2. Mathematical Writing
Ordinarily, you will use a regular assignment to satisfy this proficiency as
a
normal part of the course. To satisfy it, you must write a description of your
solution to a
non-trivial problem that meets the criteria outlined below. On your writing
assignments,
your instructor will indicate which criteria you need to work on in future
assignments. If
your assignment is very close to satisfying the baseline proficiency, your
instructor may
allow you to revise it so that it will meet all the criteria.
Please note that you should always do your writing for the
course by yourself.
You may use write-ups of problems that you worked on with others to satisfy
this
baseline proficiency, however, your writing must be your own. If your instructor
suspects that the writing is not your own, he or she will take you to the
Scholastic
Review Board.
Your writing must meet all of the following criteria:
a. Someone who hasn’t seen the problem before can follow
it. You need to
include a clear description of the problem and of any material you incorporate
from class.
You need to explain concepts or vocabulary that are beyond what a typical
student, who
is at the level of a Math 130/131 student but is not in the class, would know.
b. Your paper includes written representations of the
problem, such as pictures,
graphs , and tables, that are appropriate to the problem, clearly labeled and
presented, and
that help advance your argument.
c. The writing flows. It moves from one idea to another in
a logical fashion .
Your ideas are clearly explained.
d. The writing is convincing. You don’t necessarily have
to have solved the
problem completely to satisfy this proficiency, but if there is a piece missing
or a part you
don't understand, you must tell the reader, rather than hoping s/he won’t
notice. The
reader can tell that you know what you are talking about.
e. With only a small number of minor exceptions, the paper
is written using
complete sentences and correct mathematical terminology , grammar, punctuation,
and
spelling.
Ways to satisfy the proficiency: Out-of-class
writing as described above. You can also
do an extra assignment if necessary.
When to get extra help: You will be working on
writing in many of your other classes,
and if you improve your writing in general, it will improve your mathematical
writing. If
you haven’t satisfied this proficiency by the start of the second semester, you
should get
help from the writing center or a learning specialist.
Topic II: Number Theory
3. Number Theory
To satisfy this proficiency, you must show that you understand main concepts
of
number theory: multiples, factors, prime number factorization, and divisibility
rules . If
you use test or quiz questions to satisfy this proficiency, you will have to
correctly solve
at least four of five designated problems (i.e. over 80% of five or more
problems).
Sample problems:
Are the following numbers prime or composite? 251, 252,
253, 255, 257.
Factor 7168 into primes .
Ways to satisfy the proficiency: Test/quiz
questions, test/quiz revision, or instructor
interview.
When to get extra help: If you haven’t satisfied
this proficiency while taking Topic 2,
you should get extra help to prepare for a test covering Topic 2. If you don’t
pass the
proficiency while taking the test, then you should continue to work this
proficiency
outside of class and pass it as soon as possible.
Topic III: Rational Numbers I
4. Modeling Fractions
To satisfy this proficiency, you must demonstrate understanding of at least
two
models of fractions from different categories. Categories are:
1. Area Models: including fraction factory pieces, pies
and pizzas, pattern blocks
2. Length Models: including fraction strips, rulers, cuisenaire rods
3. Group Models : including tiles, drawings of dots, etc.
In order to demonstrate understanding, you must solve a
non-trivial problem, with
a “convince a skeptic” explanation that includes either a demonstration with
manipulatives or a drawing.
Examples of non-trivial problems (all require you to draw
a picture or use
manipulatives to convince a skeptic that your answer is correct):
What is 2/3 of 3/4?
If the purple Cuisinaire Rod represents 2/5, what rod
represents 1/4?
Ways to satisfy the proficiency: Test/quiz
questions, test/quiz revision, or instructor
interview.
When to get extra help: If you haven’t satisfied
this proficiency during the first few
weeks of Topic 3, you should get help as soon as possible. If you don’t
understand
models of fractions, it will be hard for you to do well in the rest of Topic 3.
5. Comparing Fractions
To satisfy this proficiency, you must show that you understand the size of
fractions. If you use test or quiz questions to satisfy this proficiency, you
will have to
correctly solve at least four of five designated problems (i.e. over 80% of five
or more
problems). The designated problems will be a wide assortment of types of
problems,
such as the following:
Placing fractions on a number line .
Ordering lists of fractions.
Finding fractions between two other fractions.
Identifying fractions that satisfy a specific criterion, e.g. less than 1/2.
Ways to satisfy the proficiency: Test/quiz
questions, test/quiz revision, or instructor
interview.
When to get extra help: If you haven’t satisfied
this proficiency near the end of Topic 3,
you should get extra help to prepare for a test covering Topic 3. If you don’t
pass the
proficiency while taking the Topic 3 test, then you should continue to work this
proficiency outside of class and pass it as soon as possible.
Topic IV: Rational Numbers II
6. Operations with Fractions
Operations with fractions: addition and subtraction
To satisfy this proficiency, you must solve one addition and one subtraction
problem involving fractions and give a “convince a skeptic” argument to explain
why
your solution is correct. If you use algorithms, you must justify why they work.
You
may also use manipulatives or drawings. Problems use common fractions ; they are
not
overly complicated, but addition and subtraction problems include fractions with
different denominators . Sample problems: 3/4 + 2/3, 5/6 + 13/9, 9/4 – 7/8.
Ways to satisfy the proficiency: Test/quiz
questions, test/quiz revision, or instructor
interview.
When to get extra help: If you haven’t satisfied
this proficiency near the end of Topic 4,
you should get extra help to prepare for a test covering Topic 4. If you don’t
pass the
proficiency while taking the Topic 4 test, then you should continue to work this
proficiency outside of class and pass it as soon as possible.
Operations with fractions: multiplication
To satisfy this proficiency, you must solve one multiplication problem
involving
fractions and give a “convince a skeptic” argument to explain why your solution
is
correct. If you use algorithms, you must justify why they work. You may also use
manipulatives or drawings. Problems use common fractions; they are not overly
complicated. Sample problems: 2/3 x ½; 3/2 x 1/3.
Ways to satisfy the proficiency: Test/quiz
questions, test/quiz revision, or instructor
interview.
When to get extra help: If you haven’t satisfied
this proficiency near the end of Topic 4,
you should get extra help to prepare for a test covering Topic 4. If you don’t
pass the
proficiency while taking the Topic 4 test, then you should continue to work this
proficiency outside of class and pass it as soon as possible.
Operations with fractions: division
To satisfy this proficiency, you must solve one division problem involving
fractions and give a “convince a skeptic” argument to explain why your solution
is
correct. If you use algorithms, you must justify why they work. You may also use
manipulatives or drawings. Problems use common fractions; they are not overly
complicated. Sample problems: 2/3 ÷ ½; 3/2 ÷ 1/4.
Ways to satisfy the proficiency: Test/quiz
questions, test/quiz revision, or instructor
interview.
When to get extra help: If you haven’t satisfied
this proficiency near the end of Topic 4,
you should get extra help to prepare for a test covering Topic 4. If you don’t
pass the
proficiency while taking the Topic 4 test, then you should continue to work this
proficiency outside of class and pass it as soon as possible.
