Big Questions:

1. What is a solution? How do you find them?

2. What is rate?

3. What does it mean to be a function?

4. Why is equivalency important? (this one bothers me - not sure how to word it)

I'm hoping to keep record of students' understanding of these big ideas along with their algebra skills.

I like your organization by questions. I'm confused about the first one, though. When you ask, what is a solution, what are you thinking they're solutions to?

ReplyDeleteIf I understand your idea, I would almost want to start with a question like, what is a relationship? That is, if you take 2 away from some number you're left with 3 (i.e. x-2=3). There's a relationship first, and the solution follows.

@Dan - I was thinking solutions to equations (linear, quadratic, etc.), inequalities and systems of both. I want my students to understand how solutions can be found by looking at tables or graphs and through algebraic manipulation. By not isolating those ideas, I hope my students are better able to make connections. The idea of the relationship is the natural starting point before moving to formalizing the equations.

ReplyDeleteAbsolutely Sarah! It is so critical that the students develop an understanding between the numerical, graphical & algebraic connections of functions.

ReplyDeleteAs a first year calc and ap calc teacher, this will be my montra. I'm also learning that an early focus on rates of change will set the kids up for later success in these courses.

I look forward to reading more from your blog...

Those are pretty good questions. For the first one, along with "What are solutions? How do you find them?" I would add "How do you write (or represent) them?" This really keys into the tables/graphs/equations piece that is so big in Algebra 1. Also, Rich is right: an early focus on rates of change/growth is key. You know you're doing something right when students talk about slopes in terms of "growth" (or negative growth) instead of "rise over run." The former is so much more meaningful than the latter.

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