My unit consists of properties of polynomials, specifically: combining like terms, addition,
subtraction, multiplication, and division. A solid understanding of these topics is essential
because they constitute the foundation needed to solve equations; in practice, these operations
are what many students find difficult when they make the transition to solving equations. Prior
to this lesson, students will have concluded their study of monomials. To transition into
polynomials students must first recognize how to group variables with different exponents.
While this skill may seem trivial, it is vital when students begin to perform operations with
polynomials. Addition and subtraction of polynomials teaches students skills they will need to
simplify equations while providing a review and highlighting the importance of distributing
negatives. In the next lesson, multiplication by a monomial has the distinction of introducing the
distributive property, an indispensible mathematical concept. Dividing by a monomial further
develops the law of quotients and serves as a precursor for long division of polynomials. Finally,
multiplication of two polynomials expands the distributive property to account for multiple
terms. The academic importance of these lessons greatly contributes to my desire to teach them.
My affinity to teach this unit is principally based on its crucial importance; students must not
only learn, but also intimately understand these basic concepts. This unit consists of the core
ideals that will allow my students to successfully transition from simple arithmetic to higher
level mathematics. I feel it is my duty to ensure that all of my students comprehend the material
and make it their own. Teachers can do their students a great disservice if they simply treat this
unit like any other. This approach is flawed because students who do not understand this unit
will likely have difficulty solving equations. This difficulty comes at one of the most important
times in a student’s mathematical education; a frustrated student is more likely to adopt a
negative view towards mathematics that will result in disengagement and adversely affect his or
her educational journey. As teachers, we cannot control the quality of teaching students may
encounter in later years, so we must do everything in our power to prepare them with the basics
and inspire them to think critically and embrace their education.
My summative assessment is largely limited by practices currently in place at my school. For
example, I am required to use departmental tests and quizzes. Consequently, I must ensure that
my students learn and understand the material while providing an enriching lesson and avoiding
“teaching to the test.” My challenge is to provide diversified evaluation within these constraints.
To that end, I will add comprehension, short answer, and open ended questions to quizzes (if
possible) and homework. These constraints limit many alternative assessments to a formative
role. I plan to rely primarily on class discussion, my observations, and writing prompts to
determine the extent of my students’ understanding. My teaching style will be an integrated mix
of direct and interactive instruction. Teacher led instruction will be well structured and give
students’ opportunities to integrate their schema. Class discussion will primarily consist of
working problems as a class while prompting students for explanations about the steps or
operations involved. I will observe students by searching for confused looks throughout the
class period and talking with individual students while they work problems. Finally, I will use a
writing prompt as a “ticket out of the door”; students will answer an open-ended thought based
question that I will use to evaluate their understanding of the day’s lesson.
South Carolina State Standards
Standard EA-2:
The student will demonstrate through the mathematical processes an
understanding of the real number system and operations involving
exponents, matrices, and algebraic expressions.
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.
National Standards
Algebra: Understand patterns, relations, and functions (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
Unit Objectives
Combining Like Terms:
 Students will be able to communicate verbally and in writing the definition of like terms
 Students will be able to identify like terms in polynomial expressions
 Students will be able to mathematically combine like terms in polynomial expressions
 Students will be able to generate examples and non-examples of like terms
 Students will be able to apply knowledge of like terms to practical situations
Adding and Subtracting Polynomials
 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
Multiplying Polynomials by Monomials
 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
Multiplying Polynomials
 Students will be able to multiply polynomials by adding areas of a rectangle


Students will be able to multiply polynomials with one variable using the process of
distribution
Students will be able to multiply polynomial with multiple variables using the process of
distribution
Dividing Polynomials by Monomials
 Students will be able to divide polynomials by monomials of one variable using the laws
of exponents
 Students will be able to divide polynomials by monomials with multiple variables using
the laws of exponents