Multiplying Polynomials

Class Intended: Algebra I Mathematics

Academic Standards: Standard 1 Operations with Real Numbers
Students simplify and compare expressions. They use rational exponents and simplify
square roots.

A1.1.3 Understand and use the distributive, associative, and commutative properties.

Standard 6 Polynomials
Students add, subtract, multiply, and divide polynomials. They factor quadratics.
A1.6.2 Multiply and divide monomials.

Performance Objectives:
All students will multiply two polynomials together using the FOIL or the distributive
property on the homework problems receiving 14 out of 17 correct.

Assessment:
The first assessment is working on the review packet. It will help jog their memories of
previously learned items and prep them for the Core 40 test.

The second assessment is turning in their homework assignment on time from the
previous day.

The final assessment will be by the homework assignment.

Advanced Preparation by Teacher:
· Create the review packet of previous ISTEP questions that could possibly be on the core
40 test.
· Have specific examples or types of problems that I want to show to make sure that
students grasp it.
· Look over the homework problems to help foresee any problems or questions that might
arise and go over those problems in class.

Procedure:
Introduction/Motivation:
When students enter the classroom I will start off with explaining how we are
going to do some review as advanced preparation of the Core 40 test that they need to pass. I
will split the class up into groups and hand out the packet to everyone. Once most groups are
done with their packet I will randomly pick groups to put up different problems on the board.
Once all problems are on the board someone from the group that put up a problem will have to
explain how they got the answer.

Step-by-Step Plan:

1. After the review packet is over I will have everyone get out the homework. I
will collect the homework that was assigned from the previous class.

2. Then, I will start into the lesson. Since they added and subtracted
polynomials the other day it is only logical to multiply polynomials today.
We are going to use an easy method called FOIL. The only catch is that it
will only work when multiplying a binomial by another binomial. Each letter
in FOIL is stands for another word. This is a mnemonic device call an
acronym.
a. Who can guess as to what the F stands for? (Analysis)

3. F does stand for first. We are going to multiply the first term in both
binomials together.
a. How about the second letter, O? (Analysis)
O is outside. The two outside terms (the farthest left and farthest right) will be
multiplied together.
b. Can anyone guess as to what the I will stand for? (Analysis)
I stands for the inside. The two terms that are on the inside or the two other
terms besides the outside ones.
c. Lastly, how about L? (Analysis)
L is last. The last terms in each of the binomials will be multiplied together.

4. The book does mention something about horizontal and vertical
multiplication, but this is the only one we are going to worry about.
Whenever we are multiplying a binomial by another binomial we will only
use the FOIL method.

5. I want everyone to go ahead and work on this problem using the FOIL
method. (3x + 4)(x + 5). Remember first, outside, inside, and last when
multiplying.

6. Everyone look at this problem. (4x^2 – 3x -1)(2x – 5). What is different about
multiplying these two polynomials? (Evaluation) Can I still use the FOIL
method on these two polynomials? (Comprehension). We cannot use the
FOIL method because we no longer have two binomials. What else could I do
to multiply these two? (Evaluation) I could use the distributive property. It
would look something like this:

4x^2(2x – 5) – 3x(2x – 5) – 1(2x – 5)

Each term of the first polynomial is distributed or multiplied by each term in
the second polynomial. Go ahead and finish out this multiplication. What did
someone get for an answer? (Application)

7. We can also use multiplying polynomials to find the area. There are a few
homework problems over something like this. Sometimes you will be asked
to find a polynomial expression or more often to give a quadratic trinomial.
Basically it wants you to multiply the two binomials it gives or sometimes it is
the area too.
Plank 3

8. If I have a window whose length is 3x + 10 and a width of 2x + 6. What
would the area of this window be? (Application)

Closure:
Who can tell me what FOIL stands for? When do we use the FOIL method? The
homework for today is on page 587 and it is problems (# 27 – 35, 42, 44, and 52 – 57).

Adaptations/Enrichment:
There are no modifications for this class.

Self-Reflection:
· Did students remember the FOIL method from any pervious math classes?
· Were they able to think of using the distributive method to multiply polynomials that will
not work for the FOIL method?
· Were they able to correctly apply the FOIL method?
· Were there any common problems that everyone seemed to have on the homework?
· Were they productive and on task?
· Was there excessive talking and disruptions of the class?