**2. Mathematical Writing**

Ordinarily, you will use a regular as signment 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

al low 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. Some one 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 re presentations 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.