Download Is this going to be on the test

1. Is this going to be on the test?
Short Answer: YES
Long Answer: I am curious of why you are asking. If I tell you NO then will you stop trying to learn it? If I
tell you YES then what were you planning on doing?
In all honesty, the hardest problems we face in this class are rarely on the test. As a teacher of
Mathematics I want you to learn how to solve all problems we cover in class. That is the reason that the
answer is YES.
The hardest problems on a HW assignment aren’t meant for everyone to understand and get correct.
Let the hard problems be a guide to what Math class you want to take next year. If you have no interest
in the harder problems then you should probably stay out of IB math. You could pick Pre-Calculus if you
sometimes get them right and Advanced Algebra if you never get them right. If you do have interest in
the harder problems then maybe IB Math is the right choice for you. I would pick SL if you like the
challenge but sometimes get them wrong. I would pick HL if you love the challenge and you keep trying
and trying until you get it right.
2. How much work do I have to show?
Short Answer: Use my class notes as a guide. Show at least as much work as I do. That guarantees that
you will receive all credit for showing your work.
Long Answer: When I was your age I didn’t understand why the teachers always bugged me about
showing all my work. I was able to get the correct answer very quickly and mostly in my head. I thought
that the purpose of math was to get the right answer. I got the answer using any means necessary but I
always got the right answer. I didn’t think showing my work was important. This philosophy got me
through Calculus 2 in College but in Calculus 3 I hit a wall. We would spend an entire page or two solving
one problem. The problem would have 40 or 50 steps. You had to show your work or you would never
get it right. I still hadn’t really learned how to show my work and thus struggled to pass the class.
In upper level math classes you learn that math really is a language and that the language strictly follows
the laws of logic. If you leave out a single step of logic then the answer is straight up wrong. All of you
students that use short cuts are leaving out steps of logic which is a crime against logic.
One little hint is to see how many points the problem is worth. If it is worth three points then I am
looking for specifically three things in that problem to grade. Leaving out one of the steps might cost you
a point (in addition to having to deal with the emotional fallout of committing a crime against logic) but
showing all your work never will. So, do you want to gamble with test points and take random shortcuts
or do you want to respect and follow the steps of logic?
Would you leave out words when writing an English paper?
This
This
This
Makes
Makes
Sentence
Makes
No
Sense
Sense
Without
Words
Words
Words
Of Course Not! The same applies to math!!
Showing all work
Showing some work
Showing BAD work
2( x  3)  8(2  x)  7( x  2)  19
2( x  3)  8(2  x)  7( x  2)  19
2( x  3)  8(2  x)  7( x  2)  19
2 x  6  8 x  8 x  7 x  14  19
2x  6  7x  5
2x  6  7x  5
2x  6  6  7x  7x  5  6  7x
2x  6  6  7x  7x  5  6  7x
2x  6  6  7x  7x  5  6  7x
1
1
* 5 x  * 11
5
5
11
x
5
x
5 x  11
1
1
* 5 x  * 11
5
5
11
x
5
11
5
3. Proper Decimal Technique
This is a work in progress, please let me know if you think it needs change
Most math problems don't need a calculator. But sometimes a calculator is necessary to give you a good estimate for a
non-exact answer.
1. Does the problem have specific instructions? If so, follow them.
2. Use common sense when it comes to deciding how many decimal places you should round to. If the problem is about
number of people, your answer shouldn't include a decimal. If your problem is using American dollars and cents, then you
should round to the appropriate hundredth (two decimal places). If there is not a common sense approach available for a
problem, default to rounding to the nearest thousandth (three decimal places).
3. Rounding. Keep the numbers in your calculator EXACT until the very end of the problem. Use the ANS button on your
calculator to keep your answer exact. Sometimes the situation in the problem requires you to round up, sometimes the
situation in the problem requires you to round down, and sometimes you should just round to the nearest appropriate
place value. It depends on the situation.
4. Usually the exact answer is the best answer. If your answer is 5 , answer
answer
5 and not 2.236. If your answer is
1
,
3
1
or 0.3 and NOT 0.3 , 0.33 , or 0.333 . Of course, sometimes the exact answer won't make sense. If the topic
3
for a problem is age, you wouldn't answer
300 years old, you would answer 17.321 years old (or 17 years old if the
situation didn't require a decimal).
5. In terms of showing work. Show 300  17.320508  17 years old if you are rounding. This work shows that you
know how to get the exact answer but that you thought a decimal was a more appropriate answer. Your math teacher
wants to know that you know the exact answer, even if you didn't use it in your final answer, and the work above does
that.