Teacher: 7 th Grade Teacher
Lesson Title: Operations with Polynomials and Factoring
STRANDS
Grade: STEM Math 2A
Seeing Structure in Expressions
Creating Equations Arithmetic with Polynomials and Rational Expressions
LESSON OVERVIEW Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
Students will be introduced to polynomials by learning the different classifications by number of terms and degree. They will add, subtract, and multiply polynomials and begin factoring polynomials. We will discuss the uses of polynomial products in genetics through the use of Punnett Squares. We will investigate the polynomial products link to construction in preparation for the Modern Living Unit. Students will continue to apply their leadership and collaboration skills through various tasks and activities in addition to the culminating event of the unit.
MOTIVATOR Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites, literature)
The video at http://www.history.com/videos/how-polyester-is-made# will be shown as an introduction to the polynomial unit. The purpose is to focus on the meaning of the prefix “poly,” meaning many. It fits so well with the STEM curriculum because it teaches manufacturing technology and recycling in addition to the prefix meaning.
DAY Objectives
(I can….)
Materials &
Resources
Instructional Procedures Differentiated
Instruction
Assessment
1

I CAN identify a
 iPads

Internet access
Essential Questions:

How can I identify a polynomial by the number of terms it has or its degree?
Remediation
“Polynomial
Graphic
Formative
Assessment
“Classifying

 polynomial by the number of terms it has or its degree.
I CAN simplify a polynomial and write it in standard form.

TV or
Smartboard for display

“Classifying
Polynomials
Memory Game”

“Standard Form and Classifying
Polynomials”

Materials for
Differentiated
Instruction –
Remediation:
“Polynomial
Graphic
Organizer”

Materials for
Differentiate d
Instruction –
Enrichment:
Internet access

How can I simplify a polynomial and write it in standard form?
Lesson Title: Classifying Polynomials and Adding and Subtracting Polynomials
Set: Show video (in resources folder) about biomedical engineering, a medical STEM career. Then show the Tongue-drive Wheelchair video of a biomedical engineer.
at as an example of the work
Teaching Strategy: Write a number on the board (say, -5) and ask students to name the technical math term for all similar expressions (constant). Write a binomial such as x-5 on the board and ask students how it is different from the constant. The name for two term expressions is binomial. Write 3x^2+x-5 and ask how it is different and give its name (trinomial). Tell students there is no special name for polynomials with four or more terms. Allow students to discover the rule for counting the terms in expressions. Be sure to relate other words with which students are familiar to link new terms with prior learning (for example, monorail, bicycle, triceratops, etc).
See if students can distinguish between the previously listed polynomials in a way other than the number of terms (degree of the polynomial). Give the definition of degree: largest exponent of the variable in a one-variable polynomial. Teach students the terms linear, quadratic, cubic, and quartic. Let them play the
“Classifying Polynomials Memory Game” with a partner.
Work through several examples with students on “Standard Form and Classifying
Polynomials,” teaching them to look for like terms that need to be combined before writing the expression in standard form (descending order of exponents). The remaining problems will be assigned for homework.
Summarizing Strategy: Students will create a monomial, binomial, and trinomial on paper and submit to the teacher on the way out the door.
Organizer” should be completed during the lesson and utilized throughout the unit.
Enrichment
Students may research the differences In the graphs of linear, quadratic, cubic, and quartic polynomial functions and briefly report findings to the class on Day 2 of the unit.
Polynomials
Memory
Game”
Ticket out the door
Summative
Assessment
“Standard
Form and
Classifying
Polynomials
”

2 I CAN add and subtract polynomials.
 iPads

Internet access

TV or
Smartboard for display

“Adding and
Subtracting
Polynomials with Algebra
Tiles”

“Beginning
Guide to Adding
Polynomials”

“Adding and
Subtracting
Polynomials
Examples”

“Adding
Subtracting
Practice”
Essential Question: How can I add and subtract polynomials?
Lesson Title: Adding and Subtracting Polynomials
Set: Watch “Designer Babies” video upcoming project on Day 5.
. This is to create interest in genetics for the
Teaching Strategy: Allow students to discover the rule with algebra tiles as they work in small groups to complete “Adding and Subtracting Polynomials with Algebra
Tiles.” Discuss what they learned. Give students time working alone to complete
“Beginning Guide to Adding Polynomials” to reinforce the abstract notion of like terms. Monitor and adjust as necessary. As some students finish early, check their work, and ask them to serve as peer tutors to the students who are struggling.
Summarizing Strategy: Use the PowerPoint presentation “Adding and Subtracting
Polynomials Examples” to illustrate the difference between adding polynomials and multiplying them. Tell the class that we will learn to multiply monomials on Day 3.
“Adding Subtracting Practice” will be assigned for homework.
Remediation

Hands-on
Activity with algebra tiles

Peer tutors
Enrichment
Peer tutoring
Formative
Assessment

Informal
Observa tion

Student respons es to questio ns

“Beginni ng
Guide to
Adding
Polyno mials”
Summative
Assessment
“Adding
Subtracting
Practice”

3 I CAN multiply monomials by polynomials
 iPads

Internet access

TV or
Smarboard for display

“Exponent Rules
Chart”

“Monomials
Raised to
Powers”

“Simplifying
Polynomials
Activity”

“Multiplying
Monomials and
Polynomials

Materials for
Differentiated
Instruction –
Remediation:
“Exponent Rules
Chart”
Essential Question: How can I multiply monomials by polynomials?
Lesson Title: Multiplication by Monomials
Set: Show the Medicine and Engineering Join Forces video at to make students aware of medical careers outside of becoming doctors or nurses. They should also see the great need for mathematics in creating this technology.
Teaching Strategy: Using the “Exponent Rules Chart” as a guide, teach the students how to add the exponents when multiplying like bases.
Multiply:
1.
8(2x + 2y - 6)
2.
4x(5x 2 - 6x 2 - 12)
3.
-3xy 2 (2xy +6x 2 -10)
4.
-c 2 d 3 (3c 2 + 4cd - 5d 2 )
5.
6ab(3a - 2b + 4c 2 )
Answers
1.
16x + 16y - 48
2.
20x 3 - 24x 2 + 48x
3.
-6x 2 y 3 - 18x 3 y 2 + 30xy 2
4.
-3c 4 d 3 -4c 3 d 4 + 5c 2 d 5
5.
18a 2 b - 12ab 2 + 24abc 2
Show PowerPoint lesson “Monomials Raised to Powers.” Pause and work on the board any examples that the students do not understand the first time they see them.
Students will complete “Simplifying Polynomials Activity” in pairs.
Summarizing Strategy: Students will write on paper the answer to this question:
“What is the difference for the variable factor between adding and multiplying monomials?” This will be the student’s ticket out the door.
“Multiplying Monomials and Polynomials” will be assigned for homework.
Remediation
“Exponent Rules
Chart”
Enrichment
Upon lesson completion, students will be asked to predict how to multiply a binomial times a polynomial.
Formative
Assessment
Informal observation
“Simplifying
Polynomials
Activity”
Summative
Assessment
“Multiplying
Monomials and
Polynomials
”

4
5
I CAN multiply binomials using the distributive property and/or the
FOIL method.

 iPads

Internet access

TV or Smart board for display

“FOIL”

“Multiplying
Polynomials
Match Game”

“Multiplying
Polynomials”
Materials for
Differentiated
Instruction –
Enrichment:
“Challenge
Problems”
Essential Question: How can I multiply binomials using the distributive property and/or the FOIL method?
Lesson Title: Multiplying Binomials
Set: Show video “A Beginner’s Guide to Punnett Squares” to prepare students for the project on Day 10. It shows a real-world application of the multiplication of binomials.
Teaching Strategy: Use “FOIL” PowerPoint to guide the direct instruction. Students will play “Multiplying Polynomials Match Game” with a partner.
Summarizing Strategy: Select 5 students to either write on board or airplay one of the following types of problems: adding polynomials, subtracting polynomials, multiplying monomial by polynomial, multiplying binomial by binomial, or multiplying binomial by trinomial.
“Multiplying Polynomials” will be assigned for homework. Students needing an added challenge may replace any 5 problems on the homework assignment with the three problems on “Challenge Problems.”

Remediation
“Extra Notes and
Examples”

“Multiplying
Polynomials
Match Game” with partner
Enrichment
“Challenge
Problems” may replace any 5 problems on the homework assignment.
Formative
Assessment

Informal observa tion

“Multipl ying
Polyno mials
Match
Game”
Summative
Assessment
Student’s chosen homework assignment
Project Day- Refer to Unit Plan
Zombie Epidemic

6 I CAN apply the skill of multiplying binomials to real-world problems.
 iPads

Internet access

TV or
Smartboard for display

“Mult Polys
Floor Plan Story
Problem
Activity”

“Polynomials
Perimeter Area and Volume”
Essential Question: How can I apply the skill of multiplying binomials to real-world problems?
Lesson Title: Multiplying Polynomials Applications
Set: Show video “The Opus,” an honest look at America’s educational status, especially in the areas of math and science. The hope is that the students will be inspired to change the course of our country.
Teaching Strategy: Teacher will ask several review questions from the previous week’s lesson, like “What is the exponent rule for multiplying polynomials?”
Teacher will work first three problems on “Mult Polys Floor Plan Story Problem
Activity.” Students will then work in small groups to complete the remaining problems of the activity. Teacher will monitor student work so that he/she may ask certain groups to display their solutions to exercises 4-7. Students may then begin working on “Polynomials Perimeter Area and Volume.”
Summarizing Strategy: Exit ticket—make up a story problem that requires the multiplication of binomials to solve it. Kudos to the students who can create a different scenario than those used in class today!
Completion of “Polynomials Perimeter Area and Volume” will be assigned for homework.
7 I CAN divide polynomials by monomials.
 iPads

Internet access

TV or
Smartboard for display

“Dividing
Polynomials by
Monomials”
Materials for
Remediation
Essential Question: How can I divide polynomials by monomials?
Lesson Title: Dividing Polynomials by Monomials
Set: Show the Medicine and Technology video at to continue modeling how STEM medical careers are based heavily in mathematics.
Teaching Strategy: Students will work in small groups to complete the investigation
“Dividing Polynomials by Monomials.” See StudyZone for lesson and initial assisted practice.
Remediation
Grouping
Enrichment
Extension activity on “Mult Polys
Floor Plan Story
Problem Activitiy” and Problem # 10 on “Polynomials
Perimeter Area and Volume”
Formative
Assessment

Informal observa tion

Questio ning

“Mult
Polys
Floor
Plan
Story
Problem
Activity”
Summative
Assessment
“Polynomial s Perimeter
Area and
Volume”
Remediation
“Dividing
Polynomial by
Monomial
Discovery”
Enrichment
Students may do an alternate assignment if they choose, “Dividing
Polynomials
Enrichment HW.”
Formative
Assessment
“Dividing
Polynomials by
Monomials”
Summative
Assessment
“Dividing
Polynomial by
Monomial
Practice”

8
9
“Dividing
Polynomial by
Monomial
Discovery”
Materials for
Enrichment
“Dividing
Polynomials
Enrichment HW”
Summarizing Strategy: Each student will write in words the procedure for simplifying
(-32x^3yz^4)/(4xz^3) and use it as an exit ticket.
“Dividing Polynomial by Monomial Practice” will be assigned for homework.
I CAN find the greatest common factor of a polynomial and use it to factor the polynomial.
 iPads

Internet access

TV or
Smartboard for display

“Algebra Tiles to
Intro Factoring”
Materials for
Remediation
“Methods to find
GCF Reference
Sheet”
Essential Question: How can I find the greatest common factor of a polynomial and use it to factor the polynomial?
Lesson Title: Factoring with the GCF
Set: Watch the Moving in the ICU video at as part of the continued study of math in medicine.
Teaching Strategy: Use “Methods to find GCF Reference Sheet” as a resource for finding the GCF of a polynomial. Use these examples to model the procedures for factoring out the GCF with the students. Choose homogeneous partners for the class members and ask them to use “Polynomial Flashcards” to reinforce the standards of the unit so far, including the initial practice of factoring with the GCF.
Summarizing Strategy: Ask students to summarize the difference between multiplying and factoring polynomials.
“GCF Exercises” will be assigned for homework.
I CAN factor polynomials
 iPads Essential Question: How can I factor polynomials with four terms by grouping?

Remediation
Hands-on
“Algebra Tiles to Intro
Factoring”

“Methods to find GCF
Reference
Sheet”
Enrichment
Problems 19-20 on “GCF
Exercises” will replace 3 other problems for students who want the added challenge.
Remediation

Formati ve
Assessm ent
Informal observa tion

“Polyno mial
Flashcar ds”
Summative
Assessment
“GCF
Exercises”
Formative
Assessment

10 with four terms by grouping.

Internet access

TV or
Smartboard for display

“Algebra Tiles to
Intro Factoring.”

“Factor by
Grouping
Exercises”
Materials for
Remediation http://www.mesacc.
edu/~scotz47781/m at120/notes/factori ng/grouping/groupi ng.html
Lesson Title: Factoring by Grouping
Set: Show the Finding Victims After a Disaster video at which ties in rather nicely with the Zombie Outbreak project.
Teaching Strategy: Introduce the lesson with “Algebra Tiles to Intro Factoring.”
Teach the procedure to factor by grouping using “Factoring by Grouping Lesson.”
Summarizing Strategy: Ask students how they will know to apply factoring by grouping.
“Factor by Grouping Exercises” will be assigned for homework.
Materials for
Enrichment “Factor by Grouping
Enrichment”
STANDARDS
Project Day- Refer to Unit Plan
Teresa and Carl
Identify what you want to teach. Reference State, Common Core, ACT
College Readiness Standards and/or State Competencies.
Enrichment
“Factor by
Grouping
Enrichment”
Informal observation
“Algebra
Tiles to Intro
Factoring.”
Summative
Assessment
“Factor by
Grouping
Exercises”


CCSS.A.SSE.A.2. Use the structure of an expression to identify ways to rewrite it.

CCSS.A.SSE.B.3a. Factor a quadratic expression to reveal the zeros of the function it defines.

CCSS.A.CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

CCSS.A.APR.A.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.

CCSS.A.APR.B.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.