Core Unit Plan Template
Salem State University
School of Education
OPERATIONS on POLYNOMIALS
I.
Setting the Stage
A. Curriculum Framework Standards: Which MA Curriculum
Frameworks/Common Core Standards address your topic content and
objectives?
o
List MA and/or national curriculum standards that connect to the Unit’s goals.

N-RN.3 Explain why the sum or product of two rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that
the product of a nonzero rational number and an irrational number is irrational. 1

A-APR.1 Understand that polynomials form a system analogous to the integers,
namely, they are closed under the operations of addition, subtraction, and
multiplication; add, subtract, and multiply polynomials. 1

A.SSE.1.a Interpret parts of an expression, such as terms, factors, and
coefficients. 1
From the Common Core State Standards for Mathematics and Appendix A: Designing
High School Courses based on the Common Core State Standards for Mathematics.
B. Generative Topic: What is the focal concept or skill of the unit?
This unit focuses on critical area 1 “deepen and extend understanding of linear
and exponential relationships” and critical area 2 “contrast linear and exponential
relationships with each other and engage in methods for analyzing, solving, and
using quadratic functions”2
“This topic explores polynomial operations through a construction scenario.
Students learn how to multiply, add, and subtract polynomials using concrete
models and analytic techniques. Students [will] apply their new skills in working
with rational expressions.” 2
2
From the Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
C. Topical Essential Question(s): What question(s) to students will guide
their exploration and activities in the unit?

How are operations on polynomial expressions performed?
D. Summative Assessment: How will you assess students’ learning at the end
of the unit?
o
The summative assessment will be a unit test with fill in, multiple choice and open response
questions where students will be asked to perform addition, subtraction, multiplication and division
of polynomial expressions. Students will also be asked to classify polynomials, identify the degree
and leading coefficient of a polynomial, and rewrite polynomials in standard form.
II.
Content of the unit
A. Content and Skills: What do you know about what you are planning to
teach?
o
Map or outline the underlying principles, concepts, skills, or strategies covered in your topic for the
entire unit in an organized fashion.

Define polynomial, Identify parts of a polynomial (leading coefficient and degree), rewriting
polynomials in standard form, classifying polynomials by degree and number of terms

Adding polynomials

Subtracting polynomials (distributing the negative)

Multiplying polynomials: distributive property and FOIL

Dividing by a monomial
o
Define key terms (vocabulary for the lesson) using your own words.

Polynomials: A string of terms connected with addition and subtraction signs. All exponents
must be positive & can’t be fractions.

Terms: The parts of an expression that are added together

Rational expression: A fraction that has nonzero polynomials in the numerator and/or
denominator

Irrational: A number that cannot be written as the fraction of two integers

Integers: The numbers on the numbers line that are not fractions, decimals, or mixed numbers.

Trinomials: A polynomial with three terms

Coefficients: A number being multiplied to a variable

Constant: A term with no variable

Degree of a Polynomial: The greatest exponent in a polynomial expression

Standard Form of a Polynomial; The polynomial is written starting with the term that has the
greatest exponent in descending order to the lowest or zero exponent.

Distributive Property: Used to multiply every term of one polynomial by every terms of
another polynomial

Closure: Operations on polynomials are closed because adding, subtraction, multiplying or
dividing results in another polynomial.
o
Scaffold concepts to demonstrate unit cohesion

Combining Like Terms

Distributive property

Properties of exponents
B. Rationale: Why teach the unit?
o
III.
IV.
This unit will reinforce student skills with combining like skills and the distributive property
helping students look for and express regularity in repeated reasoning. Rewriting and simplifying
polynomials will encourage students to make use of structure. Simplifying polynomials so they can
be used in a more manageable form develops students’ ability to make sense of problems and
persevere in solving them.
Knowledge of Students: Why does knowing your students matter?
o
Describe the class characteristics, including grade/age level, class/group size, and any other relevant details.
o
Class Characteristics: Algebra 1 students are in 9th grade, usually between ages 14 – 16. Average class size is 25
students. Many of the Algebra 1 students in LEHS score poorly on diagnostic test to assess content knowledge from
prior grades at the beginning of their freshman year. Most classes have 5 or more FLEP students. One to three
freshmen per class are referred to School Study Team..
Overview of Lessons Chart: Given the targeted understandings, how will you
sequence and outline the unit plans’ lessons?
A. Curriculum Framework Standards: Which MA Curriculum Frameworks
address your topic content and objectives?
o
List MA and/or National Curriculum Frameworks that connect to each individual lesson’s goals.
B. Content: What concepts and skills will you teach in this lesson?
o
o
List of concepts and skills that will be taught in each individual lesson.
Demonstrate scaffolding of concepts across lessons throughout the unit.
C. Measurable Objectives: What do you want students to know and be able
to do?
o
o
Present the measurable, observable outcomes (i.e., student performances of understanding) that
demonstrate what they will know and be able to do by the end of the lesson.
Lesson plan objectives are age appropriate and are organized to help students construct knowledge
of the concepts over the course of the unit.
D. End of Individual Lesson Assessment: How will you assess students’
learning?
o
List the type of tool that assesses the lesson plan’s measurable outcomes (from the lesson’s
objectives).
E. Teaching activities of the lesson: How will you outline beginning, middle
and end of each lesson and scaffold content from lesson to lesson?
o
o
o
o
Beginning of the Lesson: How will you immediately engage all of your students in the content?
Middle of Lesson: What are your students doing (e.g., speaking, writing, drawing, performing,
documenting, observing) to explore the content?
End of Lesson: How will you help all students process the experience?
Over the course of the unit, make sure the teaching activities construct content knowledge and
skills.
F. Differentiation: How will you accommodate the range of learners
(referring to your “knowledge of students”) in each lesson?
o
For each lesson, list the ways you will accommodate students with specific disabilities and/or
exceptionalities and how you will address students’ varied backgrounds, interests, language
learning needs and learning styles. Be sure to consider how to reinforce concepts for struggling
students and have room for advanced students to keep progressing.
Lesson A.
Plan # Curriculum
Framework
Standards
A.SSE.1.a
1
2
N-RN.3,
A-APR.1
B. Content
Defining and
classifying
polynomials
Adding
polynomials
C.
Measurable
Objectives
SWBAT…
Identify
polynomial
expressions;
Rewrite
polynomials
in standard
form;
Identify the
parts of a
polynomial;
Classify a
polynomial
by degree
and number
of terms.
Find the sum
of 2 or more
polynomials
D. End of
Individual
Lesson
Assessment
Formative:
“Try now”
examples and
worksheet to
be completed
for
homework
E. Teaching
activities of
the lesson
F.
Differentiation
Complete
note taking
guide.
Independent
work may be
done
collaboratively.
Teaming
students with
varying levels
of skills and
understanding
to encourage
peer tutoring.
Think aloud
and “Try
Now”
examples
Completing
extra
examples
independently
Formative:
“Try now”
examples and
worksheet to
be completed
for
homework
Combining
Like Terms
“match
game”
Copy steps
into their
notebooks
Think aloud
and “Try
Now”
examples
3
A-APR.1
Subtracting
polynomials
Find the
difference of
two
polynomials
Independent
work may be
done
collaboratively.
Teaming
students with
varying levels
of skills and
understanding
to encourage
peer tutoring.
Completing
extra
examples
independently
Formative:
Copy steps
Independent
“Try now”
into their
work may be
examples and notebooks
done
worksheet to
collaboratively.
be completed Think aloud
Teaming
for
and “Try
students with
homework
Now”
varying levels
examples
of skills and
understanding
Completing
to encourage
extra
peer tutoring.
4
N-RN.3,
A-APR.1
Multiplying
polynomials
5
A-APR.1
Dividing an
Find the
expression by quotient of a
a monomial
polynomial
divided by a
monomial
V.
Find the
product of a
monomial
and a
polynomial
using the
distributive
property;
Find the
product of 2
binomials
using FOIL
examples
independently
Formative:
Copy steps
Independent
“Try now”
into their
work may be
examples and notebooks
done
worksheet to
collaboratively.
be completed Think aloud
Teaming
for
and “Try
students with
homework
Now”
varying levels
examples
of skills and
understanding
Completing
to encourage
extra
peer tutoring.
examples
independently
Formative:
Copy steps
Independent
“Try now”
into their
work may be
examples and notebooks
done
worksheet to
collaboratively.
be completed Think aloud
Teaming
for
and “Try
students with
homework
Now”
varying levels
examples
of skills and
understanding
Polynomial
to encourage
BINGO
peer tutoring.
Bibliography: Where did you find your information and resources?
“Adding and Subtracting Polynomials”
http://cdn.kutasoftware.com/Worksheets/Alg1/Adding%20and%20Subtracting%20Polynomials.pdf. April 2015.
Algebra: Tools for a Changing World-Practice Workbook. Prentice Hall. 1997.
Chvatal.”Worksheet: Polynomials” http://mvyps.org/~kchvatal/Algebra%20II%20Worksheets/Worksheet%20%20polynomials.pdf. April 2015.
“Dividing Polynomials by a Monomial”. www.mathworksheets4kids.com. April 2015.
Larson, Ron, Boswell, Laurie, Kanold, Timothy D., Stiff, Lee. Algebra 1. Evanston, IL: McDougal Littell, 2001.
VI.
Reflection after Teaching: What did you learn from teaching the unit?
A. Looking at Student Performance
o
It appeared from the analysis of the midterm exam on questions involving combining like terms
and distributive property; almost half the class answered these types of problems correctly.
o
Based on the comparison of midterm question #24 and the open response question of the unit test,
more real-life application questions need to be practiced by these Algebra 1 students.
B. Looking at Your Teaching
o
o
o
o
The students seemed to grasp multiplying polynomials will when I draw arcs over the terms as I
multiplied them to illustrate that even though we were now multiplying coefficients and variables
being raised to exponents, that it was still just the distributive property with which they are very
familiar. I saw this when many students wanted to use multiplication for all problems, ignoring
addition and subtraction signs as the indicated operation.
One of my challenges was teaching the material to students with very low prerequisite skills. Too
much class time seems to be used reviewing strands from previous grades that should be
scaffolding. Another challenge is keeping students actively engaged for the duration of class. The
students told me that the enjoyed the “games” involving combining like terms and polynomials and
seemed to remain on task during such activities.
From teaching this unit, I learned that I do not have to create new materials all of the time and that
there are lots of notes and worksheets appropriate for my classes online. I learned a lot of new
reliable site to find resources. I learned I need to slow my students down so they read problems
more carefully as many used the incorrect operation to simplify polynomial expressions on the unit
test.
Next year, I would like to teach this unit earlier in the year as the distributive property and combing
like terms are also essential for solving multistep equations. Thus, I feel this unit would be a good
follow-up to that topic. Currently in using the District Curriculum Map, the units prior to
operations on polynomials are Exponential Models and Arithmetic and Geometric Sequences
which do not need property and combing like terms skills as much.
I would also like to find more engaging activities for kinesthetic learners and that encourage more
collaboration with group work.