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If it leads to them wanting to combine functions in operations, this is great! The idea of a story is a neat way to get them to notice features of a graph, and inherently invites switching representations from visual to verbal and back again. Good stuff!
ReplyDeleteThanks for stopping by, much appreciated.
DeleteTo the story I would add the discussion of how many possible turns could the graph have. Love the rest, especially how the a value stretches the graph but it doesn't change the zeros.
ReplyDeleteGreat point. Yes we did talk about n-1 maximum or minimum extrema, failed to mentiion it. I have an goose bump story to share of one student's work around to avoid factoring at all costs!
DeleteI love pushing them to realize that a positive definition of a polynomial is anything that can be broken down into a series of linear multiplications. f(x) = (2x-5)(3x-sqrt(2))(x+5)(x-2i)(x+2i) etc. Once they grasp this, then they realize what the last year and a half of algebra is for, and why linear functions are so vitally important.
ReplyDeleteNever thought to mention that, only the single variable part. Like. So where do we give them the practice factoring 9x^2-2 as a valid difference of squares. This one throws them for a loop looking for REAL linear factors. Love having students factor over the rationals, reals, AND linear factors, finally they think deeply about what those numbers mean.
DeleteThanks for reading and giving me yummy brain food.
Hello! This post was recommended for MTBoS 2015: a collection of people's favorite blog posts of the year. We would like to publish an edited volume of the posts and use the money raised toward a scholarship for TMC. Please let us know by responding via email to tina.cardone1@gmail.com whether or not you grant us permission to include your post. Thank you, Tina and Lani.
ReplyDelete