Once a week the whole school stops what they are doing and reads for 30 minutes. Today West Reads fell during my grade 10 applied class so we read (most of us did anyway) for part of class.
We then continued with slope which we had really seen in terms of steepness yesterday. I emphasized that it is the ratio of the change in the dependent variable to the change in the independent variable, as opposed to talking about rise over run which many students seem to mix up. To explain why the ratio is not the other way around we looked at some examples and figured out what slope represented in each case. Here are a couple of those examples:
Next we talked about a slope of 0, an undefined slope along with positive and negative slope.
On to examples. We started with finding the slope of a graphed line.
Then we found the slope between two points without a graph. I like to have them focus on looking at the change in each variable separately. For the example below, I asked what the values of the y-variables were (some did not know), then "How do you get from -5 to -7?", "You go down 2", from which we get -2. Repeat for the change in x... "How do you get from -1 to 5?", "You go up 7", so +7. The slope is then the ratio of those numbers.
Students then started to work on a handout. We will need more time tomorrow to finish it up, but I think they understand the concept. I would like to tie this in with the equation of a line now, but you'll have to check back tomorrow to find out what I decided to do as I also feel the need to wrap up this cycle soon.
This was much more of a "lesson" than we usually do in this class. I could change that for next time, but I think it's okay to direct them a little more some of the time. I am happy that I can see how to tackle a topic differently. Teaching this course through spiraling or cycling is really helping me grow as a teacher.