Download Algebra_II_with_Trig_Common_Core_Pacing_Calendar

Curriculum Pacing Guide Grades 9-12
Subject:__Algebra II_with Trigonometry_____________
Time
10
Days
CCR
S
Stran
d
CCR
S
Clust
er
CCRS
ID
Lesson
Pre-requisite Skills & Rules and
Procedures
Identify Properties of numbers
and use them and the correct
order of operations to simplify
expressions
Factor trinomials in the form
ax2+bx+c
Solve single-step and multistep
equations and inequalities
Solve systems of linear
equations using various
methods, including elimination,
substitution, and graphing
Write linear equations in
standard form and slopeintercept form when given two
points, a point and the slope, or
the graph of the equation
Graph a linear equation using a
table of values, x-and yintercepts, or slope-intercept
form
Find the distance and midpoint
between two points in the
coordinate plane
Use inductive reasoning to
make conjectures and
deductive reasoning to arrive at
valid conclusions
Unit 1 Introduction to Algebra II:
The Purposes and Predictability
of Patterns
Effective Year:____2016-2017______________________
Knowledge
(Nouns)
Skills
(Verbs)
Academic Vocabulary
10
Days
A-SSE4
Find the nth term of an
arithmetic or geometric
sequence

Algebra
Seeing Structure in Exressions

A-SSE4
Find the position of a given term
of an arithmetic or geometric
sequence
A-SSE4
Find sums of a finite arithmetic
or geometric series
A-SSE4
Use sequences and series to
solve real-world problems
A-SSE4
Use sigma notation to express
sums
Students know:
Characteristics of a

geometric series,
Techniques for
performing algebraic
manipulations and

justifications for the
equivalence of the
resulting expressions
(including Tables 3, 4, 
and 5).
Students are able to:

Identify the regularity that 
exists in a series as being 
that which defines it as a
geometric series.
Accurately perform the
procedures involved in
using geometric series to
solve contextual problems,
Explain with mathematical
reasoning why each step in
the derivation of the
formula for the sum of a
finite geometric series is
legitimate, including
explaining why the formula
does not hold for a
common ratio of 1.
Geometric series
Finite
Common Ratios
A601
Manipulate expressions and
equations
Assessment
Create equations
A-CED1
Algebra
7
Days
A-CED1
A-CED2
Unit 2 Linear Equations &
Inequalities: The Poetry &
Prose of Algebra
27. Solve linear inequalities
containing absolute value

27. Solve compound
inequalities containing “and”
and “or” and graph the solution
set
21. Solve algebraically a system
containing three variables





Student know:
When the situation

presented in a
contextual problem is
most accurately
modeled by a linear,
quadratic, exponential,
or rational functional
relationship.
Students are able to:
Write equations or
inequalities in one
variable that accurately
model contextual
situations.
Students know:
When a particular two 
variable equation
accurately models the
situation presented in a
contextual problem.

Students are able to:

Write equations in two
variables that accurately
model contextual
situations,
Graph equations involving
two variables on coordinate
axes with appropriate
scales and labels.
Linear functions
Quadratic functions
Rational functions
Exponential functions
Simple root functions
A-CED2
A-CED3
21., 22 Graph a system of linear
inequalities in two variables with

and without technology to find
the solution set to the system
Create Equations
Algebra

A-CED1
A-CED2
A-CED3
Solve linear programming
problems by finding maximum
and minimum values of a
function over a region defined
by linear inequalities
A-CED4
Rearrange formulas to highlight
a quantity of interest, using the
same reasoning as in solving
equations
A601
Manipulate expressions and
equations
AF603
Interpret and use information
from graphs in the coordinate
plane
Students know:
When a particular

system of two variable
equations or inequalities
accurately models the
situation presented in a
contextual problem,
Which points in the
solution of a system of 
linear inequalities need
to be tested to maximize
or minimize the variable
of interest.

Students are able to:

Graph equations and

inequalities involving two

variables on coordinate
axes,
Identify the region that
satisfies both inequalities
in a system,
Identify the point(s) that
maximizes or minimizes
the variable of interest in
a system of inequalities,
Test a mathematical
model using equations,
inequalities, or a system
against the constraints in
the context and interpret
the solution in this
context.
Constraint
Viable
Nonviable
Students know:
Properties of equality and
inequality
Students are able to:

Accurately rearrange

equations or inequalities to

produce equivalent forms
for use in resolving
situations of interest.
Ohm's law
Literal equation
Simple Root Function
Solve routing one-step
arithmetic problems using
positive rational numbers, such
as single-percent
DEV602
Show effective movement
between general and specific
ideas and examples
ORI601
Provide a unified coherent
organizational structure that
presents a logical progression
of ideas
REL601
Order simple sequences of
events in somewhat challenging
literary narratives
REL403
Identify clear cause-effect
relationships in somewhat
challenging passages
N-VM7
N-VM8
N-VM9
Vector and Matrix
Quantities
Number and Quantity
7
Days
AF301
Unit 3 What is a Matrix-Really?
Add, subtract, and multiply
matrices


Students know:
The aspects of a matrix 
with regard to entries,
rows, columns,
dimensions, elements,
and subscript notations.
Students are able to:
Write percents as decimals.
Increase or decrease an
amount by multiplying by a
percent (i.e., increase of
10% would multiply by 1.1)
The aspects of a matrix 
with regard to entries,
rows, columns,
dimensions, elements,
and subscript notations.
Strategically choose and
apply appropriate
representations of matrices
on which arithmetic
operations can be
performed.
Scalars
Appropriate Dimensions
N-VM7
N-VM9
Use addition, subtraction, and
multiplication of matrices to 
solve real-world problems
Vector and Matrix Quantities
Number and Quantity


N-VM10
Calculate the determinant of 2 ×
2 and 3 × 3 matrices



N-VM10
Find the inverse of a 2 × 2
matrix
N-VM10
Solve systems of equations by
using inverses of matrices and
determinants
N-VM6
N-VM7
N-VM8
N-VM9
Use technology to perform
operations on matrices, find 
determinants, and find inverses
Assessment
Unit 4 Functions, Relations, &
Conics
Students know:
Commutative and

associative properties of
multiplication.
Distributive property.
The aspects of a square
matrix.
Students know:
The additive and

multiplicative identity
properties for real

numbers.
The aspects of the zero 
and identity matrices.
A matrix multiplied by its
multiplicative inverse
equals the identity matrix.
Students are able to:
Add, subtract, and multiply
matrices.
Students know:
The aspects of a matrix 
with regard to entries,
rows, columns,
dimensions, elements,
and subscript notations.
Students are able to:
Translate data into a
matrix.
Students are able to:

Find the determinant of a 
square matrix.

Find the multiplicative

inverse of a square matrix.
Add and multiply matrices.



Matrix Multiplication
Square Matrix
Commutative Property
Associative Property
Distributive Property
Zero Matrix
Identity Matrix
Determinant
Multiplicative Inverse
Matrix/Matrices
Incidence Relationship
Payoffs
9
Days
F-BF1
F-BF1a
Perform operations on
functions, including function 
composition, and determine
domain and range for each of
the given functions
Building Functions
Functions

F-BF4
Find inverse functions



Students know:
Techniques to find key 
features of functions when
presented in different
ways,
Techniques to convert a 
function to a different form
(algebraically, graphically,
numerically in tables, or 
by verbal descriptions).
Students know:
Graphing techniques of 
functions,

Methods of using
technology to graph
functions,
Techniques to identify
even and odd functions
both algebraically and 
from a graph.
Creating
Equations
Algebra
Functions

A-CED1
A-CED2
F-IF5
Determine the domain and
range of a quadratic function;
graph the function with and
without technology
Students are able to:
Accurately determine which
key features are most
appropriate for comparing
functions,
Manipulate functions
algebraically to reveal key
functions,
Convert a function to a
different form
(algebraically, graphically,
numerically in tables, or by
verbal descriptions) for the
purpose of comparing it to
another function.
Students are able to:
Accurately graph functions,
Check conjectures about
how a parameter change in
a function changes the
graph and critique the
reasoning of others about
such shifts,
Identify shifts, stretches, or
reflections between graphs,
Determine when a function
is even or odd.
Linear function
Exponential function
Quadratic function
Absolute value function
Step function
Piecewise-define function
Even and odd functions
Composite functions
Horizontal and vertical
shifts
Horizontal and vertical
stretch
Reflections
Translations
F-IF5
F-BF3
Use transformations (e.g.,
translation, reflection) to draw 
the graph of a relation and
determine a relation that fits a 
graph




Interpreting Functions
Functions
F-IF7
Graph functions expressed
symbolically and show key

features of the graph by hand in

simple case and using
technology in more complicated
cases.
Students know:
Techniques for graphing
functions,
Techniques for
determining the domain of
a function from its context.
Graphing techniques of
functions,
Methods of using
technology to graph
functions,
Techniques to identify
even and odd functions
both algebraically and
from a graph.
Students are able to:
Interpret the domain from
the context,
Produce a graph of a
function based on the
context given.
Even and odd functions
Function
Domain
Accurately graph functions,
Students know:
Techniques for graphing,
Key features of graphs of
functions.


Check conjectures about
how a parameter change in
a function changes the
graph and critique the
reasoning of others about
such shifts,
Identify shifts, stretches, or
reflections between graphs,
Determine when a function
is even or odd.
Students are able to:

Identify the type of function
from the symbolic

representation,

Manipulate expressions to
reveal important features 
for identification in the

function,

Accurately graph any

relationship.


F-IF8
Write a function defined by an
expression in different but

equivalent forms to reveal and
explain different properties of

the function

Students know:
Techniques to factor and
complete the square,
Properties of exponential
expressions,
Algebraic properties of
equality
Students are able to:
Accurately manipulate
(e.g., factoring, completing
the square) expressions
using appropriate
technique(s) to reveal key
properties of a function.
Piece-wise function
Square root function
Cube root function
Step function
Absolute function
Logarithmic function
Trigonometric function
Period
Midline
Amplitude
Exponential Functions
Zeros
Extreme values
Symmetry
Exponential growth or decay
Interpreting Functions
Functions
F-IF9
Compare properties of two
functions each represented in a
different way.

AL#28
Identify conic sections (e.g.,
parabola, circle, ellipse,

hyperbola) from their equations
in standard form


Conic Sections
Functions

Students know:
Techniques to find key 
features of functions when
presented in different
ways,
Techniques to convert a 
function to a different form
(algebraically, graphically,
numerically in tables, or 
by verbal descriptions).
Students know:
Vertex form of a parabola.

Standard form of a circle.
Vertex and axis of
symmetry of a parabola. 
Completing the square.
Factoring a quadratic

function.



AL#28
Graph circles and parabolas
and their translations from given
equations or characteristics with
and without technology
Students are able to:

Accurately determine which

key features are most
appropriate for comparing
functions,
Manipulate functions
algebraically to reveal key
functions,
Convert a function to a
different form
(algebraically, graphically,
numerically in tables, or by
verbal descriptions) for the
purpose of comparing it to
another function.
Students are able to:

Create graphs of parabolas

from second degree

equations.

Create graphs of

hyperbolas from second 
degree equations.

Create graphs of ellipses 
from second degree

equations.

Create graphs of circles

from second degree
equations.
Create graphs of
degenerate conics from
second degree equations.
Formulate equations of
conic sections given a set
of determining
characteristics.
Quadratic function
Algebraic expression
Hyperbola
Ellipse
Degenerate conic
Focus (foci)
Latus rectum (focal distance)
Major axis (transverse axis)
Minor axis (conjugate axis)
Eccentricity
Asymptote
Directrix
Locus
AL#28
AL#28
Determine characteristics of
circles and parabolas from their
equations and graphs
Identify and write equations for
circles and parabolas from
given characteristics and
graphs
F201
Solve problems in one or two
steps using whole numbers and
decimals in the form of money
F504
Attend to the difference
between a function modeling a
situation and the reality of the
situation
Understand the concept of a
function as having a welldefined output value at each
valid input value
Understand the concept of
domain and range in terms of
valid input and output and in
terms of function graphs
Find the domain of polynomial
functions and rational functions
Find the range of polynomial
functions
F505
F506
F508
F509
F604
DEV601
DEV602
REL603
AF301
Evaluate composite functions at
integer values
Provide ample development in
support of ideas; Substantiate
ideas with precise use of
specific, logical reasons and
illustrative examples
Provide ample development in
support of ideas; substantiate
ideas with precise use of
specific, logical reason and
illustrative examples
Identify clear comparative
relationships in complex
passages
Solve routine one-step
CCRS
Strand
Number and Quantity
8
Days
The Complex Number
System
Time
arithmetic problems using
positive rational numbers, such
as a single –step percent
AF302
Solve one-step equations to get
integer or decimal answers
A701
Solve simple absolute value
inequalities
SYN201
Make simple comparisons
between two passages
TST301
Analyze how one or more
sentences in somewhat
challenging passages relate to
the whole passage when the
function is simple
TST401
Analyze how one or more
sentences in somewhat more
challenging passages relate to
the whole passage
Assessment
CCRS
CCRS
CCRS Standard
Cluster
ID
Unit 5 Quadratic Equations,
Inequalities, & Functions
N-CN1
Identify complex numbers
N-CN3
and write their conjugates 

N-CN2
Add, subtract, and multiply
complex numbers


Knowledge
(Nouns)
Skills
(Verbs)
Students know:
Which manipulations of radicals

produce equivalent forms, for
example,<i√8 +="" √18="" ≠=""
√26="" but="" 2√2=""
3√2="5√2,</i√8>
That the extension of the real
numbers which allows
equations such as x2 = -1 to
have solutions is known as the
complex numbers and the
defining feature of the complex
numbers is a number i, such
that i2 = -1.
Students know:
Combinations of operations on
complex number that produce
equivalent expressions,
Properties of operations and
Students are able to: 
Perform manipulations
of radicals, including
those involving square
roots of negative
numbers, to produce a
variety of forms, for
example,√(-8) = i√(8) =
2i√(2).
Students are able to:
Perform arithmetic
manipulations on
complex numbers to
produce equivalent
Academic Vocabulary





Complex number
Complex number
Relation
Commutative property
Associative property
Distributive property
Simplify quotients of
complex numbers



equality that verify this
equivalence.
Students know:
The definition of the conjugate
of a complex number.
A complex number divided by
itself equals 1.
The product of a complex
number and its conjugate is a
real number (the square of the
modulus).
expressions.
Students are able to: 
Find the product of two

complex numbers. 
Conjugate
Complex number
Modulus/Moduli
Arithmetic with Polynomials and Rational Expressions
Creating Equations
Reasoning with Equations and Inequalities
Algebra
A-APR3
A-CED1
A.REI.4

The
Complex
Number
System
Students know:
When a factorization of a
polynomial reveals a root of that
polynomial,
When a rearrangement of the
terms of a polynomial
expression can reveal a
recognizable factorable form of
the polynomial,
Relationships of roots to points
on the graph of the polynomial.
When the situation presented in
a contextual problem is most
accurately modeled by a linear,
quadratic, exponential, or
rational functional relationship.





N-CN9
Number
and
Quantity
Solve quadratic equations
and inequalities using

various techniques,
including completing the
square and using the

quadratic formula
Use the discriminant to
determine the number and 
type of roots for a given
quadratic equation

Any real number has two
square roots, that is, if a is the
square root of a real number 
then so is -a,
The method for completing the
square,
Notational methods for
expressing complex numbers,
A quadratic equation in
standard form (ax2+bx+c=0)
has real roots when b2-4ac is 
greater than or equal to zero
and complex roots when b2-4ac
is less than zero.
Students know:

The definition of the degree of a
polynomial.

The difference between real
and complex roots.
Students are able to:
Use techniques for
factoring polynomials.

Write equations or 
inequalities in one

variable that accurately

model contextual
situations.


Accurately use

properties of equality 
and other algebraic 
manipulations

including taking square

roots of both sides of
an equation,
Accurately complete
the square on a
quadratic polynomial
Factor quadratic
polynomials
Rewrite solutions to
quadratic equations in
useful forms
including a ± bi and
simplified radical
expressions,
Make strategic choices
about which
procedures to use to
reach a solution to a
quadratic equation.
Find roots of a

quadratic polynomial.

Zeros of polynomials
Factorization
Linear functions
Quadratic functions
Rational functions
Exponential functions
Completing the square
Quadratic equations
Quadratic formula
Inspection
Imaginary numbers
Binomials
Trinomials
Fundamental Theorem of
Algebra
Quadratic Polynomial
N-CN7
Solve quadratic equations
with complex number

solutions
Students know:
strategies for solving quadratic
equations
Creating
Equations
Algebra

A-CED1
A-CED2
Solve quadratic systems
graphically and algebraically

with and without technology
Student know:
When the situation presented in

a contextual problem is most
accurately modeled by a linear,
quadratic, exponential, or
rational functional relationship.
Students are able to: 
apply the quadratic 
equation

provide solutions in 
complex form
Students are able to:
Write equations or
inequalities in one
variable that accurately
model contextual
situations.
Complex solution
Complex solution
Quadratic equation
Real coefficients
Students are able to:
Communicate the
connection between
the rules for arithmetic
on integers and the
corresponding rules for
arithmetic on
polynomials,
Accurately perform
combinations of
operations on various
polynomials.
Students are able to:
Accurately perform
procedures for dividing
a polynomial p(x) by a
linear polynomial (x a),
Evaluate a polynomial
p(x) for any value of x.
Polynomials
Closure
Analogous
Linear functions
Quadratic functions
Rational functions
Exponential functions
Assessment
Unit 6 Polynomials
Arithmetic with
Polynomials and
Rational Expressions
A-APR1
Algebra
8
Days
Multiply monomials and
binomials


A-APR2
Evaluate and simplify
polynomial expressions and

equations
Students know:
Corresponding rules of

arithmetic of integers,
specifically what it means for
the integers to be closed under
addition, subtraction, and
multiplication, and not under
division,
Procedures for performing

addition, subtraction, and
multiplication on polynomials.
Students know:
Procedures for dividing a

polynomial p(x) by a linear
polynomial (x - a), (e.g., long
division and synthetic division).

If and only if
Remainder theorem
Seeing Structure in
Expression
Arithmetic with
Polynomials and Rational
Expressions
Algebra
Factor polynomials using a
variety of methods (e.g., 
factor theorem, synthetic
division, long division, sums

and differences of cubes,
grouping)
Students know:
Techniques for long division of
polynomials,
Techniques for utilizing a
computer algebra system.

A-APR3
Determine the number and
type of rational zeros for a 
polynomial function
Students know:
When a factorization of a

polynomial reveals a root of that
polynomial,
When a rearrangement of the
terms of a polynomial
expression can reveal a
recognizable factorable form of
the polynomial,
Relationships of roots to points
on the graph of the polynomial.


A-APR3
Find all rational zeros of a
polynomial function
N-CN9
Recognize the connection
among zeros of a

polynomial function, xintercepts, factors of

polynomials, and solutions
of polynomial equations
The
Complex
Number
System
Number and
Quantity
Algebra
Algebra
A-SSE2
A-APR3
A-APR6
Students know:
The definition of the degree of a
polynomial.
The difference between real 
and complex roots.
Students are able to:
Accurately perform
polynomial long
division,
Efficiently and
accurately use a
computer algebra
system to divide
polynomials.
Students are able to:
Use techniques for
factoring polynomials
Rational expression
Degree of polynomial
Inspection
Students are able to: 
Find roots of a
quadratic polynomial. 
Rewrite an imaginary
number as a complex
number.
Fundamental Theorem of
Algebra
Quadratic Polynomial
Zeros of polynomials
Factorization
A-APR3
F-IF7
Use technology to graph a
polynomial function and 
approximate the zeros,

minimum, and maximum;
determine domain and
range of the polynomial
function
Students know:
Techniques for graphing,
Key features of graphs of
functions.



Assessment
Unit 7 Rational & Radical
Expressions and Equations
Students are able to:
Identify the type of
function from the
symbolic
representation,
Manipulate
expressions to reveal
important features for
identification in the
function,
Accurately graph any
relationship.
Piece-wise function
Square root function
Cube root function
Step function
Absolute function
Logarithmic function
Trigonometric function
Period
Midline
Amplitude
Exponential Functions
Interpret the structure of Expression
Creating Equations
Algebra
ays
A-SSE1
A-CED1
Seeing
Structure in
Equations
Students know:
Interpretations of parts of

algebraic expressions such as
terms, factors, and coefficients.


A-SSE2
Algebra
Solve mathematical and
real-world rational equation
problems (e.g., work or rate
problems)
Use the structure of an
expression to identify ways
to rewrite it

Students know:
Algebraic properties (including
those in Tables 3, 4, and 5),
When one form of an algebraic
expression is more useful than
an equivalent form of that same
expression.
Students are able to: 
Produce mathematical
expressions that model

given contexts,
Provide a context that
a given mathematical
expression accurately
fits,
Explain the reasoning
for selecting a
particular algebraic
expression by
connecting the
quantities in the
expression to the
physical situation that
produced them, (e.g.,
the formula for the
area of a trapezoid can
be explained as the
average of the two
bases multiplied by
height).
(a + b)/ ) h
2
Students are able to:
Use algebraic
properties to produce
equivalent forms of the
same expression by
recognizing underlying
mathematical
structures.
Terms
Factors
Coefficients
Differences of Squares
Factoring
Reasoning with Equations
and Inequalities
Reasoning with Equations
and Inequalities
Algebra
Algebra
A-REI2
Simplify radicals that have
various indices


Students know:
Algebraic rules for manipulating

rational and radical equations,
Conditions under which a
solution is considered
extraneous.

A-REI2
Use properties of roots and
rational exponents to
evaluate and simplify
expressions
A-REI2
Add, subtract, multiply, and
divide expressions
containing radicals
A-REI2
Rationalize denominators
containing radicals and find
the simplest common
denominator
Evaluate expressions and
solve equations containing
nth roots or rational
exponents
Evaluate and solve radical
equations given a formula
for a real-world situation
Assessment
A-REI2
A-REI2
Unit 8 Exponential &
Logarithmic Functions
Students are able to:
Accurately rearrange
rational and radical
equations to produce a
set of values to test
against the conditions
of the original situation
and equation, and
determine whether or
not the value is a
solution,
Explain with
mathematical and
reasoning from the
context (when
appropriate) why a
particular solution is or
is not extraneous.
Rational equations
Radical equations
Extraneous solutions
Interpreting
Functions
F-IF7
Students know:
Techniques for graphing,
Key features of graphs of
functions.


F-LE4
For exponential models,
express as a logarithm the 
solution to a bct=d where a,
c, and d are numbers and
the base b is 2, 10, or e;

evaluate the logarithm using
technology
F-LE4a
Convert exponential
equations to logarithmic
form and logarithmic
equations to exponential
form
Provide a unified, coherent
organizational structure that
presents a logical
progression of ideas
Assessment
ORI6601
7
Days
Graph exponential and
logarithmic functions with 
and without technology


Linear, Quadratic,
and Exponential
Models
Functions
7
Days
Unit 9 Trigonometry
Use the law of cosines and
the law of sines to find the
lengths of sides and
measures of angles of
triangles in mathematical
and real-world problems
Students know:
Methods for using exponential 
and logarithmic properties to
solve equations,
Techniques for rewriting
algebraic expressions using 
properties of equality (Table 4).
Students are able to:
Identify the type of
function from the
symbolic
representation,
Manipulate
expressions to reveal
important features for
identification in the
function,
Accurately graph any
relationship.
Students are able to:
Accurately use
logarithmic properties
to rewrite and solve an
exponential equation,
Use technology to
approximate a
logarithm.
Piece-wise function
Square root function
Cube root function
Step function
Absolute function
Logarithmic function
Trigonometric function
Period
Midline
Amplitude
Exponential Functions
Exponential models
Logarithmic base
Functions
F.TF2
Trig Functions
F.TF1
AL
F.TF5
Use the unit-circle definition
of the trigonometric
functions and trigonometric
relationships to find
trigonometric values for
general angles
Measure angles in standard
position using degree or 
radian measure and convert
a measure from one unit to
the other
Graph the sine and cosine
functions with and without
technology
Determine the domain and
range of the sine and cosine
functions, given a graph
Find the period and
amplitude of the sine and
cosine functions, given a
graph
Use sine, cosine, and
tangent functions, including
their domains and ranges,
periodic nature, and graphs,
to interpret and analyze
relations
Students know:
The circumference of any circle
is 2πr and therefore, the
circumference of a unit circle is
2π.
Students are able to:
Translate between arc
length and central
angle measures in
circles.
Radian measure
Subtended
Unit circle
Unit Circle
Quadrant
Students know:
Key features of trigonometric
functions (e.g., amplitude,
frequency, and midline),
Techniques for selecting
functions to model periodic
phenomena.
Students are able to:
Determine the
amplitude, frequency,
and midline of a
trigonometric function,
Develop a
trigonometric function
to model periodic
phenomena.
Trigonometric functions
Periodic phenomena
Amplitude
Frequency
Midline
Standard position
Students know:
Methods for describing events 
from a sample space using set
language (subset, union,
intersection, complement).

Students are able to:
Interpret the given
information in the
problem,
Accurately determine
the probability of the
scenario.
Subsets
Sample space
Unions
Intersections
Complements
6
Days
Statistics and
Probability
Assessment
Unit 10 Probability & Data
Analysis
S-MD6
S-MD7
S-CP1
Use the fundamental
counting principle to count 
the number of ways an
event can happen
Use Probability to evaluate outcomes of a decision
Understand Independence and conditional probability and
use them to interpret data.
S-MD6
S-MD7
S-CP1
Use counting techniques,
like combinations and

permutations, to solve
problems (e.g., to calculate
probabilities)

Students know:
The characteristics of a random

sample.
Techniques for finding
probabilities of simple,
compound, and conditional
events and from probability
distributions.



S-MD6
S-MD7
S-CP1
Find the probability of
mutually exclusive and nonmutually exclusive events
Students are able to:
Randomly select a
sample from a
population (using
technology when
appropriate).
Choose the
appropriate probability
concept for the given
situation.
Use and apply the
selected probability
rule.
Communicate the
reasoning behind
decisions.
Fair decisions
Random number
generator
Probability
S-MD6
S-MD7
S-CP4
S-CP5
S-CP7
S-CP9
S-CP8
Find the probability of
independent and dependent
events



Students know:
Techniques to construct twoway frequency tables,
Techniques to find simple and
conditional probability in twoway frequency tables.
Possible relationships and
differences between the simple
probability of an event and the
probability of an event under a
condition.
Techniques for finding
probabilities of simple,
compound, and conditional
events.
Order is the determining factor
in whether a event requires a
permutation or a combination to
count the number of possible
outcomes of the event.
Techniques for finding the
number of permutations or

combinations of an event.




Students are able to:
Accurately construct a
two-way frequency
table,
Accurately find simple
and conditional
probability from a twoway frequency table.
Communicate the
concepts of conditional
probability and
independence using
everyday language by
discussing the impact
of the occurrence of
one event on the
likelihood of the other
occurring.
Accurately determine
the probability of
simple and compound
events.
Determine the
probability of a single
and conditional event.
Evaluate factorial
expressions.
Apply the multiplication
and addition rules to
determine probabilities.
Interpret and apply the
different notations for
combinations and
permutations.
Perform procedures to
evaluate expressions
involving the number of
combinations and
permutations of n
things taken r at a
time.
Two way frequency tables
Sample space
Independent
Conditional probabilities
Probability
Random sample
Categorical data
Quantitative data
Independence
Probability
Addition Rule
Uniform probability model
General Multiplication
Rule
Simple events
Conditional events
Permutations
Combinations
Compound events
Possible outcomes
Understand independence
and conditional probability
and use them to interpret
data.
S-MD6
S-MD7
S-CP1
Use unions, intersections,
and complements to find
probabilities
S-MD6
S-MD7
S-CP3
S-CP4
S-CP5
S-CP6
Solve problems involving
conditional probability


Students know:
Methods to find probability of 
simple and compound events,
Techniques to find conditional
probability.

Students are able to:
Accurately determine
the probability of
simple and compound
events,
Accurately determine
the conditional
probability P(A given
B)from a sample space
or from the knowledge
of P(A∩B) and the
P(B).
Conditional probability
Independence
Probability
Sample space
Simple event
Compound event
Assessment
Final Exams
Resources:
Alabama Course of Study for Mathematics
Alabama Insight Tool which provides Evidence of Student Attainment, Vocabulary, ALEX resources, and AMSTI
Resources
Glencoe Algebra II Resource Kit
Dinah Zike’s Big Book of Math
Teacherspayteachers.com
Math-aids.com
Algebra Out Loud
Illuminations.nctm.org