Download Pre-Calculus Honors - Unit 2 Polynomial Functions

Pre-Calculus Honors Unit 2 – Polynomial Functions
Introduction:
Grade Level:
Mathematical
Practices
Conceptual
Overview(inform
Suggested Unit Pacing (# of days):
The Mathematical Practices are
K-12 standards and together with
the content standards prescribe
that students experience
mathematics as a coherent, useful,
and logical subject. Teachers of
mathematics should intentionally
provide daily opportunities for
students to develop these
mathematical habits of mind.
During this unit students will…
P4
P5
P6
P7
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of
others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
P8
Look for and express regularity in repeated reasoning.
P1
P2
P3
ation for parents)
Essential
Understandings(
By the end of this unit students will be able to…
Common Core
Standards
information for
students)
CCSS.9_12.MA.
N.CN.3
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
CCSS.9_12.MA.
N.CN.8
(+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
CCSS.9_12.MA.
N.CN.9
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
Domain
Domain
SCS.9_12.MA.P
C.2.01
Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results.
SCS.9_12.MA.P
C.2.01.a
Solve using graphs and algebraic properties.
SCS.9_12.MA.P
C.2.01.b
Interpret the constants, coefficients, and bases in the context of the problem.
SCS.9_12.MA.P
C.2.03
For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions.
SCS.9_12.MA.P
C.2.03.a
Interpret the constants, coefficients, and bases in the context of the data.
These suggested learning targets were determined based on the intentions of the CCSS and/or NCES. Teachers
will need to add the criteria for success in order to create outcome-based targets.
Learning
Targets
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Graph a quadratic function, finding the vertex (formula method and completing the square method), x-intercepts and y-intercept.
Use long division and synthetic division to divide polynomials by other polynomials.
Perform operations with complex numbers and plot complex numbers in the number plane.
Graph polynomial functions by finding the x-intercepts and y-intercepts, including double and triple roots.
Determine the number of rational and real zeros of polynomial functions, and find them.
Write a polynomial equation given its roots. Know and apply the Fundamental Theorem of Algebra. Apply ponynomial functions to model and solve problems.
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Use a polynomial function to model and solve a real-life problem.
parabola
polynomial function
axis of symmetry
vertex
continuous
Leading Coefficient Test
extrema
multiplicity
Intermediate Value Theorem
long division of polynomials
synthetic division of polynomials
Remainder Theorem
Factor Theorem
Rational Zero Test
upper and lower bound
imaginary unit i
complex number
complex conjugates
complex plane
real and imaginary axes
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Essential
Terminology

Literacy
Integration
Technology
Integration
Fundamental Theorem of Algebra
Literacy
Standards
Literature
Connections
Technology
Standards
Technology
Resources
Additional
Resources
Cross
Curricular
Integration
Assessment
Pre-/Postassessment
On-going/
Formative
Assessment
Summative
Teachers determine the learning plan while reflecting on the range of abilities, styles, interests and needs of
students. How will the work be personalized and differentiated in order to achieve the desired learning targets?
Considerations
for the Learning
Plan
Quadratics 2.1
Polynomials 2.2
Modeling-Quadratics/Formative Assessment
Roots of Polynomials 2.3
Complex Numbers 2.4
Fundamental Theorem of Algebra 2.5
Modeling-Polynomial Functions
Formative Assessment
Review/Circles
Assessment
Re-teaching
Enrichment