Anna Smoak Short Range Lesson Plan
Title of Lesson: Multiplying Polynomials by Monomials
Subject: Algebra I
Grade level: 9th
Teacher: Ms. Burgess
Objective(s):
 Students will be able to multiply a monomial with a positive coefficient by a polynomial
 Students will be able to multiply a monomial with a negative coefficient by a polynomial
 Students will be able to apply the distributive property and the product of powers
property to simplify expressions
SCSDE Curriculum Standard(s) Addressed:
EA-2.2
Apply the laws of exponents and roots to solve problems.
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 must able to use the process of combining like terms to simplify an expression
 Students must be able to apply the laws of exponents to multiply monomials
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 (15 minutes):
o Review of the distributive property of multiplication
 Students will be shown the expression 3x
 As a class they will be asked what this expression means (“What
does it mean to have 3x of something?” I will look for student
responses such as “tripling x” “multiplying three times an
unknown quantity”)
 They will then be asked, “Is there another way to write this
expression without using the property of multiplication?”
 Students will be shown the expression 3(x+1)
 As a class they will be asked “What does it mean to have 3 times
the quantity x+1?” ( I will ask students to interpret this in as many
ways as they can think of including: providing a real life example
to fit this situation and a mathematical explanation such as adding
(x+1) three times, or adding (x+1) and then multiplying this value
by three)
 They will then be asked, “Is there another way to write this
expression without using the property of multiplication?”
 After writing the expression in expanded form I will ask students
to simplify the new expression by combining like terms.
 Students will then be shown the expression 2(x - 3)
 As a class they will be asked about the meaning of this expression.
(“What does it mean to have 2 times the quantity x-3 of
something?”)
 They will then be asked, “Is there another way to write 2(x – 3)
without using the property of multiplication?”
 After writing the expression in expanded form I will ask students
to simplify the new expression by combining like terms.
 We will then note that we have seen that 3(x + 1) = 3x + 3 and
2(x – 3) = 2x – 6.
 Students will then be asked, “What property can we use to get
from our original expression to our simplified expression?” (I will
be looking for students to respond with the distributive property.
My students take departmentalized tests and on these tests there are
often multiple choice problems such as 2(x + 1) = 2x + 2 and
students are required to chose the correct name for the property so
I am using this opportunity to review with them for the cumulative
portion of their test.)
 Students will then be given -2(x + 1) and will be asked to use the
distributive property to simplify the expression.
 We will then go over this problem together and students will be
able to check their work for accuracy
o Review of multiplication of monomials
 Students will be shown the expression 32 x 34
 They will then be asked to write (on their own paper) 32 without
using exponents and will be prompted to expand this expression

through the use of multiplication by the question “What does it
mean for something to be squared?” (I will look for students to
answer with responses such as “multiply the base which is 3 by
itself”)
 They will then be asked to write 34 without using exponents. They
will again be prompted by the question “What does it mean for
something to be raised to the fourth power?” (I will look for
student responses such as “multiply the base together 4 times”)
 Students will then multiply 32 x 34 using our expanded notation.
 Students will be asked, “What property can we use to get from our
original expression to our simplified expression?” (Again I am
using this as an opportunity to review the names of different
properties with my students for their cumulative tests.)
 Instead of simply restating the rule for multiplication of
monomials, students will be shown the expression (y4)(12y7) and
will be asked to multiply the two monomials together. I will then
ask students to discuss their different solution strategies.
 Students will then be given time to simplify the expression in their
notes before we go over the problem as a class
 I will then give students time to simplify (4ab6) (7a2b3). I will
walk around the room as students work on this problem. I will
then ask for a student to volunteer their answer. I will then ask the
class if anyone agrees/disagrees with this students’ response. We
will then work through the problem on the board.
Main Activity (20 minutes):
o To begin I will ask students to discuss in pairs how they think 3x (2x + 5) is
different from 3 (2x + 5)
 I will then ask for student responses for the entire class to hear
o I will show students the expression 3x2 (2x2 + 5x – 1) and have them discuss in
pairs how they think we could simplify this expression.
 I will ask for ideas about how to approach this problem—looking for
students to mention distribution and properties of exponents. I will ask
for other students to agree or disagree with the speaker and explain
their reasoning.
 We will then work this problem on the board together with students
offering the appropriate steps to follow as well as the answers to each
step
 I will then have students work in groups to simplify the expression
- (x – 2) + x (6x – 7)
 I will walk around the room and answer any questions and make
sure pairs stay on task
 If students are having difficulty we will work the problem together
on the board. However, if each pair seems to understand the new
material I will ask a pair of students to present the problem on the
board and justify each step to the class


Students will again work in pairs to simplify 6rs(r2s - 3) and -9x (x2 +
xy - 2y2)
 I will again walk around the room and answer any questions and
make sure pairs stay on task
 As before, I will work through the problems on the board if
students are having difficulty. If they are not I will have two
different pairs present their solution and solution strategy to the
problems.
Closure (5 minutes):
o I will present the ticket out of the door activity for today which is, “When a
monomial is multiplied by a binomial, will the product always, sometimes, or
never be a binomial?” Students will write their response and an explanation for
their answer on a note card which will be collected at the end of class.
Assessment:
 Students can successfully complete written in class and homework problems (included)
which require students to multiply monomials (with both positive and negative
coefficients) by polynomials and simplify their results
 Students are able to answer the questions presented in the lesson as well as provide
justification for their responses
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
Follow-up Lessons/Activities:
 The beginning of the next lesson will include a review of multiplying a monomial by a
polynomial
 Students will complete homework problems for extra practice and will be given the
opportunity to ask questions when they are reviewed the next day
 I will also make sure to review the ticket out of the door question at the beginning of the
next class period
Reflection:
Clemson: Teaching this lesson as my individual lesson in class helped with my timing of the
lesson. While I did not teach this lesson to my students at Wren, this was great practice for next
semester. Even though we did not take the time to work in pairs during class, I was able to see
the need for providing time for students to work together in pairs and having time to individually
try problems on their own.