functions

Discussion in 'Secondary Education' started by WaterfallLady, Nov 4, 2009.

  1. WaterfallLady

    WaterfallLady Enthusiast

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    Nov 4, 2009

    I am a special ed. teacher and I am teaching a self-contained algebra class. Next week, I am supposed to teach them functions! I never learned functions. or I probably did, but don't remember it! Does anyone know of a good resource I can use to get caught up? I am a fast learner and learn best from seeing answers and figuring out how the problem was solved. Does anyone else have advice? EEK!
     
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  3. WaterfallLady

    WaterfallLady Enthusiast

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    Ok...I looked them up and I do remember them, the book presents them in an awful way and I can't understand it.
     
  4. HMM

    HMM Cohort

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    Are you given any more detail about what specifically you are supposed to cover? What level is this?
     
  5. HMM

    HMM Cohort

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  6. Aliceacc

    Aliceacc Multitudinous

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  7. groisamomma

    groisamomma Rookie

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    Nov 4, 2009

    The first time I taught functions (almost completely foreign to me, too) I got hold of the Barron's Regents Prep book they use in New York high schools. It breaks down everything in a simple, easy-to-understand format, yet it gives a broader scope of information than just what you'll be teaching middle schoolers.

    Good luck!
     
  8. WaterfallLady

    WaterfallLady Enthusiast

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    The level is algebra I b. THe students are pretty low functioning special ed. students in self-contained classes who are trying to get their standard diploma.

    We use Prentice-Hall. We are on chapter 5 so basic functions have already been introduced. I showed them using a function machine. For example, you put 4 in and get 8 and 5 in and get 9 so the function is +4.

    The first example for 5-2 is using a mapping diagram. I don't understand it at all. I know my students won't. For example 2, it teaches the vertical line test. Can I just teach that? It's still really confusing. Is there another way to explain it?

    I think they will be fine with the evaluating functions part but the other part is so confusing!

    I'm looking in the teacher's edition and let me see if I got this right please (including the reason,because the TE gives the answers but not why).

    Use a mapping diagram to determine whether each relation is a function.

    [(3,7), (3,8), (3,-2), (3,4), (3,1)] no because 3 needs to only match with one number so it can either be (3,7) or (3,8) or (3,-2) but not more than one match with the 3.
     
  9. Aliceacc

    Aliceacc Multitudinous

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    Basically, a relation (or equation) is a function if its graph passes the vertical line test: a vertical line, no matter where it's drawn, can only hit the function once. So the shape of the letter V is a function, but S is not.

    Translated into ordered pairs, it means that no "X" value (the first in the ordered pair) can repeat. The y's can repeat, but not the x's.

    So you're correct; the value x=3 is used more than once, so it's not a function.
     
  10. WaterfallLady

    WaterfallLady Enthusiast

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    Thanks ALice!

    I looked at the Regents site some of you told me to; its wonderful! I've used it before but forgot about it. Actually, I got a good deal of my Algebra 1a materials from there because they give good examples and have fun reinforcement activities.

    I swear, in an effort to make things simpler, our math book confuses us. You should see the adapted (special ed) study book. The way they explain it is even more confusing than the way they explain it in the regular book.
     
  11. Aliceacc

    Aliceacc Multitudinous

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    Math textbooks are notoriusly difficult to read!!!
     
  12. ddb23

    ddb23 Companion

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    Nov 12, 2009

    One idea to help with mapping:

    Create two columns: Students and Favorite Colors

    List about 10 students and 5 or six common favorite colors (+ other). Ask the students to identify their ONE favorite color and then draw a line from the name to the color. If everyone follows directions and only names one color from the list, you will map a function. If someone doesn't follow directions, then you don't have a function. Compare what happens when someone "malfunctions" and doesn't follow direction.




    Also, you could compare functions to a vending machine. This also really helps with mapping.

    The buttons on a vending machine are the inputs, the drink that you receive is the output. Each button has only one output. List the buttons down the left side (input or x) and the drinks down the right (output or y). Map the choices and again compare with what happens when the machine "malfunctions."

    You can do this for a variety of different scenarios - student names + their 3rd period class (can't be in two places at once); students + their ages (two people can have the same age, but one person can't be two different ages). The idea behind mapping is to see that an input can't "split" between two or more outputs.

    I have a few presentations on this. PM me if you want me to email them to you.

    Good luck!
    db
     

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