Pre-calculus material?

Discussion in 'High School' started by MrsRed, Jul 16, 2011.

  1. MrsRed

    MrsRed Rookie

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    Jul 16, 2011

    I will be starting my first year as a high-school math teacher in August - I was just hired a week ago, and I am so excited! I will be teaching five periods, three preps - Alg I, Alg II, and Pre-Calc.

    Now, I took pre-calc about 8 years ago, and so I don't remember what topics we covered in that class. The sequence for the school at which I will be teaching is Alg I, Geometry, Alg II OR Applied Alg II (Applied is considered the lower track, and plain Alg II is the higher track), and finally either Pre-Calc OR Financial Literacy (Financial Literacy is the lower track). Therefore, I am kind of at a loss as to where Alg II ends and Pre-Calc starts. I am teaching in Arizona, and our state standards just provide objectives for subjects, with no differentiation between Alg I and Alg II or Pre-Calc. I can't post a link, but if you go to Google and search for "AZ math standards" it is the first result there.

    So my question to the math teachers here is this: what is typically covered in a Pre-Calc course? The intent is to prepare the kids to take college calculus after graduation, of course, but as you can see at the link to the AZ Standards, there is nothing specifically laid out for pre-calc. Should I just cover the topics which are not part of Algebra or Geometry, and therefore wouldn't be covered at any other point? Or are there subjects which are commonly associated with pre-calc which should form the basis of my class?

    I know that this is somewhat difficult to answer due to the fact that every school has a different curriculum, but I am just looking for a general overview of topics that I should be reviewing now to prepare myself. My reporting date is July 27th, and we start class on August 8th. I have two days which have training sessions on the districts math curriculum, but the principal told me, when I got hired, that the woman who has designed our curriculum program will be working on the material for pre-calculus this year, and so I am not sure exactly how defined the curriculum they have for this class will be. I will be working at a charter school, not a public school, which is the reason the curriculum is not well-defined yet, just FYI.

    Thanks for any help you can provide! :) :thanks:
     
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  3. Aliceacc

    Aliceacc Multitudinous

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    Jul 16, 2011

    How incredibly bizarre that they haven't given you any idea of what you'll be teaching! I realize you were only hired a week ago, but still..

    The good news, of course, is that you can still work on your other 2 preps. Also, consider calling and asking for last year's syllabus. While it is being worked on, I doubt that it's being totally scrapped. At least you'll have an idea of their direction. (Oh, and ask about calculator usage-- which courses use what calculators. You'll want to know as you plan.)

    "Precalculus" is a very vague term-- kind of like "science." So your school may be totally different from mine.

    But here's our Precalc syllabus:

    PRECALCULUS SYLLABUS

    Trimester#1:

    Chapter 8: Sequences, Series, and Probability
    8.1 Sigma, Factorial, Defining a Sequence
    8.2 Arithmetic Sequences
    8.3 Geometric Sequences
    8.5 Binomial Expansion using Pascal’s Triangle
    8.6 Counting Principle, Permutations, Combinations, Distinguishable Permutations
    8.7 Probability

    Chapter 7
    7.2 Solving Systems of Equations and Word Problems

    Appendix B.3: Solving Equations
    Solving Linear Equations, Fractional Equations
    Solving Quadratics
    Factoring, Quadratic Formula, Extracting the Square, Completing the Square,
    Solving Absolute Value Equations, Solving 1 Radical, 2 Radical Equations,
    Word Problems

    Appendix B.4: Inequalities
    Interval Notation
    Solving Inequalities
    Linear, Polynomial, Abs Value, Rational

    Chapter 2: Polynomial and Rational Functions
    2.3 Synthetic Division and Uses, Rational Zero Test, Descartes Rule of Signs
    2.4 Complex Numbers Imaginary Numbers and Imaginary Roots
    2.5 Fundamental Theorem of Algebra
    Solving Higher Degree Equations



    Trimester # 2

    Chapter 2 2.6, 2.7
    Graphing Polynomial Functions (3rd and 4th degree)
    Graphing Rational Functions

    Chapter 9: Conic Sections
    9.1 Circles and Parabolas
    9.2 Ellipses
    9.3 Hyperbolas

    Appendix F.1
    Graphing Lines, Graphing Inequalities

    Appendix F.2
    Linear Programming

    Chapter 7
    7.5 Operations with Matrices
    - Determinants and Cramer’s Rule

    Trimester # 3:


    Chapter 3: Exponents and Logarithms
    3.1 Exponential Functions and Interest Formulas
    3.2 Logarithmic Functions
    3.4 Solving Exponential and Logarithmic Equations
    3,5 Exponential and Logarithmic Models



    Please let me know if I can be of any further help to you.
     
  4. Aliceacc

    Aliceacc Multitudinous

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    Jul 16, 2011

  5. The Fonz

    The Fonz Math teacher (for now...)

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    Jul 16, 2011

    Pre-calc at my school was actually "Pre-calc and Trig"...so we spent a good amount of time on Analytic Trig and trigonometry proofs in addition to the stuff alice posted above (except for sequences).

    I would say a good start would be your textbook...the person working on the curriculum had to have picked out the textbook to suit it, so i would draw out an outline for a year long based on the textbook. then, revise it as you get more information.
     
  6. Aliceacc

    Aliceacc Multitudinous

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  7. Catcherman22

    Catcherman22 Companion

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    Jul 16, 2011

    My Pre calc teach splits into three parts basically...

    First part covers advanced alg 2 topics ( graphing things higher than x^2, solving those types of equations, advanced factoring, rational root theorem, logs, etc)

    Second part is all things trig ( I split it into three parts: basic trig, trig proofs, trig applications and polar coordinates)

    Third part is the catch all, this has things like series, probability, and then finally I hit basic limits and limit definition of a derivative.

    I do make sure the kids understand that the topics build on one another most likely moreso than any other math class they've taken.. so they need to understand each part in order to be successful. This does allow me to go back and spiral in older information within the same part.. which does help
     
  8. MrsRed

    MrsRed Rookie

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    Jul 17, 2011

    Thank you all very much for your help! I have emailed my principal in order to see if I can find out some more information even as quickly as this weekend. I asked to get a copy of the previous syllabus for each course, and I also asked about the textbook, so that should be a good place to start. I am also looking through all of these websites that you posted, Alice -- thank you so much for finding these for me! Like you said, this is such a broad subject matter, but at least now I have some sort of clue as to what I will need to cover. :thanks:

    I have another, related question that you all can probably help me with. Where is the line typically drawn between Alg I and Alg II? On the Regents website, for instance (which I LOVE so far), what material is typically associated with Alg I as opposed to Alg II?
     
  9. Aliceacc

    Aliceacc Multitudinous

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    Jul 17, 2011

    Really good question; there tends to be a LOT of overlap.

    For starters, at least in NY, Algebra II also includes most of trig-- everything beyond SOHCAHTOA. So tney do reference angles, quadrants, cofunctions, reciprocals, half and double angle formulas, graphs, proving Trig identities, Laws of Sines and Cosines...

    But in terms of Algebra, and off the top of my head. (I'm groggy and haven't taught Algebra II in at least 17 years.)
    - in terms of quadratics, Algebra I kids learn how to factor. Algebra II kids learn and can use Quadratic Formula.
    - system of equations: Algebra I kids use 2 variables; II kids learn 3. II kids also see quadatic/ linear systems and quadratic/quadratic systems.
    - Verbal problems: I kids get some of the eaiser problems; II kids go more into depth. My school places a HUGE prioity on verbal problems.
    - complex numbers
    - logs,
    - graphs of exponential and log functions.
     
  10. Aliceacc

    Aliceacc Multitudinous

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    Jul 17, 2011

    I just PM'd you our Algebra I and Algebra II syllabus.

    FYI, we're a college prep Catholic high school in NY As such, we don't follow the state's curriculum; we're free to create our own as long as we can prove it's at least as rigorous as New York's-- and it certainly is.
     
  11. ddmath

    ddmath Rookie

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    Jul 29, 2011

    Alice,
    Can you PM me that Alg I syllabus?
     
  12. math_teacher

    math_teacher Companion

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    Aug 10, 2011

    At our school this is the sequence:

    Unit 1: Functions

    Unit 2: Limits

    Unit 3: Polynomials

    Unit 4: Rational Functions

    Unit 5: Exponential Functions / Logs

    Unit 6: Beginning Trigonometry

    Unit 7: Mini Trig Unit

    Unit 8: Graphing Trig Functions

    Unit 9: Trig Identities (Part 1 -- 3 pythag. identities)

    Unit 10: Solving Triangles

    Unit 11: Trig Identities (Part 2 -- half, double, sum, difference angles)

    Unit 12: Inverse Trig Functions

    Unit 13: Solving Trig Equations

    Unit 14: Vectors

    Unit 15: Conics

    Unit 16: Polar Coordinates

    Unit 17: Sequence & Series

    Unit 18: Parametric Equations & Mathematical Induction

    Unit 19: Intro to Calculus
     
  13. Aliceacc

    Aliceacc Multitudinous

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    Aug 10, 2011

    Sorry; I missed this while I was on vacation.

    I'll send it now.
     
  14. Aliceacc

    Aliceacc Multitudinous

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    Aug 10, 2011

    Math teacher, that's Algebra II, right???
     
  15. Catcherman22

    Catcherman22 Companion

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    Aug 10, 2011

    That's pretty close to my Pre Calc.. we cover conics in Alg 2, so I don't re do it in Pre Calc...

    I also throw in work with Matracies and Kramer's rule.
     
  16. math_teacher

    math_teacher Companion

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    Aug 11, 2011

    Pre-Calc.....
     
  17. Aliceacc

    Aliceacc Multitudinous

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    Aug 11, 2011

    Sorry, I thought you were answering the Algebra I question in a prior post, and KNEW something was out of whack. The trig jumped out at me; we cover that in Algebra II & Trig with our juniors.
     
  18. math_teacher

    math_teacher Companion

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    Aug 12, 2011

    Our curriculum actually doesn't have trig in Algebra -- I know many school do. We do some basic trig in geometry ~ SOHCAHTOA. But we save the real fun stuff including trig proofs for pre-calc. :thumb:
     

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