UNIT TITLE:
SUGGESTED UNIT TIMELINE:
3 weeks
Polynomials
ESSENTIAL QUESTION(S):
•
•
What is a polynomial?
What is the distinction between an expression and an equation?
REFERENCE/
STANDARD #
A-SSE.1
A-SSE.2
STANDARDS:
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single
entity.
Use the structure of an expression to identify ways to rewrite it.
A-SSE.3.
Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
a. Factor a quadratic expression
b. Complete the square in a quadratic expression to reveal the maximum or minimum
value
of the function it defines.
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.
F-BF.1b
Combine standard function types using arithmetic operations.
UNIT DESCRIPTION
MAJOR
STANDARD
(M)
SUPPORTING
STANDARD
(S)





UNIT VOCABULARY
Students will become fluent in simplifying and identifying the parts of expressions. This includes using the order exponents, factors, terms,
of operations, simplifying polynomial expressions, and simplifying expressions with exponents.
bases, coefficients, expression,
-Identify: terms, factors, coefficients, bases, and exponents
like terms, degree of
-Operations with polynomials (add, subtract, and multiply).
polynomials, GCF, monomial,
binomial, trinomial,
Students will become fluent in factoring quadratic expressions.
distributive property, standard
-Include GCF’s, difference of squares, trinomials method for all values of A and grouping.
form
Students will be able to translate a verbal expression to an algebraic expression.
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE
FACILITATING ACTIVITIES
HOW WILL
WE
RESPOND
WHEN
STUDENTS
HAVE NOT
LEARNED?
Strategies and methods for teaching and learning
STAND
ARD #
A-APR.1
TEACHER INSTRUCTION
Add, Subtract and Multiply Polynomials
Algebra 1 textbook (7.5- 7.8)
BoardWorks – HS Algebra I: Operations with Polynomials – 8
slides Polynomials of different degrees, substituting into
polynomials, adding and subtracting polynomials, and
multiplying and dividing polynomials.
SMART Board Lessons – Polynomials: Adding, Subtracting, and
Multiplying
Teaching Lesson - Geometric Investigation of (𝒂 + 𝒃)𝟐
Teaching Lesson - Add, Subtract and Multiply Polynomials
Teaching Lesson - Polynomial Puzzler: Students explore
polynomials by solving puzzlers. To solve, students factor
polynomials and multiply monomials and binomials (May also
use with standard A.SSE.3a)
Teaching Lesson - Introduction to Polynomial Functions:
Identifying types of polynomials and determine requirements
to be a polynomial
Teaching Lesson - Applying Exponential Rules when
Multiplying Polynomials Many examples from simple to
complex
Teaching Lesson - Multiplying Binomials: Instructional lesson
specific to FOIL
Teaching Lesson - Multiplying Binomials: Binomial Squares
STUDENT LEARNING
Interactive Lesson and Worksheets - After
completing lesson click on worksheets and
then choose type of practice
Worksheet: Adding & Subtracting Polynomials
30 problems with answers
Worksheet: Multiplying Polynomial.
24 problems with answers
Worksheet – Arithmetic with Polynomials 10
Questions with WS KEY
Worksheet – Adding and Subtracting
Polynomials Worked out examples, numerous
practice and challenge problems with answers
and web resources
Game – Battleship for Polynomials: Adding
and Subtracting
Game - Multiplying Polynomials
Game – Poker: Multiplying Box Method
INTERVENTIONS
HOW WILL
WE
RESPOND
WHEN
STUDENTS
HAVE
ALREADY
LEARNED?
EXTENSIONS
A-SSE.1
Identify Parts of a Polynomial Expression and Explain the
Context of Different Parts of an Expression:
• Introduction to Polynomials & Related
Terminology
•
Identify parts of a polynomial expression and the
context of the parts
Algebra 1 textbook (7.4)
BoardWorks – HS Algebra I: Equations, Formulas, and
Identities – 7 slides Distinguishing between expressions,
equations, identities and formulas.
Teaching Lesson – Combining Like Terms
Teaching Lesson - Interpret parts of an expression such as
terms, factors, and coefficients
Teaching Lesson - Interpret complicated expressions by
viewing one or more of their parts as a single entity
Teaching Lesson – Rewrite Expression in an Equivalent Form
Teaching Lesson - Identify Parts of a Polynomial using correct
terminology
Worksheet - Number of Terms, Degree
30 problems with answer key
Worksheet – Statements translated to
mathematical expressions and vice versa with
WS KEY
Activity: Intelli-Gum – These interesting
activity sheets were created to introduce
polynomial operations. To do this Don
“invented” a product call “Intelli-Gum” which
comes in several different sizes containers.
Students use polynomial operations to make,
process, and consolidate orders.
Activity: Animal Populations - In this task,
students have to interpret expressions
involving 2 variables in the context of a real
world situation. All given expressions can be
interpreted as quantities that one might study
when looking at 2 animal populations.
Activity: Delivery Trucks - The task has
students look for structure in algebraic
expressions related to a context, and asks them
to relate that structure to the context. In
particular, it is worth emphasizing that the task
requires no algebraic manipulation from the
students.
Activity: Kitchen Floor Tiles - The purpose of
this task is to give students practice in reading,
analyzing and constructing algebraic
expressions, attending to the relationship
between the form of an expression and the
context from which it arises.
A-SSE.2
A.APR.1
Simplify or Rewrite the Expression in an Equivalent Form:
Multiplying Polynomials
Algebra 1 textbook (7.6, 7.7, 7.8)
SMART Board Lesson – Multiplying Polynomials
Teaching Lesson – Multiplying Polynomials: Numerous
Examples and Web Resources
NCSM Great Tasks for Mathematics:
Proving Patterns p 89-93 Students will
develop an intuitive formula for the difference
of squares and then prove that the relationship
using the distributive property to multiply two
binomials.
Worksheets - Multiplying Polynomial with
video tutorials; monomials, binomials and
polynomials
Worksheet – Worked out examples, numerous
practice and challenge problems with answers
and web resources
Activity: Equivalent Expressions - This is a
standard problem phrased in a non-standard
way. Rather than asking students to perform
an operation, expanding, it expects them to
choose the operation for themselves in
response to a question about its structure.
A-SSE.3a
Factoring Quadratics
Factoring – Explanation and Online Practice
Algebra 1 textbook
(8.1-8.6)
Worksheet –Factor GCF and Trinomials
WS Key
BoardWorks – HS Algebra I: Factoring Quadratics – 26
slides: Methods for factoring quadratic expressions, including
using the difference of squares, and solving quadratic
equations using factoring.
Worksheet – Factoring trinomial when a=1
26 problems with answer key
SMART Board Lesson – Factoring Polynomials: GCF
SMART Board Lesson – Factoring Trinomials
SMART Board Lesson – Factoring by Grouping
Teaching Lesson - Factoring Polynomials: GCF
Teaching Lesson - Factoring Trinomials: Positive Leading
Coefficient
Teaching Lesson - Factoring Trinomials: Degrees other than
2nd
Teaching Lesson –Factoring: Difference of 2 Squares
Teaching Lesson – Factoring: By grouping
Teaching Lesson - Factoring Polynomials: Comprehensive
lesson including all types of factoring with numerous examples
Teaching Lesson - Polynomial Puzzler: Students explore
polynomials by solving puzzlers. To solve, students factor
polynomials and multiply monomials and binomials
Worksheet – Factoring trinomial when a>1
18 problems with answer key
Worksheet – Factoring Difference of 2 Squares
and Perfect Square Trinomials
22 problems with answer key
Worksheet – Factor by Grouping
28 problems with answer key
Worksheet – Factoring Trinomials
Includes 3 examples with steps, 20 problems, 4
challenge problems and answers
Worksheet – Mixed Review of all types of
Factoring 40 problems with answers
Worksheet – Mixed Factoring Review
4 examples and 32 problems with answers
A-SSE.3b
Solving Quadratic Equations by Completing the Square
Completing the square: Explanation and
Online Practice
Note: In this unit, we are introducing the skill of completing
the square as a tool to factor into a perfect square trinomial. If
a lead coefficient other than 1, keep A as a factor of B. B and C
can be in fraction form as needed but avoid decimals.
Worksheet – Find “c” when completing the
square
Algebra 1 textbook (9.4)
BoardWorks – HS Algebra I: Completing the Square – 20 slides
Writing quadratic expressions as perfect squares, deriving the
general formula for completing the square, and solving
quadratic equations by completing the square.
Worksheet - Solving by completing the square
24 problems with answer key
Worksheet – Solving Quadratics by Completing
the Square; 20 problems with answers
Teaching Lesson – How and Why Solve Quadratics by
Completing the Square
F-BF.1b
Combine Standard Function Types Using Arithmetic
Operations:
• Add Functions
• Subtract Functions
• Multiply Functions
SMART Board Lesson – Adding Functions
SMART Board Lesson – Subtracting Functions
SMART Board Lesson – Multiplying Functions
SMART Board Lesson – Dividing Functions (reinforces need to
factor in order to simplify)
Teaching Lesson - Sum of Functions:
Add f(x) = x2 – 3x + 7 to g(x) = 5x – 8
Teaching Lesson - Performing Operations on Functions:
Adding, subtracting, multiplying, and dividing functions
ADDITIONAL UNIT RESOURCES
Live Binders: Polynomial Operations:
Animated movies made easy
Polynomial activities and tasks
Discovering Algebra Practice Worksheets
Online Quizzes
Math worksheets to go
Kuta Software Worksheets (Algebra I and Algebra 2)
Interactive Computer Tutorial: Combining 2
Functions with addition, subtraction and
multiplication
Worksheet – Adding, Subtracting and
Multiplying Functions
14 problems with answer key
Worksheet – Performing Operations on
Functions 20 problems + 5 Challenge
problems and answer key
Illustrative Mathematics
Algebra I Unit Resources: Notes and Practice
Math is Fun – Exponents: Lessons on many topics in the exponents unit. Step by step how to do lessons with questions at the end of each lesson topic
The Math Page – Algebra: Numerous teaching lessons
Soft Schools Math – Algebra: Worksheets, quizzes and activities
Complete Teaching Module – Radicals: 3 Complete Lessons on Radicals with PP Notes, Interactive Notes, Classwork WS, Practice WS, Review and Quiz
Select Lessons - Radicals and Rational Exponents: Lessons 5 – 7: 3 Complete Lessons on Radicals and Rational Exponents with PP Notes, Interactive Notes,
Classwork WS, Practice WS, Review and Quiz
Algebra Lab – Interactive Exponential Activities – Go To: Show Related AlgebraLab Documents