Polynomials Lesson Plan
Lesson Objectives:
Students will examine polynomials/non-polynomials in order to identify
characteristics of polynomials.
Students will add and multiply polynomials.
Problem Solving:
As students enter the room they should complete the problem solving as a review
of combining like terms from an Algebra unit last fall. (Attachment One)
“What is a Polynomial” Exploration/Discussion:
Hand out list of expressions that are/are not polynomials (Attachment Two).
Allow for individual reflection, and then have groups discuss characteristics of “is” and
“is not” a polynomial.
Provide cards with extra examples of “is” or “is not” and have groups decide
which category they would fit into. After groups have placed the new cards into
categories, have volunteers share ideas about which categories the examples fall into and
why.
During discussion, include vocabulary such as “degree” of polynomial,
monomial, binomial, trinomial, etc. (Attachment Three)
“Adding Polynomials” Exploration/Discussion:
Once students are comfortable with “polynomial” introduce operations with
polynomials. Hand out Adding Polynomials activity (Attachment Four). Have students
connect what they know about combining like terms to working with polynomials with
higher degrees. Discuss “like terms” and how to identify them.
“Adding Polynomials” Pairs Practice:
Have students practice by working with a partner (Attachment Five). One partner
tries a problem while the other observes and coaches if necessary. Then partners switch
roles for the next problem. Discuss solutions and answer questions.
“Multiplying Polynomials” Powerpoint: (copy of slides is Attachment Six)
Connect what students already know about multiplication, distributive property,
and multiplying powers to model multiplying a monomial by a polynomial. Use the area
method to help visual learners break up the problem into sections. The use of the area
method with basic problems will help students understand the method when using it to
multiply binomials/binomials and binomials/trinomials later.
Have students try setting up a problem independently either using “just” the
distributive property, or by the area method.
LESSON BREAK HERE….below this point is
covered in the 45 minute class on the day following the videotaped lesson.
“Multiplying Polynomials” Powerpoint continued…
Continue by showing students how the area method can be used for multiplying
binomials.
Have students look at an example of “FOIL” to determine the meaning of the
Acronym.
Have students work in pairs using the “Sage and Scribe” method where one
student tells the other what to write on the paper (Attachment Seven). Students should
switch roles after each problem and alternate using “FOIL” and the area method to show
understanding of each.
Students can then extend by determining how to multiply a binomial by a
trinomial.
Checking for Understanding: Have students complete a foldable to “Show what you
know”(Attachment Eight)
Students who finish the foldable with remaining time should switch foldables
with someone else in the room and check their answers, or work on extension activities
independently.
(Attachment Eight)
!
Make a foldable to show what
you learned about operations with
polynomials.
Write 3 problems on the outside,
and explain how to determine the
answers on the inside.
1) Adding Polynomials
2) Multiplying a Monomial by a Polynomial
3) Multiplying a Binomial by a Binomial
Turn in to group folders when you are
finished, then try the area model with
the problems on the back of the
multiplying binomials paper!
(Attachment One)
Algebra One Problem Solving #102
Write a simplified expression to represent
the perimeter of the following figure.
Explain!
2x  3
3x  5
Group Directions
(Attachment Two)
Examine the two lists below and discuss
the following:
 What characteristics do polynomials
have in common?
 What do the expressions in the second
list have/not have that makes them “not
polynomials”?
Polynomials
Not Polynomials
4 x3  2 x  8
1
n2  1
5  y x
2 4
x 
x
5 w3  7 w3 2
x3  2 x  1
y  y4
a 2b  3a  b 2
5w  1
7z 2  6z
9x5 + 2xy – 8
b 2  2b  b 1
(Attachment Three)
1
2
x
4ab  3ab
2
6p
3
-5a – 5a + 5a – 4
5
2
y  5y  9
2
8w  5w  17
4
2
1
m  2m  3
12c+5
7x  3
3
Adding Polynomials
5
n 8
(Attachment Four)
ADDING POLYNOMIALS
How would you simplify the following?
5x  4  (2 x  1)  5
How can you use that example to simplify
the following?
3m2  5m  2 (6m2  2m  1)  m2  10
How is adding these polynomials the
same/different?
7 y 2  3 yz  2z 2  4 y 2  5 y 
Problem Solving
 Lesson Objectives
 “What is a Polynomial”
o Individual thoughts
o Rotate desks for group discussion
o Additional cards and class discussion.
 “Adding Polynomials”
o Class Brainstorm and Discussion
o Pair practice with 4 problems
 “Multiplying Polynomials”
o Powerpoint
 Distributive Property
 Multiplying monomial/polynomial
 Multiplying binomials