Problem Set for Previewing Unit 2

In the second unit of Math I students
will be shown the 4 basic operations (addition, subtraction, multiplication and
division) when given polynomials. We
begin the unit with showing the students to identify monomials, binomials, and
trinomials; then we have the students identify the leading coefficient and the
degree of the polynomial.

__Vocabulary__

Monomial Binomial Trinomial Coefficient Degree of
a Polynomial Like Terms Distributive
Property

__Background__

To begin we
need to develop an understanding of the differences between monomials,
binomials, and trinomials. We want to
connect this back to the functions that the students learned about in the first
preview of unit 1. The function f(x) = x
is a monomial, it is written in the form ax where a in this case is 1. If we take this monomial and add to it
whether it be a constant or an unlike term we have a binomial (ex 2x+1; x^{2}-2x);
thereafter, if we add an additional unlike term we have a trinomial (Ex. x^{2}+x+3;
x^{4}+x^{3}+3).

__Adding and Subtracting Polynomials__

Now that
the students can identify polynomials, we begin with addition and
subtraction. Using various examples and
this activity we can show students
that addition and subtraction of polynomials is the combination of like
terms. We need to make sure that
students understand that x and x^{2} or two different terms. Also that even though x is the most commonly used
variable we want to make sure students now that any letter may be in place of
x.

__Multiplying Polynomials__

Here we
want to begin by multiplying by monomial times a polynomial and have the
students understand that this multiplication is using the distributive
property. This notes
sheet from Henrico School District can help to review distributive
property. Once the review is complete we
move on to teaching about multiplication of binomials. Here is a PowerPoint
presentation to help. We want to make
sure that the students understand that the multiplication of any two binomials
can be represented as the area of a rectangle.
Here is two worksheets representing the multiplication of binomials in
both ways students need to understand as the area
of a rectangle and using the FOIL method.