Guidelines and Procedures for Mr. Byrd’s Precalculus Class

Early April 2011

Help!

Help from Me

I’m always interested in helping you if I can—and with anything, not just math. No kidding. But when can I help you? Most periods other than when I teach (Gold 1 and Green 4), most Tuesdays and Thursdays after school, and various other times. Please, please don’t hesitate to ask! My email is: .

Helping Yourself

I may not be available to help when you need it, so how can you help yourself? First, keep all of your notes including the 2-column notes I’ve started using, and bring them to class every time. Second, look at the class website. Speaking of which…

Class Website

I’m putting as much helpful stuff as I can find on the class website. Among other things, it has all the 2-column notes (except sometimes the most recent); the handouts of formulas from the textbook; the unit circle chart; my own “Tips for Solving Mathematical Problems” (which includes links to math websites I think you’ll find useful); this document; etc. It’s at:

A much shorter URL that will take you there is:

Textbook

Our textbook is Swokowski, Earl, & Cole, Jeffrey (2006). Algebra and Trigonometry, with Analytic Geometry, Classic 11th edition. Thomson Brooks/Cole.

Extra Credit

I welcome suggestions for extra credit. The only option so far is this:

  • Anyone who can show me they’ve memorized pi to at least 50 decimal places gets 1 unit of extra credit. (How much is 1 unit of extra credit worth? I have no idea yet.) (Is it important to memorize lots of decimal places of pi? No; this is just for, uh, fun :-) .)

Guidelines for Your Math Work

In General

Three major problems for students in my classes are (1) basic algebra, (2) fractions, and (3) word problems. For #1, believe it or not, almost everyone makes algebra mistakes; you certainly know I do. The best solutions are to minimize mistakes by working very carefully, and get in the habit of checking your work as thoroughly as you can.

There are good Web sites for all three of the above problems. My own “Tips for Solving Math Problems” (available on the class webpage) includes pointers to other sites I like as well as tips. Again, please let me know if I can help you!

Accuracy and “Exact” Answers

Unless the problem statement indicates otherwise—e.g., with wording like “to four decimal places”, “approximate”, or “estimate”, or the answer is an amount of money—all numbers in answers should be exact.

Note that an “exact” answer can be an algebraic expression instead of a number!—and if the answer is an irrational number, you can’t write the exact value as a number. For example, the exact value of 360 in radians is 2; no matter how many digits you give, 6.2831853071795864769252867665590057683943387987502… is just an approximation.

Form of Expressions

Fractions vs. decimals. If the result of a computation involves fractions, whenever possible, leave them as such rather than converting them to decimal form! (Naturally, this doesn’t apply if the problem asks for an answer to so many decimal places.) Of course converting a fraction to a decimal equivalent tends to lose accuracy, but what’s equally important is it tends to lose information. For example, the answer to one problem on the Chapter 9 test was 55/31, or about 1.774194. One student gave the answer as 55/23; from the numerator, I knew immediately that person had a pretty good of idea how to solve the problem and I could give them credit for that, even though they had the wrong answer. But if they’d used the decimal equivalent of 55/23, 2.391304, it wouldn’t have been nearly as clear. Similarly, 2.82843 is very close to. But, unless the context makes it clear or I notice that it’s very close to, the number doesn’t give a clue as to how someone got it; the expression does.

Finally, if you convert fractions to decimals that aren’t exactly the same, in many situations it’ll be impossible to check your answers. If an expression is supposed to equal zero but—when you fill in your results—it comes out –0.03, who knows what that means?

I especially want you to avoidconverting a fraction to decimal form early in the solution to a problem, since the more steps follow the conversion, the greater the chance of problems resulting from either the loss of accuracy or the loss of information, and the harder it’ll be for me to follow your calculations.

Expressions involving mathematical functions (trigonometric functions, logarithm, etc.): for clarity, minimize the number of function references involved. For example, write

instead of the equivalent but less meaningful

Irrational numbers in fractions. For clarity, it’s generally best to keep irrational numbers out of denominators. They should be rationalized in the following way, using as an example:

Showing Work

Showing work is required. (It’s also desirable from your standpoint, since you’ll get some credit for trying even if your answer is completely wrong.) Not showing your work automatically loses points. (But why? To help me know what to emphasize in future lessons. Several people got the right answer to one of the questions on the Chapter 9 assessment despite making a serious mistake at one point; they were just lucky. I wouldn’t have known that if they hadn’t shown their work. True, they lost a point for the mistake, but learning about the mistake should save them many points in the future—in other classes and/or real life, if not in Precalculus.)

If you got the answer by trial and error,that’s okay, but say so, and in that case your work is your trying different things. Show me at least one or two things you tried before you found the solution (unless it was the first or second thing you tried).

Forms of Answers

If there’s more than one solution to a problem and it involves (e.g.) ordered pairs, show them together—not a list of x values and a separate list of y values, where it’s not clear which x goes with which y.

About Tests

In general

  • Talking during a test may result in your getting a 0 for the test.
  • You can always use a scientific calculator or graphing calculator unless I say otherwise.
  • If you put any of your work on paper other than the test itself, please staple it to the test, and be sure your name is on whichever page is in front.
  • Show your work or lose points for not showing it!
  • Try every problem even if you have no idea of how to do it; you’ll get points for trying!

Rubric for Grading

True/false problemsare worth 2 points.

  • Correct answer: 2
  • Wrong answer: 1
  • No answer: 0

“Sketch graph” or similar problems are worth 5 points.

  • Rubric similar to “Other problems” (below), e.g., correct sketch but wrong values in accompanying table of values or vice-versa: 3 or 4

Other problems are worth 5 points.

  • Correct method, with work shown, and correct answer (in some cases allowing for rounding): 5
  • Correct method, with work shown, but wrong answer (due to sign error, early rounding, decimal point in the wrong place, order of operations, etc.): 4
  • Correct general idea but wrong details of method and wrong answer: 3
  • Correct answer but work not shown: 3
  • Wrong method and wrong answer, but evidence of some effort: 1 or 2
  • No answer; orwrong method and answer, and no evidence of effort: 0

Making Up Lost Points

When announced only, if you correct your mistakes on a test and turn it in again, with an explanation of why they made each mistake, you’ll get back half of the points you lost, except that: (1) Fewer than half of the points will be restored for problems you didn’t attempt in the first place. (2) Explanations must show some thought. For example, “I made an algebra mistake” or “I forgot what ln means” are fine; “I didn’t know” may or may not be.

If you redo the work on the original paper, you must make it clear what’s what, e.g., by using a different color or section of the paper for the new work. Please don’t make me guess.

DAB, rev. 10 April 2011

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