Download Unifying Concept: Solving and Applying Polynomial

2016-2017 Mathematics Curriculum Map Algebra II, Q1
Unifying Concept: Solving and Applying Polynomial, Rational and Radical Equations; Factoring
Quarter 1
Target Standards are emphasized every quarter and used in formal assessment to evaluate student mastery.
Highly-Leveraged Standards1
A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as
(x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
A-APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the
remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
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.
A-REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers
asserted at the previous step, starting from the assumption that the original equation has a solution.
Construct a viable argument to justify a solution method.
A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing
how extraneous solutions may arise.
A-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing
on pairs of linear equations in two variables.
A-REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two
variables algebraically and graphically. For example, find the points of intersection between the line y =
–3x and the circle x2 + y2 = 3.
F-IF.C.7c Graph polynomial functions, identifying zeros when suitable factorizations are available,
and showing end behavior.
Additional Standards
Complementary Standards: (Standards to be
assessed in classroom and/or future benchmarks)
N-Q.A.2
N-CN.A.1, 2
N-CN.C.7
A-APR.C.4
A-APR.D.6
A-REI.B.4b
G-GPE.A.2
Supporting Standards2
- There are no Supporting Target Standards for this quarter.
6th – 12th Grade Literacy in History/Social
Studies, Science, and Technical Subjects Focus
Standards:
(http://www.azed.gov/standardspractices/files/2015/04/accs-6-12-ela-contentliteracy-standards-final10_28_2013.pdf)
Standards for Mathematical Practice: (quarterly
focus)
Mathematically proficient students:
SMP 1. Make sense of problems and persevere in
solving them.
SMP 2. Reason abstractly and quantitatively.
SMP 4. Model with mathematics.
SMP 7. Look for and make use of structure.
SMP 8. Look for and express regularity in repeated
reasoning.
Mathematical Practices Poster
1
Highly-Leveraged Standards are the most essential for students to learn because they have endurance, leverage and essentiality. This definition for highly-leveraged standards
was adapted from the website of Millis Public Schools, K-12, in Massachusetts, USA. http://www.millis.k12.ma.us/services/curriculum_assessment/brochures
Specifically for mathematics, the Highly-Leveraged Standards are the Major Content/Clusters as defined by the AZCCRS Grade Level Focus documents. They should encompass
a range of at least 65%-75% for Major Content/Clusters and a range of 25%-35% for Supporting Cluster Instruction. See the Grade Level Focus documents at:
https://cms.azed.gov/home/GetDocumentFile?id=57069edaaadebe0bccd0a8af
2
Supporting Standards are related standards that support the highly-leveraged standards in and across grade levels.
*Highly-Leveraged standards in bold and supporting standards are normal text.
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/11/2016 3:09 PM
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2016-2017 Mathematics Curriculum Map Algebra II, Q1
Adopted and Supplemental Texts
Big Ideas
Eureka Math/ Engage NY:
Module 1: Polynomial, Rational, and Radical Relationships
 Topic A: Polynomials-From Base Ten to Base X
 Topic B: Factoring-Its Use and Its Obstacle
 Topic C: Solving and Applying Equations-Polynomial, Rational, and
Radical
 Topic D: A Surprise from Geometry-Complex Numbers Overcome All
Obstacles
Essential Concepts:
 Polynomial or rational expressions can sometimes be rewritten to find relevant
characteristics for the situation including finding zeros, asymptotes, or extrema.
 The zeros of a polynomial are turned into linear factors and can be used to
factor polynomials of any power.
 The multiplicity of a zero tells us how the polynomial "behaves" about this
value and aids us in sketching a rough graph of the polynomial.
 The properties of equality and order of operations can be used to solve an
equation by using inverse operations.
 We solve rational or radical equations by transforming the equation into a
simpler form to solve. (i.e.: into linear or quadratic) However, this can produce
solutions that do not exist in the original domain.
 Systems of equations may be solved using graphs, tables, elimination, or
substitution.
 The solution to a system, if it exists, is an ordered pair.
 The sketch of a polynomial is a continuous graph with possible changes in
shape and direction. The zeros are located where the graph crosses the x axis.
The end behavior is determined by the leading coefficient and the degree of the
polynomial.
Holt McDougal Algebra II (Blue Book):
Chapter 3 – Sections 1, 3, 4, 5, 6, 7
Page 173 (3-4 Algebra Lab)
Chapter 5 – Sections 5 and 8
Chapter 12 – Section 7
Instruction must be supplemented to meet the expectations of the standards.
McDougal Littell Algebra II (Green Book):
Chapter 3 –Section 6
Chapter 6 – Sections 2 and 8
Chapter 7 – Section 6
Chapter 9 – Section 6
Chapter 10 – Section 7
Instruction must be supplemented to meet the expectations of the standards.
Additional Resources:
https://www.khanacademy.org
http://achievethecore.org
https://www.illustrativemathematics.org/
www.insidemathematics.org
https://learnzillion.com/resources/75114-math
http://maccss.ncdpi.wikispaces.net/ (Choose your grade level on the left)
http://www.pbslearningmedia.org/standards/1
http://nlvm.usu.edu/en/nav/vlibrary.html
http://nrich.maths.org
https://www.youcubed.org/week-of-inspirational-math/
http://illuminations.nctm.org/Lessons-Activities.aspx (choose grade level and
connect to search lessons)
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Essential Questions:
 Why do we rewrite polynomials or rational expressions?
 How can we rewrite polynomial or rational expressions to use previously
learned methods to find zeros?
 Why are the zeros of a polynomial important?
 How do I use the zeros of a polynomial function to graph the function?
 What does the multiplicity of each zero mean to the construction of the graph?
 How do the properties of equality and order of operations extend to support the
solving of an equation?
 How do I solve a rational or radical equation?
 How are extraneous solutions generated from a rational or radical equation?
 What does it mean to find the solution(s) to a system of linear equations in
three variables?
 What are the solutions to a pair of equations where one is linear and the other
quadratic?
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2016-2017 Mathematics Curriculum Map Algebra II, Q1
 What does a polynomial function look like?
 How do I identify the zeros?
 How do I identify the end behavior?
http://www.yummymath.com/birds-eye-of-activities/
http://map.mathshell.org/tasks.php?collection=9&unit=HE06
http://www.shmoop.com/common-core-standards/math.html
http://www.njcore.org/standards?processing=true#
https://hcpss.instructure.com/courses/163
https://www.desmos.com/
http://www.geogebra.org/
http://ccssmath.org/?page_id=1303
www.mathalicious.com
http://robertkaplinsky.com/lessons/
http://www.livebinders.com/play/play_or_edit?id=330579
http://www.cpalms.org/Public/ToolkitGradeLevelGroup/Toolkit?id=14
Vocabulary
addition property of equality
algebraic proof
degree of a polynomial
difference of cubes
difference of squares
distributive property
division property of equality
domain
end behavior
equation
extraneous
Additional Resource: http://www.graniteschools.org/mathvocabulary/
extraneous solutions
polynomial long division
factor theorem
radical equations
factors
rational equations
graphing
Rational Root Theorem
laws of exponents
reflexive property
leading coefficient
remainder
linear combination (elimination)
remainder theorem
multiplication property of equality
roots
multiplicity of zeros
simplify
perfect squares
solution
points of intersection
substitution
subtraction property of equality
sum of cubes
symmetric property
synthetic division
synthetic substitution
system of equations
variable
x-intercept
zeros
zeros of a function
Interdisciplinary Connections
Multicultural Math Connections:
https://www.deltacollege.edu/dept/basicmath/Multicultural_Math.htm
http://www.edchange.org/multicultural/sites/math.html
http://users.wfu.edu/mccoy/mgames.pdf
http://www.ericdigests.org/1996-1/more.htm
A Course in Multicultural Mathematics
Integrating Mathematics of Worldwide Cultures into K-12
Teaching Mathematics through Multicultural Literature
http://www.nea.org/tools/lessons/47756.htm
https://www.teachervision.com/
Math Modeling Projects
https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWk
Literacy Connections:
http://mathsolutions.com/wpcontent/uploads/1995_Writing_in_Elem_Grades.pdf
http://www.edutopia.org/blog/four-tips-writing-math-classroom-heather-wolpertgawron
http://files.eric.ed.gov/fulltext/ED544239.pdf
http://www-tc.pbs.org/teacherline/courses/rdla230/docs/session_1_burns.pdf
Writing Prompts for Math
http://writingfix.com/wac/numberfix.htm
http://www.nea.org/tools/lessons/47756.htm
https://www.teachervision.com/
TUSD Department of Curriculum and Instruction
Revised 5/11/2016 3:09 PM
Curriculum 3.0
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2016-2017 Mathematics Curriculum Map Algebra II, Q1
TQEsfqouLWNNC6Z4/pub?output=html
http://msms.ehe.osu.edu/2010/05/20/teaching-with-trade-books-math/
http://letsreadmath.com/math-and-childrens-literature/
Assessment Guides and Resources
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Instructional Resources
http://www.azed.gov/assessment/files/2015/12/math-pld-algebra-ii.pdf
http://achievethecore.org/category/1020/mathematics-assessments
http://www.azed.gov/assessment/azmeritsupportmaterials/
http://www.ccsstoolbox.org/
http://www.insidemathematics.org/tools-for-educators
http://map.mathshell.org/materials/index.php
http://www.orglib.com/home.aspx
http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWo
rk/default.htm?s=Z3JhZGVzPTgmc3ViamVjdD0y
https://www.illustrativemathematics.org/8
https://hcpss.instructure.com/courses/99
http://www.cpalms.org/Public/ToolkitGradeLevelGroup/Toolkit?id=14
DOK Levels
http://www.azed.gov/assessment/files/2014/11/dok-levels.pdf
DOK Stems
http://www.azed.gov/assessment/files/2014/11/dok-question-stems.pdf
Hess’s Matrix
http://static.pdesas.org/content/documents/M2-Activity_2_Handout.pdf
Bloom’s Taxonomy
http://www.bloomstaxonomy.org/Blooms%20Taxonomy%20questions.pdf
TUSD Department of Curriculum and Instruction
Revised 5/11/2016 3:09 PM
Curriculum 3.0
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