remarks on recent work

there’s info on assignments here;
i’m hoping everyone knows this already.

i only graded three homework problems.
three points possible apiece, plus one
for appearing-to-have-done-most-of-the-rest:
ten points possible. the 5-day-a-week classes
have a scale of “grade *two* problems at
*two* points apiece, plus one for completeness”.
so, while any slight mistake (using my scale) is
already 10% of the grade on the whole paper,
this is a heck of a lot better than 20%.

when i noticed something without even trying…
an inappropriate long-digit decimal approximation,
for example… on an *ungraded* problem, i went
ahead an remarked on it. but there’ll be quite a
bit of interesting work going *unremarked* here
of course. ideally, every student would talk over
the homework with at least one other student…

a few papers had “no slope” for “zero slope”;
don’t. i let these go by… but, unfortunately,
some writers use “no slope” for *undefined* slope.
so it’s best not to use this language at all.

using graph *paper* for graphs seems to correlate
(positively) with “good grades on HW1”.

intercepts are points, not numbers…
the x-intercept might be (3,0) for example
(not 3). not an enormous big deal…
but it pays to try to be as precise
as we know how.

there was a system-of-equations having
*no solution* on the quiz. i gave full
credit for “parallel lines” in one case…
but we’re looking for “no solution” here.

at least one student panicked pretty badly
on this problem… and *erased* what looks
to’ve been pretty good progress toward the
answer. when you get an equation that
*can’t be solved*… remember that this
doesn’t necessarily mean you’ve done
anything wrong! (and *whatever* you
do… don’t “blank out” on a problem!).

when there *is* a solution for a system,
we’ll prefer *ordered pair* solutions
(for “abstract” problems like the ones at
hand… for “word” problems, it is of course
more appropriate to give “word” answers
[typically including units]).

fractions are *more algebraic* than decimals
and much to be preferred. the calculator is
pretty good at making the conversions, too.
so-called “mixed numbers” like $3{1\over8}$ are
much harder to work with than (so-called)
“improper fractions” like 25/8. students
of algebra should make the effort to get
used to this situation. again, the calculator
can be very helpful.