We started with a few proportions questions as a warm-up. I've noticed that many students are able to solve these questions but they lack structure in their presentation and in explaining their solutions.

I posted these problems on the board and had groups solving the problems at the boards.

I told them to focus on making sure their solution was easy to follow for someone who happened to stop by to read their work. Most students had no trouble doing the work so I had them work on their presentation a bit. We talked as a group about part/part relationships vs. part/whole relationships. We summarized ratios and proportions in their notes and they tried some examples on their own.

We revisited yesterday's work on Staircase and Steepness. Only two students completed the work I assigned for homework. One was able to find a ratio for the base divided by the height that worked. We talked about how the order that his method gave might seem backwards to what would be intuitive. The other student who found a solution went home and taught himself (with the help of the internet) how to use trigonometry to find and angle in a triangle given two sides. I was blown away.

Eventually we settled on the base over the height as a good measure of the steepness. We called it slope. I went back to the suggestion by a student yesterday to put the line on a grid. We looked at how to find the slope then the class worked on practicing solving proportions and calculating slopes.

## Wednesday, September 27, 2017

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