Transforming How I Teach Transformations

I haven’t blogged in a while, and frankly can never think of something interesting enough to blog.  Or when I do, I completely forget and then cannot find time.  Every once in a while though, I teach a lesson that I want to share with others in hopes I can get insight on how to make it better than it currently is.  

This past week with my Algebra 2 students, I started teaching Applying Linear Transformations. In the past, I’ve always just flat out taught the rules to applying them.  Mainly because I, myself, didn’t fully understand it all and the book did a terrible job at helping me. (as did many internet resources..granted I never looked too hard). Last year, I thought I had THE lesson for teaching it and explained to students that equations are not written in terms of x, so horizontal movements must take that into account.  At this point I had students tediously re-write equations in terms of x, apply the horizontal transformation, and then rewrite for y and look for pattern to make this easier.  It went well for some, but confused many others.  The time it took to perform this did seem worth the outcome.  

This year I tried something different in hopes the students would finally get it.  I gave them a real context problem “Verizon Wireless offers a plan for $15 per month and an application fee of $50.” and gave them a situation to model.  For example: “Verizon give you the first 2 months free” — students were able to identify this would be a horizontal translation right (due to a previous lesson).  I then posed the question: “since this equation is in terms of cost, how will two free months affect cost?”.  The answers I got were incredible.  In the past where I’ve had to show them different ways to think about it, they were coming up with themselves.  By the end of the lesson, I asked students to write their own rules for each transformation.  Again, I got some really amazing responses. A few of my favorites were: “because it’s in the form y = , even if the transformation is related to x, we need to think of how that will change y.” and “to perform a horizontal stretch or compression we can just multiply x by factor a^-1.” It felt good because I literally taught nothing, just used questions to guide them to a conclusion they made on their own.  I dropboxed (i made it a verb) the documents I used.  I apologize now as my class responses are still on the doc, I’m just too lazy to reset it right now.