So today was the first day of "line week." We started by breaking into teams and sending them out to staircases through-out the school to measure how 'steep' they are/were. I did this without any direct instruction on how to measure steepness, it was the first thing we did in class.
I only allowed about 15 minutes and each team had to post their solution prior to the end of the time. The answers were all over the board and we spent time discussing and revising but we concluded that rise and run were the critical components! That allowed us to move into lines and graphing stairs of a steepness ratio of 1 - which we then defined as slope.
Then we were able to graph stairs of 1:1 rise to run, 2:3 rise to run, and 3:1 rise to run, etc. Then I graphed slope of 1 and another line of slope -1 and we discussed if they were the same. We then made some analysis of the lines with the idea that the x-axis was class periods and the y-axis being the money they had in their possession (to receive, positive slope or pay, negative slope). That worked really well! That ended the period and we are now moving into the computer lab to use units to tie slope to y = mx + b using excel. My goal is to have the students see that by multiplying mx you get the same units as b..... And Why that allows us to add (like terms!).
Day one was a success.... (playing the theme from Jaws did not hurt either)