After a first half of the semester filled with Probability and Statistics goodness, my freshman course now shifts to algebra topics, and a bridge between topics many have not seen for 2 years as many of these students took algebra 1 in 7th grade. The next few days will be a blitz of past ideas: slope, linear functions, inequalities and absolute value. Today, one of my favorite pictures from Dan Meyer‘s fun site, 101qs, is quite a conversation starter:
Why did they built it like that? How do they eat in that house? How do they get in the front door? What’s the bathtub like? All are questions generated by the class. You can enjoy more interesting questions generated by guests to the 101qs site. And we are off are running with slope!
I find that my students coming to the HS from our middle school have been trained well in navigating slope-intercept form for linear equations. There are some stumbling blocks with fractions, and I need to do some hand slapping to keep kids away from their calculators, but I am mostly satisfied with where students are with slope-intercept form.
Standard form, meanwhile, is quite a different story. Asking students to convert from slope-intercept form leads to painful moments: moving terms, and multiplying to rid ourselves of fractions. But it also allows for entry to a new idea – leveraging relatioships with standard form and developing a new formula for slope, m = – A/B. Developing this via some examples, and letting a few crackerjack students summarize this finding for the class, opens the door for a new method for finding the equation of a line. Now, when presented with a slope and a point, we have two options.
OPTION 1: find the equation in slope-intercept form and convert to standard form. Messy, and some nasty fractions can appear!
OPTION2: use what we have now discovered about slope and standard form to build our equation directly in standard form, and solving for C.
“Why didn’t they just show us this in middle school?!!!” Well, maybe you weren’t quite ready then, or maybe standard form isn’t the star of the show it needs to be. In any case, today was a great day to combine old skills with some new explorations and keep things feeling “fresh”. Tomorrow, the payoff will continue when we look at parallel and perpendicular lines, as homework tonight expands on today’s theme.