ADVANCED ALGEBRA & TRIGONOMETRY HIGHER-LEVEL FUNCTIONS UNIT PLAN GOAL:

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Oct 10, 2013 (4 years and 29 days ago)

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ADVANCED ALGEBRA & TRIGONOMETRY


HIGHER
-
LEVEL FUNCTIONS UNIT PLAN

GOAL:

Students will understa
nd and apply characteristics of higher
-
level functions.


Day 1

Day 2

Day 3

Day 4

Day 5

Essential Question:


How do I find the vertex
and intercepts of a
quadra
tic function?

Essential Question:

How do I analyze and
graph polynomial
functions?

Essential Question:


How do I find real and
complex zeros of a
polynomial function?

Essential Question:

How do I show
conceptual mastery of
quadratic and general
polynomial
functions?

Essential Question:

How do I graph rational
functions and their
asymptotes?

Standard:

M.AAT.1.1 Graphing
Functions: Concepts

The learner will be able to
graph relations and functions
using concepts including
domain, range, rule of a
function,

symmetry,
asymptotes, and periodicity
and end behavior

M.AAT.1.12 Graphing
Functions: Methods

The learner will be able to
graph polynomial, rational,
and algebraic functions using
appropriate techniques and
tools.



Standard:

M.AAT.1.2 Polynomials:
Solv
e

The learner will be able to
solve polynomial equations
over the field of complex
numbers, using the
following theorems:
Remainder, Factor,
Rational Root, and
Fundamental Theorem of
Algebra.

M.AAT.1.1 Graphing
Functions: Concepts

The learner will be able

to
graph relations and
functions using concepts
including domain, range,
rule of a function,
symmetry, asymptotes, and
periodicity and end
behavior

M.AAT.1.12 Graphing
Functions: Methods

The learner will be able to
graph polynomial, rational,
and algebra
ic functions
using appropriate
techniques and tools.


Standard:

M.AAT.1.2 Polynomials:
Solve

The learner will be able to
solve polynomial equations
over the field of complex
numbers, using the
following theorems:
Remainder, Factor,
Rational Root, and
Fun
damental Theorem of
Algebra.


Standard:

M.AAT.1.2 Polynomials:
Solve

The learner will be able to
solve polynomial equations
over the field of complex
numbers, using the
following theorems:
Remainder, Factor,
Rational Root, and
Fundamental Theorem of
Alg
ebra.

M.AAT.1.1 Graphing
Functions: Concepts

The learner will be able to
graph relations and
functions using concepts
including domain, range,
rule of a function,
symmetry, asymptotes, and
periodicity and end
behavior

M.AAT.1.12 Graphing
Functions: Methods


The learner will be able to
graph polynomial, rational,
and algebraic functions
using appropriate
techniques and tools.

Standard:

M.AAT.1.1 Graphing
Functions: Concepts

The learner will be able to
graph relations and functions
using concepts including
do
main, range, rule of a
function, symmetry,
asymptotes, and periodicity
and end behavior

M.AAT.1.12 Graphing
Functions: Methods

The learner will be able to
graph polynomial, rational,
and algebraic functions using
appropriate techniques and
tools.


Object
ives:


1. Students will find the
vertex and intercepts of any
quadratic function.


2. Students will recognize
and understand the
inherent characteristics of
the various forms of a
quadratic function.


Objectives:


1. Students will
understand the
character
istics and
linkages between the
graphs of various
polynomial functions.


2. Students will continue
their discovery and
understanding of domain
and range, end behavior,
and behavior intervals of
graphs.

Objectives:


1. Students will
understand the
synonyms
“x
-
intercepts,
zeros, solutions, roots”
and will find them for
various polynomial
functions


2. Students will
understand and apply the
different and most
efficient ways of
determining roots for
various polynomial
functions.

Objectives:


1. Students will
de
monstrate formative
mastery by illustrating
their conceptual
understanding of
quadratic and general
polynomial functions.

Objectives:


1. Students will understand
degree relationships and
their effects on end
-
behavior asymptotes; the
various types of end
-
b
ehavior asymptotes; the
various discontinuities


infinite versus removable.


2. Students will know the
basic steps of graphing
rational functions of various
types.

Activities
:

1. Notes

2. P. 233 textbook
assignment


Activities
:

1. Notes

2. P. 246 textboo
k
assignment

Activities
:

1. Notes

2. Finding zeros handout

Activities
:

1.
Quadratics/general
polynomials q
uiz

2. Discovering rational
functions handout

Activities
:

1. Review discovery
handout

2. Notes

3. Rational functions
handout


Day 6

Day 7

Essential

Question:


What are the concepts of
higher
-
level functions that I
still am unsure of? Can I
summarize in a simple way
the characteristics of
higher
-
level functions?

Essential Question:


How will I demonstrate
summative mastery of
higher level functions,
including their
characteristics and
applications?

Standard:

M.AAT.1.2 Polynomials:
Solve

The learner will be able to
solve polynomial equations
over the field of complex
numbers, using the following
theorems: Remainder, Factor,
Rational Root, and
Fun
damental Theorem of
Algebra.

M.AAT.1.1 Graphing
Functions: Concepts

The learner will be able to
graph relations and functions
using concepts including
domain, range, rule of a
function, symmetry,
asymptotes, and periodicity
and end behavior

M.AAT.1.12 Grap
hing
Functions: Methods

The learner will be able to
graph polynomial, rational,
and algebraic functions using
appropriate techniques and
tools.



Standard:

M.AAT.1.2 Polynomials:
Solve

The learner will be able to
solve polynomial equations
over the fiel
d of complex
numbers, using the following
theorems: Remainder, Factor,
Rational Root, and
Fundamental Theorem of
Algebra.

M.AAT.1.1 Graphing
Functions: Concepts

The learner will be able to
graph relations and functions
using concepts including
domain, rang
e, rule of a
function, symmetry,
asymptotes, and periodicity
and end behavior

M.AAT.1.12 Graphing
Functions: Methods

The learner will be able to
graph polynomial, rational,
and algebraic functions using
appropriate techniques and
tools.

Objectives:


1. S
tudents will utilize
group
-

and self
-
inquiry
Objectives:


1. Students will
demonstrate summative
about their understanding
of higher
-
level functions.


2. Conceptual “loose
-
ends”
will be summarized and
tied up.


understanding of higher
-
level functions at th
e
mechanical and
conceptual levels.

Activities
:

1. Review discussion

2. P. 291, 689 textbook
review assignment

Activities
:

1.
Higher
-
level functions
test