Algebra II Essential Guide
This class furthers awareness of algebraic operation on monomial and polynomial expressions. Students will study simplifying and solving quadratic equations, irrational and complex
equations, and quadratic inequalities. Students will work with and analyze systems of equations, quadratic functions, and polynomial functions. This course offered at Chamberlain Academy,
Springfield Academy, McCrossan Boys Ranch, and High Impact/Career Academy is based on the South Dakota Content Standards. This course offered at Elmore Academy is based on Minnesota
Academic Standards. This class will prepare students for higher-level mathematics classes and for the Dakota Step test or Minnesota Comprehensive Assessment.
Prerequisites include Algebra 1 and Geometry.
Essential Question
How are exponents
and exponential
functions important
to simplifying and
solving many real
world problems
involving math and
science?
How are inequalities
important to use in
representing some
real world problems?
How can powers,
roots and radicals be
used in solving realworld problems?
Content
Vocabulary
South Dakota State
Content Standards
Relations and functions 9-12.A.1.1
Equivalent forms
Linear equations
Having the same
value when
Slope
evaluated.
9-12.A.1.1
(Comprehension)
Students are able to
write equivalent
forms of algebraic
expressions using
properties of the set
of real numbers.
Writing linear
equations
Using scatter plots
Graphing inequalities
Algebraic
expressions: A
mathematical
combination of
numbers, variables,
and operations. It is
not an equation.
Properties of real
numbers: A set of
mathematical rules
or laws that results in
an equivalent
expression.
Real Number: Any
number that can be
graphed on the
South Dakota Skills:
Expectations of
learning in Student
Speak
(9-12.A.1.1)
I am able to write
(determine)
equivalent forms of
algebraic expressions
using (applying)
properties of the set
of real numbers.
9-12.A.2.1.
(Comprehension)
Students are able to
use algebraic
properties to
transform multi-step,
single-variable, firstdegree equations.
(9-12.A.2.1)
I am able to use
(apply) algebraic
properties to
transform (solve)
multi-step, singlevariable, first-degree
equations.
9-12.A.4.1
(Application)
Students are able to
use graphs, tables
and equations to
represent linear
(9-12.A.4.1) I am
able to use (create)
graphs, tables and
equations to
represent (model)
linear functions.
Minnesota Academic
Benchmarks
Minnesota Academic
Standards
Assessments
A.9.2.1.5 Identify the
vertex, line of
symmetry and
intercepts of the
parabola
corresponding to a
quadratic function,
using symbolic and
graphical methods,
when the function is
expressed in the form f
(x) = ax2 + bx + c, in the
form
f (x) = a(x – h)2 + k , or
in factored form.
A.9.2.1 Understand the
concept of function,
and identify important
features of functions
and other relations
using symbolic and
graphical methods
where appropriate.
* Rubrics
* Achievement Series
formative
assessments
* Student selfassessment – written
reflection
*Teacher-made
assessments
formative and
summative
assessments
* Textbook formative
and summative
assessments
* Performance – pre
and post test
* South Dakota State
Test of Educational
Progress (Dakota
STEP)/Minnesota
Comprehensive
Assessments (MCAs)
A.9.2.1.6 Identify
intercepts, zeros,
maxima, minima and
intervals of increase
and decrease from the
graph of a function.
A.9.2.2.3 Sketch graphs
of linear, quadratic and
exponential functions,
and translate between
A.9.2.2 Recognize
linear, quadratic,
exponential and other
common functions in
real-world and
mathematical
situations; represent
these functions with
tables, verbal
descriptions, symbols
and graphs; solve
problems involving
these functions, and
explain results in the
original context.
A.9.2.3.Generate
equivalent algebraic
number line. This
includes integers and
rational numbers.
9-12.A.4.1.A
Domain: The set of
inputs. The set of
possible values for x
or the independent
variable.
Range: The set of
outputs. The set of
possible values for y
or f(x) or the
dependent variable.
Intercepts: The
value(s) where the
graph of a function
crosses the axes.
Function: A
mathematical
relation that
associates each
object in a set with
exactly one value.
9-12.A.4.6.A.
Linear inequality: A
comparison of two
first degree
expressions.
functions.
9-12.A.4.1.A.
Analysis Students are
able to determine
the domain, range,
and intercepts of a
function.
9-12.A.4.6.A.
Application Students
are able to graph
solutions to linear
inequalities.
9-12.A.4.1.A
Given a function in
any form (numerical,
graphical, or
algebraic), I can find:
•Domain (The set of
inputs. The set of
possible values for x
or the independent
variable.)
•Range (The set of
outputs. The set of
possible values for y
or f(x) or the
dependent variable.)
•Intercepts (The
value(s) where the
graph of a function
crosses the axes.)
•Horizontal
asymptotes
•Vertical asymptotes
9-12.A.4.6.A.
•I can solve a linear
inequality
algebraically.
•I can match the
graph of an
inequality with its
algebraic
representation.
•I can determine the
type boundary
created by the
graphs, tables and
symbolic
representations. Know
how to use graphing
technology to graph
these functions.
A.9.2.3.1 Evaluate
polynomial and rational
expressions and
expressions containing
radicals and absolute
values at specified
points in their domains.
A.9.2.3.2 Add, subtract
and multiply
polynomials; divide a
polynomial by a
polynomial of equal or
lower degree.
A.9.2.3.3 Factor
common monomial
factors from
polynomials, factor
quadratic polynomials,
and factor the
difference of two
squares.
A.9.2.3.4Add, subtract,
multiply, divide and
simplify algebraic
fractions.
A.9.2.3.5 Check
whether a given
complex number is a
solution of a quadratic
equation by
expressions involving
polynomials and
radicals; use algebraic
properties to evaluate
expressions.
A.9.2.4 Represent realworld and
mathematical
situations using
equations and
inequalities involving
linear, quadratic,
exponential and nth
root functions. Solve
equations and
inequalities
symbolically and
graphically. Interpret
solutions in the original
context.
inequality (solid or
dashed).
•I can shade the
correct side (halfplane).
substituting it for the
variable and evaluating
the expression, using
arithmetic with
complex numbers.
A.9.2.3.6 Apply the
properties of positive
and negative rational
exponents to generate
equivalent algebraic
expressions, including
those involving nth
roots.
A.9.2.3.7 Justify steps
in generating
equivalent expressions
by identifying the
properties used. Use
substitution to check
the equality of
expressions for some
particular values of the
variables; recognize
that checking with
substitution does not
guarantee equality of
expressions for all
values of the variables.
A.9.2.4.1 Represent
relationships in various
contexts using
quadratic equations
and inequalities. Solve
quadratic equations
and inequalities by
appropriate methods
including factoring,
completing the square,
graphing and the
quadratic formula. Find
non-real complex roots
when they exist.
Recognize that a
particular solution may
not be applicable in the
original context. Know
how to use calculators,
graphing utilities or
other technology to
solve quadratic
equations and
inequalities.
How are exponents
and exponential
functions important
to simplifying and
solving many real
world problems
involving math and
science?
Solving systems of
equations:
- algebraically
- by graphing
Solve systems of
inequalities by
graphing
9-12.A.1.1.
(Application from
previous unit)
9-12.A.2.2.A.
Solutions: value or
values of the
variable(s) that make
the statement true
Systems of
equations: two or
more equations
9-12.A.1.1.
(Application from
previous unit)
9-12.A.2.1.
(Application from
previous unit)
9-12.A.1.1.
(Application from
previous unit)
9-12.A.2.1.
(Application from
previous unit)
9-12.A.2.2.A.
(Application)
Students are able to
determine the
solution of systems of
9-12.A.2.2.A.
•I can solve a system
of linear equations
(two or more
equations) using
A.9.2.4.4 Represent
relationships in various
contexts using systems
of linear inequalities;
solve them graphically.
Indicate which parts of
the boundary are
included in and
excluded from the
solution set using solid
and dotted lines.
A.9.2.3.1
A.9.2.3.2
A.9.2.3.3
A.9.2.3.4
A.9.2.3.5
A.9.2.3.6
A.9.2.3.7 (Application
from previous unit)
9.2.4.1 (Application
from previous unit)
A.9.2.3. (Application
from previous unit)
9.2.4. (Application
from previous unit)
* Rubrics
* Achievement Series
formative
assessments
* Student selfassessment – written
reflection
*Teacher-made
assessments
formative and
summative
assessments
Systems of
inequalities: two or
more inequalities
How are quadratic
equations and their
graphs useful in
solving real
problems?
Algebraic operations
Dividing polynomials
Factoring polynomials
Roots of real numbers
Radical expressions
Rational exponents
Radical equations
9-12.N.1.1
Multiple
representations:
equivalent
expressions
Real Number: Any
number that can be
graphed on the
number line. This
includes rational and
irrational numbers.
9-12.N.2.1.
Integral exponents:
Powers that are
equations and
systems of
inequalities.
9-12.N.1.1.
(Comprehension)
Students are able to
identify multiple
representations of a
real number.
9-12.N.2.1.
(Comprehension)
Students are able to
add, subtract,
multiply, and divide
real numbers
including integral
exponents.
- Substitution
- Graphing
- Elimination (linear
combination)
- Matrices
•I can solve a system
(two or more
equations) that
contains both linear
and non-linear
equations.
•I can solve a system
of inequalities (two
or more inequalities)
by graphing.
9.2.4.2 Represent
relationships in various
contexts using
equations involving
exponential functions;
solve these equations
graphically or
numerically. Know how
to use calculators,
graphing utilities or
other technology to
solve these equations.
9-12.N.1.1.
•Given a real number
(Any number that can
be graphed on the
number line. This
includes rational and
irrational numbers), I
can write and/or
classify (identify) the
subset(s) of the real
numbers to which it
belongs (rational,
irrational, integers,
whole numbers,
natural numbers).
N.8.1.1.1 Classify real
numbers as rational or
irrational. Know that
when a square root of
a positive integer is not
an integer, then it is
irrational. Know that
the sum of a rational
number and an
irrational number is
irrational, and the
product of a non-zero
rational number and an
irrational number is
irrational.
* Textbook formative
and summative
assessments
* Performance – pre
and post test
* South Dakota State
Test of Educational
Progress (Dakota
STEP)/Minnesota
Comprehensive
Assessments (MCAs)
9.2.4.8 Assess the
reasonableness of a
solution in its given
context and compare
the solution to
appropriate graphical
or numerical estimates;
interpret a solution in
the original context.
N.8.1.1.2 Compare real
N.8.1.1 Read, write,
compare, classify and
represent real
numbers, and use them
to solve problems in
various contexts.
A.9.2.2 Recognize
linear, quadratic,
exponential and other
common functions in
real-world and
mathematical
situations; represent
these functions with
tables, verbal
descriptions, symbols
* Rubrics
* Achievement Series
formative
assessments
* Student selfassessment – written
reflection
*Teacher-made
assessments
formative and
summative
assessments
* Textbook formative
and summative
assessments
integers.
9-12.A.1.2.A.
Real number
properties: A set of
mathematical rules
or laws that results in
an equivalent
expression.
Expression: A
mathematical
combination of
numbers, variables,
and operations. It is
not an equation.
Complex numbers: A
number of the form
a+bi where a and b
are real numbers and
i = −1.
9-12.A.2.1.A.
Quadratic equation:
an equation
containing , a
polynomial of degree
2 such that it can be
transformed into .
9-12.N.1.1A.
Real Number System:
The set of numbers
consisting of the
union of rational and
irrational numbers.
Complex Number
System: The set of
9-12.N.1.1A.
(Comprehension)
Students are able to
describe the
relationship of the
real number system
to the complex
number system.
•I can write (identify)
any rational number
as a fraction and
decimal.
9-12.N.2.1.
•I can add, subtract,
multiply and divide:
-Numerical
expressions
containing rational
numbers.
- Numerical
expressions
containing integral
exponents (powers
that are integers).
•I can evaluate
complex fractions.
9-12.N.2.1A.
(Application)
Students are able to
add, subtract,
multiply, and divide
real numbers
including rational
exponents.
9-12.A.1.2.A.I can
add, subtract,
multiply and divide
complex numbers (A
number of the form
a+bi where a and b
are real numbers and
i = −1).
9-12.A.1.2.A.
(Application)
Students are able to
extend the use of
real number
properties to
expressions involving
complex numbers.
9-12.A.2.1.A.
• I can solve
quadratic equations
(an equation
containing , a
polynomial of degree
2 such that it can be
transformed into ax2
numbers; locate real
numbers on a number
line. Identify the square
root of a positive
integer as an integer,
or if it is not an integer,
locate it as a real
number between two
consecutive positive
integers.
N.8.1.1.4 Know and
apply the properties of
positive and negative
integer exponents to
generate equivalent
numerical expressions.
A. 9.2.2.1 Represent
and solve problems in
various contexts using
linear and quadratic
functions.
A.9.2.3.2
A.9.2.3.3
A.9.2.3.7
(Application from
previous unit)
A.9.2.4.3 Recognize
that to solve certain
equations, number
systems need to be
extended from whole
numbers to integers,
from integers to
rational numbers, from
rational numbers to
and graphs; solve
problems involving
these functions, and
explain results in the
original context.
A.9.2.3. (Application
from previous unit)
A.9.2.4 Represent realworld and
mathematical
situations using
equations and
inequalities involving
linear, quadratic,
exponential and nth
root functions. Solve
equations and
inequalities
symbolically and
graphically. Interpret
solutions in the original
context.
* Performance – pre
and post test
* South Dakota State
Test of Educational
Progress (Dakota
STEP)/Minnesota
Comprehensive
Assessments (MCAs)
numbers consisting
of the union of
imaginary and real
numbers.
9-12.N.2.1A.
Rational Exponent: A
power that can be
expressed as a
rational number.
+ bx + c = 0, a ≠ 0
)by:
-Factoring
-Completing the
square
-Using the quadratic
formula
-Graphing (using
appropriate
technology)
• I can determine
the nature of the
roots.
• I can solve
equations that are in
quadratic form. (the
form , where u is any
expression in x, and
a, b, and c are real
numbers).
9-12.N.1.1A.
I can state the
similarities between
the real numbers and
the complex
numbers.
I can state the
differences between
the real numbers and
the complex
numbers.
I can find the
absolute value
(magnitude) of a
complex number.
real numbers, and from
real numbers to
complex numbers. In
particular, non-real
complex numbers are
needed to solve some
quadratic equations
with real coefficients.
A.9.2.4.5 Solve linear
programming problems
in two variables using
graphical methods.
I can identify the
parts (imaginary or
real) of a complex
number.
I can graph points in
the complex plane.
Given a point in a
complex plane, I can
state its coordinate.
9-12.N.2.1A.
•I can add, subtract,
multiply and divide:
-Numerical
expressions
containing real
numbers.
-Expressions in
radical form.
-Numerical
expressions
containing rational
exponents (powers
that are rational
numbers).
•I can simplify
expressions that
contain radicals.
•I can write an
expression with a
rational exponent in
radical form and viceverse.
•I can rationalize the
denominator.
•I can simplify a
How can powers,
roots and radicals be
used in solving realworld problems?
Graphing quadratic
equations
Solving quadratic
equations by:
- graphing
- factoring
Completing the square
Quadratic formula
Families of parabola
Analyzing graphs of
quadratic functions
Graphing and solving
quadratic inequalities
9-12.A.4.1.A
Domain: The set of
inputs. The set of
possible values for x
or the independent
variable.
Range: The set of
outputs. The set of
possible values for y
or f(x) or the
dependent variable.
Intercepts: The
value(s) where the
graph of a function
crosses the axes.
Function: A
mathematical
relation that
associates each
object in a set with
exactly one value.
9-12.A.4.2.A.
Polynomial: Sum of
two or more
monomials (i.e. ). In
this standard all
polynomials are
single variable.
Leading coefficient:
The coefficient of the
highest degree
9-12.A.4.1.A.
(Application from
previous unit)
9-12.A.4.2.A.
(Analysis) Students
are able to describe
the behavior of a
polynomial, given the
leading coefficient,
roots, and degree.
9-12.A.2.1.A.
(Application from
previous unit)
complex fraction that
contains expressions
with rational
exponents.
9-12.A.4.1.A
(Application from
previous unit)
9-12.A.4.2.A.
•Given a single
variable polynomial
(Sum of two or more
monomials (i.e. ))
with the leading
coefficient (The
coefficient of the
highest degree
monomial in a
polynomial.), roots
(The zeros of the
polynomial. It is also
the x-intercept if the
roots are real.) and
degree (The
exponent of a single
variable polynomial),
I can sketch the
general shape of the
polynomial.
•Given the graph of a
polynomial (Sum of
two or more
monomials (i.e. )), I
can find the roots
(The exponent of a
single variable
A.8.2.2.3 Identify how
coefficient changes in
the equation f (x) = mx
+ b affect the graphs of
linear functions. Know
how to use graphing
technology to examine
these effects.
A.9.2.1.5 (Application
from previous unit)
A.9.2.1.7 (Application
from previous unit)
A.9.2.2.1 (Application
from previous unit)
A.9.2.3.2 (Application
from previous unit)
A.9.2.4.3 (Application
from previous unit)
A.9.2.4.5 (Application
from previous unit)
A.8.2.2 Recognize
linear functions in realworld and
mathematical
situations; represent
linear functions and
other functions with
tables, verbal
descriptions, symbols
and graphs; solve
problems involving
these functions and
explain results in the
original context.
A.9.2.1. (Application
from previous unit)
A.9.2.2 (Application
from previous unit)
A.9.2.3 (Application
from previous unit)
A.9.2.4 (Application
from previous unit)
* Rubrics
* Achievement Series
formative
assessments
* Student selfassessment – written
reflection
*Teacher-made
assessments
formative and
summative
assessments
* Textbook formative
and summative
assessments
* Performance – pre
and post test
* South Dakota State
Test of Educational
Progress (Dakota
STEP)/Minnesota
Comprehensive
Assessments (MCAs)
monomial in a
polynomial.
Roots: The zeros of
the polynomial. It is
also the x-intercept if
the roots are real.
Degree: The
exponent of a single
variable polynomial.
polynomial).
•Given a polynomial
function:
-I can state the
maximum number of
roots (The exponent
of a single variable
polynomial) including
multiplicities.
-I can state the
maximum number of
turning points
(relative max and
min).
9-12.A.2.1.A.
Quadratic equation:
an equation
containing , a
polynomial of degree
2 such that it can be
transformed into ax2
+ bx + c = 0, a ≠ 0 ).
In what ways do
relations, functions,
graphs of functions
and their inverses
help us interpret
real-world events or
solve problems?
Polynomial functions
9-12.A.3.1.A.
Linear model: A
Graphing polynomial
representation of a
functions
problem that can be
expressed as an
Solving equations using equation in the form
quadratic techniques
y = mx + b where m
represents the
Roots and zeros
constant rate of
change, or slope, and
Operations on
b represents some
functions
fixed value, or the yintercept.
Inverse functions and
Quadratic model: A
relations
representation of a
problem that can be
Square root functions
expressed as an
9-12.A.2.1.A.
(Application from
previous unit)
9-12.A.3.1.A.
(Analysis) Students
are able to
distinguish between
linear, quadratic,
inverse variation, and
exponential models.
9-12.A.3.2.A.
(Synthesis) Students
are able to create
formulas to model
relationships that are
algebraic, geometric,
trigonometric, and
exponential.
9-12.A.3.1.A.
•I can classify models
(tables, graphs, or
equations) as:
-Linear (A
representation of a
problem that can be
expressed as an
equation in the form
y = mx + b where m
represents the
constant rate of
change, or slope, and
b represents some
fixed value, or the yintercept.)
-Quadratic (A
A.9.2.1.5 (Application
from previous unit)
A.9.2.2.3 (Application
from previous unit)
G/M9.3.1.4
Understand and apply
the fact that the effect
of a scale factor k on
length, area and
volume is to multiply
each by k, k2 and k3,
respectively.
G/M.9.3.3.5 Know and
apply properties of
right triangles,
including properties of
A.9.2.1. (Application
* Rubrics
from previous unit)
* Achievement Series
formative
A.9.2.2 (Application
assessments
from previous unit)
* Student selfassessment – written
G/M.9.3.1 Calculate
reflection
measurements of plane *Teacher-made
and solid geometric
assessments
figures; know that
formative and
physical measurements
summative
depend on the choice
assessments
of a unit and that they
* Textbook formative
are approximations.
and summative
assessments
G/M.9.3.3 Know and
apply properties of
* Performance – pre
geometric figures to
and post test
solve real-world and
and inequalities
equation containing ,
a polynomial of
degree 2 such that it
can be transformed
into .
Inverse variation
model: A
representation of a
problem that can be
expressed as , where
n is any natural
number .
Exponential model: A
representation of a
problem that can be
expressed as . This
also includes
logarithmic models, .
Model: A
representation of a
problem that uses
tables, graphs, or
equations.
9-12.A.3.2.A.
Formulas: Equations
that can be applied
to set of problems
that have common
parameter.
Algebraic: A relation
that can be classified
as linear, quadratic,
cubic, quartic,
absolute value,
square root, rational
9-12.A.4.4.A.
(Application)
Students are able to
apply properties and
definitions of
trigonometric,
exponential, and
logarithmic
expressions.
representation of a
problem that can be
expressed as an
equation containing
x2 , a polynomial of
degree 2 such that it
can be transformed
into y = ax2 + bx + c,
a ≠ 0 .)
-Inverse variation (A
representation of a
problem that can be
expressed as xn
y = k , where n is any
natural number .)
-Exponential (A
representation of a
problem that can be
expressed as y = a
⋅ bx , a ≠ 0 &b ≠ 1.
.This also includes
logarithmic models, .)
•I can describe the
similarities and
differences between:
-linear models (A
representation of a
problem that can be
expressed as an
equation in the form
y = mx + b where m
represents the
constant rate of
change, or slope, and
b represents some
fixed value, or the y-
45-45-90 and 30-60-90
triangles, to solve
problems and logically
justify results.
mathematical
problems and to
logically justify results
in geometry.
G/M.9.3.4.1
Understand how the
properties of similar
right triangles allow the
trigonometric ratios to
be defined, and
determine the sine,
cosine and tangent of
an acute angle in a
right triangle.
G/M.9.3.4 Solve realworld and
mathematical
geometric problems
using algebraic
methods.
G/M.9.3.4.2 Apply the
trigonometric ratios
sine, cosine and
tangent to solve
problems, such as
determining lengths
and areas in right
triangles and in figures
that can be
decomposed into right
triangles. Know how to
use calculators, tables
or other technology to
evaluate trigonometric
ratios.
G/M.9.3.4.3 Use
calculators, tables or
other technologies in
connection with the
trigonometric ratios to
find angle measures in
right triangles in
various contexts.
A.8.2.1. Understand
the concept of function
in real-world and
mathematical
situations, and
distinguish between
linear and nonlinear
functions.
* South Dakota State
Test of Educational
Progress (Dakota
STEP)/Minnesota
Comprehensive
Assessments (MCAs)
or piecewise.
Trigonometric: A
function that can be
modeled with the six
trigonometric
functions.
Exponential: A
representation of a
problem that can be
expressed as . This
also includes
logarithmic models, .
Geometric: All of the
conic sections:
circles, parabolas,
hyperbolas and
ellipses.
9-12.A.4.4.A.
Trigonometric
Expression: An
expression that uses
one of three
trigonometric
functions (sine,
cosine, or tangent) or
their reciprocals
(cosecant, secant,
cotangent).
Exponential
Expression: Any
expression of the
form
Logarithmic
Expression: An
expression of the
intercept.)
-quadratic models (A
representation of a
problem that can be
expressed as an
equation containing ,
a polynomial of
degree 2 such that it
can be transformed
into y = ax2 + bx + c,
a≠0.)
-inverse variation
models (A
representation of a
problem that can be
expressed as xn
y = k, where n is any
natural number ) and
-exponential models
(A representation of
a problem that can
be expressed as y = a
⋅ bx , a ≠ 0 &b ≠
1.This also includes
logarithmic models, y
= x a > a ≠ .) .)
9-12.A.3.2.A.
•I can classify
information
portrayed in graphs
and/or tables as:
-algebraic (A relation
that can be classified
as linear, quadratic,
cubic, quartic,
G/M.9.3.4.7 Use
algebra to solve
geometric problems
unrelated to
coordinate geometry,
such as solving for an
unknown length in a
figure involving similar
triangles, or using the
Pythagorean Theorem
to obtain a quadratic
equation for a length in
a geometric figure.
A.8.2.1.5 Understand
that a geometric
sequence is a nonlinear function that can
be expressed in the
form f (x)abx , where
x = 0, 1, 2, 3,….
form
absolute value,
piecewise, square
root, or rational.)
-geometric (All of the
conic sections:
circles, parabolas,
hyperbolas and
ellipses.)
-trigonometric (A
function that can be
modeled with the six
trigonometric
functions.)
-exponential (A
representation of a
problem that can be
expressed as . This
also includes
logarithmic models, .)
•once I determine (or
am given) the type of
relationship, I can
write the equation.
9-12.A.4.4.A.
•I can convert from
exponential form to
logarithmic form and
vice-verse.
•I can use the
product rule,
quotient rule and
power rule to
simplify logarithmic
expressions.
•I can solve
In what ways do
relations, functions,
graphs of functions
and their inverses
help us interpret
real-world events or
solve problems?
Multiplying and
dividing rational
expressions
Adding and subtracting
rational expressions
Graphing rational
functions
Direct, joint and
inverse variation
Classes of functions
Solving rational
equations
9-12.A.1.1.A.
Equivalent forms:
Having the same
value when
evaluated.
Rational algebraic
expressions: A ratio
of two or more
algebraic
expressions. It is not
an equation.
Properties of real
numbers: A set of
mathematical rules
or laws that results in
an equivalent
expression.
9-12.G.2.3.
Proportion: An
equation that states
that two ratios are
equivalent.
9-12.A.1.1.A.
(Application)
Students are able to
write equivalent
forms of rational
algebraic expressions
using properties of
real numbers.
9-12.G.2.3.
(Application)
Students are able to
use proportions to
solve problems.
logarithmic,
exponential and
trigonometric
equations.
•I can simplify
trigonometric and
exponential
expressions.
•I can verify
trigonometric
identities.
9-12.A.1.1.A.
•I can apply (use) the
laws of exponents to
simplify algebraic
expressions.
•I can apply (use) the
order of operations
to simplify algebraic
expressions.
•I can add, subtract,
multiply and divide
rational expressions
(A ratio of two or
more algebraic
expressions. It is not
an equation).
•I can determine
which polynomials
are factorable over
the set of integers.
9-12.G.2.3.
•I can write and solve
a proportion (An
equation that states
A.9.2.3.1 Evaluate
polynomial and rational
expressions and
expressions containing
radicals and absolute
values at specified
points in their domains.
G/M.9.3.3.6 Know and
apply properties of
congruent and similar
figures to solve
problems and logically
justify results.
A.9.2.3.Generate
equivalent algebraic
expressions involving
polynomials and
radicals; use algebraic
properties to evaluate
expressions.
G/M.9.3.3Know and
apply properties of
geometric figures to
solve real-world and
mathematical
problems and to
logically justify results
in geometry.
* Rubrics
* Achievement Series
formative
assessments
* Student selfassessment – written
reflection
*Teacher-made
assessments
formative and
summative
assessments
* Textbook formative
and summative
assessments
* Performance – pre
and post test
* South Dakota State
Test of Educational
Progress (Dakota
STEP)/Minnesota
Comprehensive
Assessments (MCAs)
that two ratios are
equivalent.)
•I can apply (use) a
proportion (An
equation that states
that two ratios are
equivalent) to solve
application problems.
•I can find the
missing length of a
side and/or
perimeter of similar
polygons.