Anna Smoak Short Range Lesson Plan
Title of Lesson: Adding and Subtracting Polynomials
Subject: Algebra I
Grade level: 9th
Teacher: Ms. Burgess
Objective(s):
 Students will be able to identify an expression as a monomial, binomial, or trinomial
 Students will be able to explain the difference between a monomial, binomial, and
trinomial
 Students will be able to add polynomials
 Students will be able to subtract polynomials
SCSDE Curriculum Standard(s) Addressed:
EA-2.5
Carry out a procedure using the properties of real numbers (including commutative,
associative, and distributive) to simplify expressions.
EA-2.7
Carry out a procedure (including addition, subtraction, multiplication, and division by
a monomial) to simplify polynomial expressions.
NCTM National Curriculum Standard(s) Addressed:
Algebra: Represent and analyze mathematical situations and structures using algebraic symbols
(grades 9-12)
 Use symbolic algebra to represent and explain mathematical relationships
 Understand the meaning of equivalent forms of expressions, equations, inequalities, and
relations
Communication:
 Organize and consolidate their mathematical thinking through communication
 Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others
Prerequisites:
 Students must be able to recognize as well as add and subtract monomials
 Students must be able to distribute a constant through a polynomial
 Students must be able to add, subtract, and multiply real numbers
 Students are able to use the process of combining like terms to simplify an expression
Materials/Preparation:
 Smartboard and whiteboard will be used
 Powerpoint or Smart presentation will be minimized and ready for immediate use
 Students must have notebooks and pencils
Procedures:
 Introductory Activity (5 minutes):

o Students will complete a Frayer Model in their notebooks on the topic of
monomials in which they will define the term (in their own words), list facts
and/or characteristics, provide examples, and generate non-examples
 Responses will then be shared with the class
o Students will be asked what the root word mono- means
o Students will then be asked what the root word bi- means and will as a class
generate as many words that have the root bi- (such as bicycle) as possible. They
will then be asked to predict what a binomial would be by looking at its root
word.
 An example and a non-example of a binomial will be shown
o Students will then be asked what the root word tri-means and as a class will
generate as many words that have the root tri- (such as tricycle) as possible. They
will then be asked to predict what a trinomial would be by looking at its root word
 An example and non-example of a trinomial will be shown
o Students will be asked to explain why xyz is a monomial while x + y + z is a
trinomial. (I will have them take several minutes to write down a response to this
problem in their notes and we will then have a whole class discussion.)
Main Activity (20 minutes):
o Students will then be asked “How can we represent x2 + 2x + 2 using Algebra
Tiles?” and “How can we represent 2x2 + 2x using Algebra Tiles?” (provided)
 Both of which have strictly positive coefficients
o Students will be asked to “Represent the sum of x2 + 2x + 2 and 2x2 + 2x using
Algebra Tiles.”
o Students will then use this representation to simplify the expression using the
process of combining like terms, previously learned
 We will pause after collecting like terms to translate our modified pictorial
representation into a mathematical statement
 Again after simplifying we will translate our visual representation of the
expression into a mathematical statement
o Students will then be asked “How can we represent - x2 + x + 5 using Algebra
Tiles?” and “How can we represent x2 + 2x - 2 using Algebra Tiles?”
o Students will then have students represent the sum of - x2 + x + 5 and x2 + 2x - 2
using Algebra Tiles
 Now students must account for a negative coefficient and a negative
constant but the two polynomials are still being added together
o Students will use the process of combining like terms to add the two polynomials
together and simplify the expression
 We will pause after collecting like terms to translate our modified pictorial
representation into a mathematical statement
 Again after simplifying we will translate our visual representation of the
expression into a mathematical statement
 Students will then be asked to find the sum of x2 + 2x + 3 and 3x + 1
algebraically without the use of Algebra Tiles. I will ask students to try
this individually and then check their work with a partner. After several
minutes I will ask a pair to present their strategy on the board for the rest
of the class. I will then ask for alternate solution strategies.


Students will be asked to state the property that allows the removal of
parentheses around the polynomials
o I will then ask “What is my first step in simplifying the expression – (x + 1)?”
(students have already learned to distribute constant terms throughout an
expression however, I think it would be beneficial to start with this question
because many students are having trouble with positive and negative signs during
distribution)
 Students will be asked to name the property (distribution) we use to
simplify the expression
o Students will then be asked to model the expression - (x2 + x + 5) using Algebra
Tiles
 I will ask for strategies for how to approach this problem. They will be
asked “Is there anything that we have to do before we can use the Algebra
Tiles?” After distributing the negative through the expression students
will then explain the necessary Algebra Tiles required to model the
expression
o They will then be asked “How can we represent (-2x2 + x - 3) using Algebra
Tiles?”
o Students will then be asked “How can we find the difference of the two
expressions?” They must realize that the subtraction sign must first be distributed
to each term in the second expression.
o Students will be given the opportunity to use Algebra Tiles to represent this
problem and use the process of combining like terms to simplify. They will
translate their pictorial representation to a mathematical expression after each
step.
o Students will then be asked to simplify the problem (3x2 – 5x + 3) – (2x2 – x – 4)
 I will solve this problem along with the students on the board by
implementing a t-chart. Our mathematical steps will be shown in the left
column and our explanation of our steps will be shown in the right
column.
o Students will then be presented with the problem “Find the difference of (– 2x3 +
5x2 – 4x + 8) and (– 2x3 + 3x – 4)”
o As an extension problem students will be asked to “Write an expression for the
perimeter of the rectangle. Then simplify the expression.” A visual of the
rectangle will be shown. Students will be asked to provide the formula for
finding the perimeter of a rectangle. I will then ask students how we might set
this problem up.
Closure (10 minutes):
o Students will complete a ticket out of the door: “When two binomials are added,
will the sum always, sometimes, or never be a binomial? Explain your answer and
give examples to support your answer.”
Assessment:
 Students can successfully complete written in class and homework problems (included)
which require students to add and subtract polynomials with both positive and negative
signs as well as classify expressions as monomials, binomials, or trinomials


Students are able to answer the questions presented in the lesson as well as provide
justification for their responses
Students are able to generalize their knowledge to answer and justify the “ticket out of
the door” activity
Adaptations:
 Students have the opportunity to come in during their AE period or tutoring after school
for extra assistance
 I have also increased the size of the font on the PowerPoint because several students in
class have difficulty seeing the Smartboard
 Optional guided practice worksheets will be given to all students that want one
Follow-up Lessons/Activities:
 The beginning of the next lesson will include a review of adding and subtracting
polynomials
 Students will complete homework problems for extra practice and will be given the
opportunity to ask questions when they are reviewed the next day