Oley Valley School District
Algebra 1
Unit 4: Polynomials
Subject
Mathematics
Grade /
Course
9th / Algebra I
Unit of
Study
IV.
Pacing
Weeks: 3
Polynomials
Topics Within Unit: Classifying polynomials, add & subtract polynomials, multiplying
polynomials, factoring polynomials, simplifying rational expressions
Current Priority State Standards and/or Common Core Standards
List the priority standards that will be taught during this unit of study.
CC.2.1.HS.F.2
Apply properties of rational and irrational numbers to solve real world or mathematical problems.
CC.2.2.HS.D.1
Interpret the structure of expressions to represent a quantity in terms of its context.
CC.2.2.HS.D.2
Write expressions in equivalent forms to solve problems.
CC.2.2.HS.D.3
Extend the knowledge of arithmetic operations and apply to polynomials.
CC.2.2.HS.D.5
Use polynomial identities to solve problems.
CC.2.2.HS.D.6
Extend the knowledge of rational functions to rewrite in equivalent forms.
Current Supporting State Standards and/or Common Core Standards
List the supporting standards that will be taught during this unit of study. Supporting standards should not be unwrapped.
CC.SMP.1 Make sense of problems and persevere in solving them.
CC.SMP.2 Reason abstractly and quantitatively.
CC.SMP.3 Construct viable arguments and critique the reasoning of others.
CC.SMP.4 Model with mathematics.
CC.SMP.5 Use appropriate tools strategically.
CC.SMP.6 Attend to precision.
CC.SMP.7 Look for and make use of structure.
CC.SMP.8 Look for and express regularity in repeated reasoning.
Priority Standards
CC.2.1.HS.F.2
Apply properties of rational and
irrational numbers to solve real
world or mathematical
problems.
“Unwrapped” Concepts
“Unwrapped” Skills
(Students need to know)
(Students need to be able to do)
{PA CORE Anchor Descriptor}
{PA CORE Eligible Content Anchors}
A1.1.1.1 Represent and/or use numbers in
equivalent forms (e.g., integers, fractions,
decimals, percents, square roots, and
exponents).
A1.1.1.1.1 Compare and/or order any real numbers.
Note: Rational and irrational may be mixed.
A1.1.1.2 Apply number theory concepts to
show relationships between real numbers in
problem-solving settings.
A1.1.1.2.1 Find the Greatest Common Factor (GCF)
and/or the Least Common Multiple (LCM) for sets of
monomials.
A1.1.1.3 Use exponents, roots, and/or
absolute values to solve problems.
A1.1.1.3.1 Simplify/evaluate expressions involving
properties/laws of exponents, roots, and/or absolute
values to solve problems. Note: Exponents should be
integers from –10 to 10.
A1.1.1.5 Simplify expressions involving
polynomials
A1.1.1.5.1 Add, subtract, and/or multiply polynomial
expressions (express answers in simplest form).
Webb’s Depth
of Knowledge
(Level 1, 2, 3,
4)
1 - Simplify
2 - Identify/Find
A1.1.1.1.2 Simplify square roots (e.g., √24 = 2√6).
2 - Evaluate
3 - Compare
1 - Simplify
CC.2.2.HS.D.1
Interpret the structure of
expressions to represent a
quantity in terms of its context.
A1.1.1.5.2 Factor algebraic expressions, including
difference of squares and trinomials.
2 - Identify/Find
2 - Evaluate
3 - Compare
A1.1.1.5.3 Simplify/reduce a rational algebraic
expression.
CC.2.2.HS.D.2
Write expressions in equivalent
forms to solve problems.
A1.1.1.5 Simplify expressions involving
polynomials
A1.1.1.5.1 Add, subtract, and/or multiply polynomial
expressions (express answers in simplest form).
1 - Simplify
2 - Identify/Find
A1.1.1.5.2 Factor algebraic expressions, including
CC.2.2.HS.D.3
Extend the knowledge of
arithmetic operations and apply
to polynomials.
CC.2.2.HS.D.5
Use polynomial identities to
solve problems.
A1.1.1.5 Simplify expressions involving
polynomials
difference of squares and trinomials.
2 - Evaluate
A1.1.1.5.3 Simplify/reduce a rational algebraic
expression.
3 - Compare
A1.1.1.5.1 Add, subtract, and/or multiply polynomial
expressions (express answers in simplest form).
1 - Simplify
2 - Identify/Find
A1.1.1.5.2 Factor algebraic expressions, including
difference of squares and trinomials.
A1.1.1.5 Simplify expressions involving
polynomials
A1.1.1.5.3 Simplify/reduce a rational algebraic
expression.
3 - Compare
A1.1.1.5.1 Add, subtract, and/or multiply polynomial
expressions (express answers in simplest form).
1 - Simplify
2 - Identify/Find
A1.1.1.5.2 Factor algebraic expressions, including
difference of squares and trinomials.
CC.2.2.HS.D.6
Extend the knowledge of
rational functions to rewrite in
equivalent forms.
2 - Evaluate
A1.1.1.5 Simplify expressions involving
polynomials
A1.1.1.5.3 Simplify/reduce a rational algebraic
expression.
3 - Compare
A1.1.1.5.1 Add, subtract, and/or multiply polynomial
expressions (express answers in simplest form).
1 - Simplify
2 - Identify/Find
A1.1.1.5.2 Factor algebraic expressions, including
difference of squares and trinomials.
A1.1.1.5.3 Simplify/reduce a rational algebraic
expressions.
Essential Questions
2 - Evaluate
Corresponding Big Ideas
2 - Evaluate
3 - Compare
Essential Questions are engaging, open-ended questions that educators
use to spark initial student interest in learning the content of the unit
about to commence.
Big ideas are what you want your students to discover on their own as a result of
instruction and learning activities.
Identify the Big Ideas for each corresponding essential question.
Identify the Essential Questions that will be used throughout this unit to
focus your instruction and assessment. For consideration, ask yourself
the following about each essential question:
Is this question written in student friendly language?
Can this question be answered with one of the Big Ideas?
Does the question lead the students to discovery of the Big
Ideas?
4. Does the question go beyond who, what, where, when and ask
the students to explain how and why?
1. What is a monomial?
The goal is for students to effectively be able to respond to the teacher’s essential
questions with the big ideas, stated in their
1.
2.
3.
1. A monomial is a real number, a variable, or the product of numbers and/or
variables.
2. What is a polynomial?
2. A polynomial is an algebraic addition or subtraction expression containing one or
more monomial terms.
3. How are polynomials classified?
3. Polynomials are classified by the degree (highest variable exponent) and the
number of terms they contain.
4. How do arithmetic processes work with respect to polynomials?
4. Addition, subtraction, and multiplication is polynomials is defined. The properties
of addition and multiplication which apply to real numbers also apply to polynomials.
5. What does it mean to factor a polynomial, and what purpose does it
serve?
5.The process of factoring polynomials involves converting a polynomial from
standard form to factored form. A polynomial expression written in factored can be
used to easily solve the corresponding polynomial equation.
6. How can rational expressions be simplified, and why is it useful to do
so?
6. Rational expressions containing polynomials can be simplified by first expressing
both numerator and denominator in factored form, and then cancelling out common
factors.
Plan for Instruction
Make connections between learning experiences and teaching strategies.
Engaging Learning Experiences
Performance Tasks)
(Authentic

Researched-based Effective Teaching
Strategies
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Three Act Math
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Inquiry Learning
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Cooperative Learning
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Relevant Tasks
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Assessments
Identify Formative Assessments - short, ungraded “checks for student understanding” for the educator to administer throughout the unit of study that are
directly aligned to the Project-based Assessment and that coincide with learning progressions—the “building block chunks” of instruction.
Formative (daily check-in to assess learning – used to drive future instruction) Assessments:
Project-based Assessments:
Unit Vocabulary
Tier 2
Tier 3
(Non-Content Specific Words that may cause confusion or
difficulty)
(Content Specific Words that may cause confusion or
difficulty)
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Common
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Monomial
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Factor
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Binomial

Multiple
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Trinomial
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Degree
Linear
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Quadratic

Cubic
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Domain Restriction
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Cancel
Instructional Resources and Materials
Program / Text
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Learnzillion:
https://goo.gl/7YKLVG
Mathshell:
http://map.mathshell.org/
Technology
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www.teacher.desmos.com

www.101qs.com

www.yummymath.org

https://www.illustrativemathematics.org/
Teacher
Created
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