We then move into a lesson on Direct Variation, attempting to connect it to our work with rates and proportions (with a touch of measurement and dimensional analysis thrown in). First we do some converting between kilograms and pounds, write an equation for that relationship, and graph it.
Then we see if we can apply what we've learned to a unit rate (price) problem.
Their homework is then to watch the Solving One-Step Equations Video. This is something they theoretically already know how to do, so it should be a review for all of them.
I don't feel great about today's lesson. It's okay, but I feel like I have to lead them through so much that I'm not sure it's that helpful in terms of their learning process or the actual content, and perhaps just 40 minutes of skill practice might be more effective. What do you think, would it be better to can the semi-interesting problems and just practice a bunch of dimensional analysis and then direct and indirect variation problems?
I think it might be nice for the students to find some direct variations in their own lives. They could share a picture and an equation of the direct variation. An example could be a model car placed next to a real car or a soda can with a bowl of sugar (grams of sugar/can). Our they could present a table to the class and have the group come up with the equation using the table.
ReplyDeleteI like 2 things about the first activity. (1)purposeful graphing (used to derive an answer) and (2) writing equations.
ReplyDeleteI think one of the problems people have with Algebra is the abstraction - its greatest asset. Forming equations is perhaps harder than decoding them, not to mention operating with them. The more practice students get, the better, imho. One of my experiences of this can be read here - a Maths in Music activity.
I'm mindful that I keep referring you back to my site - it's about sharing really, not self-promo (ok?). Besides,it saves me from repeating myself....you can tell me to bug off (kindly).
Catherine - Thanks, I think I'll incorporate that in, perhaps as homework over several days (to come up with at least one relevant direct variation in their lives.
ReplyDeleteMalyn - Please keep sharing/linking.
ReplyDeleteFor whatever reason, I never thought it was worth a lesson to work on direct variation. I realized that when I very impatiently tried to get through that lesson in the "Discovering Algebra" textbook, which I seem to remember is the text you have. Perhaps my preferred sequencing was just different, but whatever skills they needed for this I think they acquired later with the work we did with linear functions.
ReplyDeleteGiven the examples you have, is this an appropriate time to distinguish between discreet and continuous? Weight is continuous, while money (technically) is not, so it's there if you feel the need.
Raymond - We actually have McDougall Littell as our textbook, but I only use it as a reference for kids. I'm stealing ideas from Discovering Algebra and other texts, Dan Meyer and other bloggers, and occasionally coming up with an original idea to try to put together my class.
ReplyDeleteI touch on discrete/continuous sometime in the next week or so I think, but not today.