Monthly Archives: May 2014

Stairs, Steepness, and Using Appropriate Tools Strategically

My students are testing this week.  Boring.  However, I do have one class – an 8th grade math lab that is not testing.  The math lab is an elective course for struggling students that is taken in addition to their regular math class.  They don’t test with me because they do it in their regular math class.

The thing about math lab is that there is no set curriculum.  I can teach them whatever I want, however I want.  So a couple days ago when I saw this lesson by Fawn Nguyen about Staircases and Steepness, I decided it was something I wanted to do with my class.  And it was AMAZING!  It was interesting to me how intuitive it was for them to figure out which staircase was the steepest before they were using tools.  Here was a conversation between a student and myself.

Me: So which is steeper, D or F?
Austin: Staircase D
Me: How can you tell?
Austin: Well, F is wider than it is tall and D looks like the width and height are the same.

Perfect reasoning, right? Almost all of them made their decision based on this reasoning.  But when I let them use tools, they did all kinds of interesting things.  Ali divided up the staircases into units that were all the same size as a stair.  She then counted the number of units and then used this as her guide to determine which was steepest.  When she described her strategy, I asked if all of her units were the same size.  I wish I had let another student make that discovery, though.

Faith decided to use the Pythagorean Theorem.  She measured the total width and the total height and then set about using the Pythagorean Theorem to find the length of the slant.

A couple students pulled out the protractors and first discovered that all of the staircases had 90 degree angles, which was not helpful.  Eventually a couple of them started measuring the angle formed by the base and the slant – with a little help from me to learn how to use the protractor.

Shadow measured the total height and total width and compared which one was larger. Shane measured the height and width of just a single step from each staircase.

After we discussed their strategies, I did say the words “rise over run” and it was like a lightning bolt simultaneously hit each member of my class.  “What!!!  Why didn’t you teach us this lesson like three months ago?  I actually understand what slope means now!  Best slope lesson ever!” I agree.  It really was the best slope lesson ever and I can’t wait to use it to introduce slope next year.  I have some follow-up lessons planned for this math lab, but for now, here’s what I learned from this lesson:

My math lab students struggle to Use appropriate tools strategically.

The tools got in the way of their intuition.

So here’s what I plan to do about it in the future:

  • Give students more opportunities to select their own tools
  • Model with ‘think-alouds’ the process I go through to select an appropriate tool.  For example, I think it may have been helpful to build off Austin’s intuitive reasoning of comparing the width and the height.  I would think aloud, “I think this one is steeper because the height and the width look like they’re almost the same.  What tool could I use to measure that?”
  • Redirect more questions to students.  Allow them to evaluate whether the tools that their classmates are using are appropriate.