The conversations led to a review of some of the terminology that we've covered (quadrants, origin, axes, etc.). One student chose the lower left because it looked different. I asked what he meant. Eventually, he motioned with his hand indicating that it wasn't as steep. Another student helped him find the word steep. We talked about how the other three looked as though they were the same steepness. This led to some discussion about parallel lines and steepness.

My goal today was to introduce the idea of slope. I used Fawn Nguyen's Staircase and Steepness activity. I've used this activity before (with a grade nine applied class I believe) and I seem to remember it working out alright. Today, that was not the case. Students were able to do the first part just fine. They were even keen to measure things. Most opted for a protractor. Those that didn't weren't sure what to measure. After a while I asked how they could come up with a number for the steepness without using a protractor. I threw up Fawn's image so that we were all using the same terminology.

Some students measured the slant. I asked them whether adding a step would change the steepness? The answer was no. Would it change the measure of the slant? They went back to work. Other students wanted to find the base times height. We talked about that being the area and how we could increase or decrease the area by adding or subtracting steps but not change the steepness.

One student suggested putting the steps on a graph like we did for the warm-up. I was liking where this was headed but when I asked how he would determine which was steeper for those that were close he couldn't come up with anything. He was so close.

Many students were starting to pack it in feeling defeated (I wonder if the heat was getting to them). I stepped in and suggested that they look at a bunch of ratios to see if that would help. I told them to divvy up the ratios and complete a table with the ratios for each staircase. This was their homework.

At the end of class I handed back the assessment from yesterday. There were no overall marks on the page. I gave each question a level and students were looking at each question to see where they went wrong. I was hoping to go over a couple of troubling spots but ran out of time. Have I mentioned that it would be great if this class were fifteen minutes longer? We'll do it tomorrow.

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