So today was day 2 of Line week and it went okay, but not as well as the first day. We spent our class period creating a spreadsheet in microsoft excel that had 2 lines where we could easily adjust the slope and y-intercept of each line. I was hoping we could do that in 20-25 minutes, it took about 30 minutes, which left only 15 minutes for plugging in different values (here is the file).
We started with shifting one curve over the other (using y-intercept), making one curve steeper (using slope), one student quickly discovered parallel lines, and so on. We were able to play around and some students started noticing how the y-intercept effect the "vertical position" of the line (yippie!). When I asked how they could guarantee the lines crossed in our viewing screen they figured out the idea of using positive slope in one equation and negative slope in the other. (Tomorrow we see if they figure out using the same y-intercept!)
The graph started to lead to good discussion and reinforced the slope lesson, but we were not able to finish with why mx and b are like terms, which I hoped to do per my previous post. We will need to pick up tomorrow with placing units on our equations to help give it a context!
So it did not go as well as hoped, but we still created an excel spreadsheet that can now be used to solve 2 equations for 2 unknowns where the ordered pair are integers between -6 and 6! And we will continue tomorrow with line week - using our spreadsheet to find more relationships and make/test hypothesis. Then we will move to looking at plotted lines and figuring out formulas -- I am thinking a Jeopardy format - I plot the line on screen, they answer the equation in the form of a question - "What is y = 3x - 2?"
Overall another good day!