I feel very fortunate to be back at Twitter Math Camp. It is so great to see the Twitter friends I made last year and to meet so many fantastic new (to me) people! For the morning session (2 hours/day for 3 days), I chose Algebra 2. Being Canadian, we do not have a course called Algebra 2. In fact, the content from Algebra 2 fits in grade 10, 11 and 12 courses within our integrated Ontario curriculum! Therefore talking about the flow of the course or the connections within the course is a little less relevant for my situation. However, I am taking pieces and figuring out where they do fit and how I can adapt them to help my students make more sense of math.
Glenn Waddell () spent a large portion of the first day showing how he ties all of the algebra 2 functions together through a common algebraic form.
The one of these forms that most teachers likely don't use is the linear one:
y = a(x - h) + k.
Glenn has blogged about it here. I like the way this connects to the other equations which we do use. I like it, yet it bugs me and I'm not sure why. It makes a lot of sense and is a very useful form. 'a' represents the slope (or rate of change) and (h,k) is a point on the line. Slope-intercept form is great for graphing, but Glenn's form (I'm not sure what to call it) is so much more useful when trying to find the equation of a line given the slope and a point on the line or two points, etc. Once you determine the slope, substitute the point for h and k and you have finished! Here is an example using Desmos.
The more I think about it, the more I think that my discomfort with this form is simply that it is not what I am used to seeing, and perhaps, that it can be simplified (and I kinda like my functions to look tidy). But it really is a smart way of tying together so much of what we do with functions and their graphs. I think I will work with this at the beginning of my grade 10 academic class in September. They will all know y = mx + b and will be working through transformations of quadratics before long, so it seems like a natural fit. Thanks, Glenn!