Saturday, December 05, 2009

Interpreting Functions

I think the kids get functions this year. After we looked at graphs and tables and mappings and saw what functions looked like for these situations (one day) and got a formal definition of functions, the next block day, I started by giving them pairs of objects like: rainfall and tulips. I asked which one depends on the other one? Which one is the input? Which one would be "x" and which one would be "y"? And, the new one for them: which one is a function of the other one? (we discussed what that means). We did that for 3 pairs of things.

Then I noted that THAT was a ton of writing, and we assigned variables to things like r and t, and I showed them t(r) and noted that the input, r, was INSIDE the parentheses, and the output, t, was OUTSIDE the parentheses, and if you were talking to your math boyfriend over the phone, you'd say, "t of r" or "t is a function of r".

Then we got to things like B(h) where B is your tutoring bill and h is the hours of tutoring. I asked them to interpret: B(3) = 120. We did this for 4 problems or so. I liked those types of questions, and we took them to graphs and tables the next day where I made them interpret v(5) or m(10) where there was context around the problems.

Next up, studying for finals and finals and a LONG BREAK to get more than 6.something hours of sleep each weeknight.

7 comments:

  1. David K10:06 PM

    I teach Algebra to 8th graders in the state of Washington. We, too, are on Functions this week (using the Glencoe text). I like the way you help the students see the meaning of function and the relation between the input (domain) and the output (range). What other illustrations did you use besides the one for rain and tulips?
    David K

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  3. Hi David,

    Off the top of my head, I think we did the following:
    weight of rabbits vs available food,
    money left in pocket vs clothing bought,
    weight gained vs. calories consumed,
    area vs. diameter

    I had to be careful with the wording because some of them could be either way. For example, the original wording for the rabbits was: number of rabbits vs. available food, and of course you could make the argument that both depend on each other. Since I didn't want to have that discussion, I carefully worded it.

    There are some great tables in "Functions Modeling Change" by Hughes-Hallett (sp?)

    Ms. Cookie

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  4. Love that idea! Unfortunatly, I went through functions last week... but I'll store this under great ideas for next years planning! Great to hear the voice of other Math teachers!

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  5. Love the idea! I was just telling another algebra I teacher at my school that I did not care for the way McDougal Littell algebra I text handled functions and that we really needed to revisit the topic. Most students are confused about function notation and why it is necessary. Thanks for the inspiration.

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  6. Ooh, that reminds me. I told the kids one of the reasons we need the notation is because it's cumbersome and too much writing to say "___ is a function of ____" all the time when we're doing the math problems. I also know that in "higher math/life", sometimes something is a function of more than one thing, so you could ostensibly have notation such as B(x,y) since B depends both on x and on y.

    Ms. Cookie

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