## Staircases and Steepness, Continued

Here is the first part that we did on Thursday.

By Friday morning the kids who did "base times height" learned that these numbers didn't match up with the steepness ranking. They said, "That just gives you area."

So I made these sketches, and hopefully the kids understood why finding area wasn't the same as finding steepness:

Those who did not do "base times height" shared what they'd calculated for steepness:

Because almost everyone got the correct steepness ranking the day before, they knew their homework calculations had to match the order, with staircases B and E yielding the same number.

Rapha: My dad helped me. I learn that the steeper it is, the number gets closer to zero.
Jocelyn: I measured one of them wrong. Did I just get lucky then?
Ryan: I tried base divided by height first, then I changed my mind to height divided by base because it made more sense for the numbers to go up instead of down... if it's gonna get steeper.
Matt: My base minus height did not work!
Arthur: Rapha's kinda the same as Ryan's, except backwards. And if you add her step widths, you get the base.

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I was on cloud nine — the same way I felt after doing Mr. Stadel's File Cabinet lesson with my geometry kids. Mr. Stadel wrote a wonderful post of how the lesson went in his classroom.

Then I finally said the word slope, but I never said "rise over run." We ended class with this video "Tutorial - Measure Slope Steepness" by Bruce Tremper, Director of the Utah Avalanche Center.

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We had a busy but fun Friday as it was also our 3rd quarter PFO-funded Einstein pizza party. Luckily my prep period is right before lunch to allow me to leave campus to get the 8 pizzas at Costco. The weather was gorgeous and we had 10 minutes left of geometry, so I took the kids outside to play Fizz-Buzz. If you've never played Fizz-Buzz with your kids, then don't start unless you want them to constantly pester you to play the game, even when there's only a minute left of class.

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• May 5, 2012 11:22 PM Peter Price wrote:
Love your comment 'Then I finally said the word slope, but I never said "rise over run."' - the focus of your pedagogy on having students think is captured in this short sentence.

There's a reason great teachers of math DON'T jump in with the formula as soon as they can, which you illustrate beautifully in this pair of posts, Fawn.

I love the way you allow your students space to express what they are thinking, and work through the problem of working out the mathematics in the question you have set them. (By the way, your recent class video showed just how much freedom your kids have to say what they are thinking, and to *argue* for their hypothesis!)

This all takes time, but the payoff is surely worth it. Please share these insights with other teachers when you get the chance - everyone who teaches math should hear this!
1. May 6, 2012 8:52 AM fawnnguyen wrote:
I'm grateful you picked up on that. I was guilty of explaining slope as rise-over-run all the time, and kids of course get them mixed up. I'm trying hard to undo the lessons that I sucked at. No more excuses! What is lovely is the less I talk, the more my kids get out of the lesson!

Your support and encouragement help me more than you know, Peter. This online community is amazing. Thank you!!