a very excited hand shoot up in the room and ask if she could teach her classmates a trick. I can take no credit to this trick as she had learned it from a previous teacher but she called this method, The Snail Method. It's best to approach this by going from log to exponent and then doing the reverse.

The method goes like this. Create a snail head around your log base b. And then you create the snail shell by raising this b to the power and being set equal to our last part.  Now, my kids loved this method  but weren't truly convinced that it looked like a snail (we slightly forced it).

It's important to also discuss the inverse property of log base b and the exponent with base b as this leads into being able to solve exponential/logarithmic equations but if you constantly refer back to this method, it creates a comfort zone, a Linus blanket, if you will. I used this method to also discuss graphing logarithmic functions in terms of an exponential function.

Welp, that's really all there is to this short cut but it did create an "ah hah" moment and also created some of the success in this unit. 98% of my trig class doesn't have to retake their test. It's part of my policy that kids have to retake a test if they do not master any learning targets. When I announced this stat, both classes applauded. I haven't heard applause since the day I let them listen to Dr. Seuss. So thank you, my student, for your enthusiasm and helping your classmates out, a practice, which I always ALWAYS encourage!

Winning Miss Rudolph, Winning :)


  1. I just wanted you to know I am reading your blog and really enjoying your great ideas! Thank you for taking the time to share!

  2. I totally use this circle method in my class and what's funny is that last year some of my students started calling it the Snail Method too! You definitely have to use your imagination, but hey, whatever works right? It would be even funnier if your student was one of mine last year (I come from a highly transient school with a lot of military kids). Thank you for sharing this and making me feel like I'm not the only one who finds these sometimes silly shortcuts useful. =)

    1. Sometimes, we need to find a way to laugh in a math classroom :) I may act completely ridiculous sometimes but it gets a laugh out of them and holds their attention. Glad you too like this shortcut!

  3. I actually learned very similarly! My teacher used the phrase "Circle the base and run the race" and to finish our work we would have to get to the finish line "equal sign." When simplifying log expressions, she would say "Jump back jack, or take the cowboy off the horse."


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