KCAIT Algebra II
Map
Unit
# of Days- Approximate Dates
MDC Lessons Included
Unit 1: Equations,
Inequalities,
Functions
Unit 2 - Quadratic
Functions
34 Days – August 13 – September 23
 Interpreting Algebraic
Expressions
38 Days – September 24 – November
21
 Forming Quadratics
Unit 3 - Polynomials
26 Days – November 24 – January 16
 Representing Polynomials
Unit- 4 Series,
Exponential and
Logarithmic Functions
Unit – 5 Radical and
Rational Functions
32 Days – January 20 – March 6
 Comparing Investments
30 Days – March 9 – April 28
 Functions and Everyday
Situations
Course __Algebra II___________
Unit 1: Equations, Inequalities, Functions
Number of Days - ______34________
Progression of Concepts and Skills Developed in this Unit
In this unit, students model real-world situations by using one- and two-variable equations. They study inverse
functions, composite functions, and piecewise-defined functions, perform operations on functions, and solve systems of
equations and inequalities.
Academic Vocabulary/Math Terms
Absolute value equation
Absolute value inequality
Constraints
Consistent
Inconsistent
Independent
Dependent
Ordered triple
Gaussian elimination
Matrix
Dimensions of a matrix
Square matrix
Multiplicative identity matrix
Multiplicative inverse matrix
Matrix equation
Coefficient matrix
Variable matrix
Constant matrix
Piecewise-defined function
Step function
Parent function
Composition
Composite function
Inverse function
MDC Lesson(s) for the Unit
Lesson: Interpreting Algebraic Expressions
Skills/Reasoning addressed in the Lesson
Distributive property
Rules of exponents
Algebraic manipulation
Skills Assessed in the Getting Ready
In which lesson is the skill first utilized
Evaluating functions
Finding slope and intercepts
Graphing linear equations
Writing linear equations
Finding additive and multiplicative inverses
Solving linear and literal equations
Understanding absolute value
Finding domain and range
Identifying lines of symmetry
4-1
1-2
1-2
1-2
1-1
1-1
1-3
4-1
4-2
Embedded Assessment 1: ___Gaming Systems (1 day) – allow for extended time________________________________
What students need to be able to do
Write a linear equation
Graph a linear equation
Solve a linear equation
Write a linear inequality
Graph a linear inequality
Solve a linear inequality
Find a feasible region
Write and solve absolute value equations
Write a system of three equations
Solve a system of three equations
Activity 1: Creating Equations—One to Two
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
1-1: One-Variable Create an equation in one variable from a
Equations
real-world context.

1-2: Two-Variable
Equations

1-3: Absolute

Value Equations
and Inequalities

Solve an equation in one variable.
Create equations in two variables to
represent relationships between
quantities.
Vocabulary students need to understand
Absolute value equation
Absolute value inequality
Constraints
Consistent
Inconsistent
Independent
Dependent
Ordered triple
Pacing
Notes
3 days (MDC –
2 days; 1.1 – 1
day)
MDC: Interpreting Algebraic
Expressions before this lesson;
Complete all. No omissions.
Supplements: Homework/PreAssessment
2 days
Complete all. No omissions.
2 days
Complete all. No omissions.
Homework, pages 15-16
Pacing
Notes
1 day
Complete all. No omissions.
Graph two-variable equations.
Write, solve, and graph absolute value
equations.
Solve and graph absolute value
inequalities.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity 2: Graphing to Find Solutions—Choices
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
2-1: Graphing
 Write equations in two variables
Two-Variable
to represent relationships
Equations
between quantities.

Graph equations on coordinate
axes with labels and scales.
2-2: Graphing
Systems of
Inequalities

Represent constraints by
equations or inequalities.

Use a graph to determine
solutions of a system of
inequalities.
3 days
Complete all. No omissions. 2-2 – 2
days; one extra graphing day with
ACT practice
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity 3: Systems of Linear Equations—Monetary Systems Overload
Lesson
How does the lesson contribute to the EA Pacing
or End of Unit Assessment?
3-1: Solving
3 days
 Use graphing, substitution, and
Systems of Two
elimination to solve systems of
Equations in Two
linear equations in two variables.
Variables
 Formulate systems of linear
equations in two variables to
model real-world situations.
3-2: Solving
Systems of Three
Equations in Three
Variables
3-3: Matrix
Operations
3-4: Solving Matrix
Equations

Solve systems of three linear
equations in three variables using
substitution and Gaussian
elimination.

Formulate systems of three linear
equations in three variables to
model a real-world situation.

Add, subtract, and multiply
matrices.

Use a graphing calculator to
perform operations on matrices.

Solve systems of two linear
equations in two variables by
using graphing calculators with
matrices.

Solve systems of three linear
equations in three variables by
using graphing calculators with
matrices.
EA 1
Connections to ACT: (Critical Content/Problem sets from wiki)
Notes
Complete all. No omissions.
2 days
Complete all. No omissions.
Complete this lesson after
completion of 3-3
1 day
Complete all. No omissions.
Complete this lesson before
completion of 3-2
Skip
Accelerated only
1
Embedded Assessment 2: ___Currency Conversion_(1 day)_________________________________________
What students need to be able to do
 Piecewise-defined functions
 Composition of functions
 Inverse functions
Activity 4: Piecewise-Defined Functions—Absolutely Piece-ful
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
4-1: Introduction
 Graph piecewise-defined
to Piecewisefunctions.
Defined Functions
 Write the domain and range of
functions using interval notation,
inequalities, and set notation.
4-2: Step
Functions and
Absolute Value
Functions

Graph step functions and absolute
value functions.

Describe the attributes of these
functions.
4-3: Transforming
the Absolute
Value Parent
Function

Identify the effect on the graph of
replacing f(x) by f(x)
+ k, k · f(x), f(kx), andf(x + k).

Find the value of k, given these
graphs.
Vocabulary students need to understand



Composition
Composite function
Inverse function
Pacing
Notes
2 days
Complete all. No omissions.
2 days
Complete all. No omissions.
2 days
Complete all. No omissions.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity 5: Function Composition and Operations—New from Old
Lesson
How does the lesson contribute to the EA Pacing
or End of Unit Assessment?
Notes
5-1: Operations
with Functions
5-2: Function
Composition
5-3: More
Function
Composition

Combine functions using
arithmetic operations.

Build functions that model realworld scenarios.

Write functions that describe the
relationship between two
quantities.

Explore the composition of two
functions through a real-world
scenario.

Write the composition of two
functions.

Evaluate the composition of two
functions.
1 day
Complete all. No omissions.
2 days
Complete all. No omissions.
2 days
Complete all. No omissions.
Pacing
Notes
1 day
Complete all. No omissions.

1 day
Use composition of functions to
determine if functions are inverses
of each other.
Complete all. No omissions.

Graph inverse functions and
identify the symmetry.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity 6: Inverse Functions—Old from New
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
6-1: Finding
 Find the inverse of a function.
Inverse Functions
 Write the inverse using the proper
notation.
6-2: Graphs of
Inverse Functions
EA 2
1 day
Connections to ACT: (Critical Content/Problem sets from wiki)
Unit Review and
Assessment
2 days
Course - Algebra II
Unit 2 - Quadratic Functions
Number of Days - __________35_____________
Progression of Concepts and Skills Developed in this Unit
This unit focuses on quadratic functions and equations. You will write the equations of quadratic functions to model
situations. You will also graph quadratic functions and other parabolas and interpret key features of the graphs. In
addition, you will study methods of finding solutions of quadratic equations and interpreting the meaning of the solutions.
You will also extend your knowledge of number systems to the complex numbers.
Academic Vocabulary/Math Terms
 Justify
 Derive
 Verify
 Advantage
 Disadvantage
 Counterexample
 Quadratic equation
 Standard form of a quadratic equation
 Imaginary number
 Complex number
 Complex conjugate
 Completing the square
 Discriminant
 Root
 Zero
 Parabola
 Focus
 Directrix
 Axis of symmetry
 Vertex
 Quadratic regression
 Vertex form
MDC Lesson(s) for the Unit
Lesson:
Forming Quadratics (2 days)
(complete after Lesson 12, replace Lesson 13 with this)
Skills Assessed in the Getting Ready
Factoring polynomials
Graphing functions (Linear and Absolute Value)
Solving quadratic equations
Skills/Reasoning addressed in the Lesson
 Understanding how the factored form of the
function can identify a graph’s roots.

Understanding how the completed square form of
the function can identify a graph’s maximum or
minimum point.

Understanding how the standard form of the
function can identify a graph’s intercept.
In which lesson is the skill first utilized
#1-4 7-2
#5 -7 7-1
#8 7-3
Embedded Assessment - _#1_Applications of Quadratic Functions and Equations – No Horsing Around (1 day)
What students need to be able to do
Vocabulary students need to understand









Quadratic Functions
Quadratic Equations
Discriminants
Complex numbers
Activity -7 Applications of Quadratid Functions - Fences
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
7-1 Analyzing a
 Formulate quadratic functions in a
Quadratic
problem-solving situation.
Function

Graph and interpret quadratic
functions.
7-2 Factoring
Quadratic
Expressions

Factor quadratic expressions of the
form x2 + bx + c.

Factor quadratic expressions of the
form ax2 + bx + c
7-3 Solving
Quadratic
Equations by
Factoring

Solve quadratic equations by factoring.

Interpret solutions of a quadratic
equation.

Create quadratic equations from
solutions.

Solve quadratic inequalities.

Graph the solutions to quadratic
inequalities.
7-4 More Uses for
Factors
Connections to ACT: (Critical Content/Problem sets from wiki)
Quadratic equation
Standard form of a quadratic equation
Imaginary number
Complex number
Complex conjugate
Completing the square
Discriminant
Root
Zero
Pacing
Notes
2 days
Pre-Assessment – Getting Ready, 1-4
Extra Practice, 5-7
Complete all. No omissions.
4 days
Complete all. No omissions. Use
KUTA Software supplements as
necessary for extra repetition.
3 days
Complete all. No omissions. Use
KUTA Software supplements as
necessary for extra repetition.
1 day
Complete all. No omissions.
Activity – 8 Introduction to Complex Numbers
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?

Know the definition of the complex
number i.

Know that complex numbers can be
written as a + bi, where a and b are
real numbers.

Graph complex numbers on the
complex plane.
8-2 Operations
with Complex
Numbers

Add and subtract complex numbers.

Multiply and divide complex numbers.
8-3 Factoring with
Complex Numbers

Factor quadratic expressions using
complex conjugates.

Solve quadratic equations with
complex roots by factoring.
8-1 Introduction
to Complex
numbers
Pacing
Notes
2 days
Complete all. No omissions.
2 days
Complete all. No omissions.
Skip
Connections to ACT: (Critical Content/Problem sets from wiki)
Lesson
Activity How does the lesson contribute to the EA
or End of Unit Assessment?

Solve quadratic equations by taking
square roots.

Solve quadratic
equations ax2 + bx + c = 0 by
completing the square

Derive the Quadratic Formula.

Solve quadratic equations using the
Quadratic Formula.

Solve quadratic equations using the
Quadratic Formula.

Use the discriminant to determine the
nature of the solutions of a quadratic
9-1
9-2
9-3
Pacing
Notes
1 day
Complete all. No omissions.
1 day
Formulate lesson using Lesson 9-2
Practice on page 143 only.
2 days
Complete all. No omissions.
equation.
EA1
1 day
Connections to ACT: (Critical Content/Problem sets from wiki)
Embedded Assessment - __#2 Writing and Transforming Quadratic Functions – The Safari Experience (1 day)
What students need to be able to do
 Standard form of a parabolas
 Vertex form of a parabola
 Transformations
 Directrix
 Focus
 Axis of symmetry
Vocabulary students need to understand
 Parabola
 Focus
 Directrix
 Axis of symmetry
 Vertex
Notes: Complete transformation problem 3 on the Embedded Assessment. Replace the rest of the Embedded
Assessment with a KUTA software quiz for standard and vertex forms of a parabola, directrix, focus, and axis of
symmetry.
Lesson
Activity How does the lesson contribute to the EA
or End of Unit Assessment?
10-1

Derive a general equation for a
parabola based on the definition of
a parabola.

Write the equation of a parabola
given a graph and key features.

Explain why three points are needed to
determine a parabola.

Determine the quadratic function that
passes through three given points on a
plane.

Find a quadratic model for a given
table of data.

Use a quadratic model to make
predictions.
10-2
10-3
Pacing
Notes
Skip
Embedded Assessment 2 will be
supplemented by a quiz to
demonstrate further student
understanding of quadratic
transformations in Lesson 11.
Skip
Embedded Assessment 2 will be
supplemented by a quiz to
demonstrate further student
understanding of quadratic
transformations in Lesson 11.
Skip
Embedded Assessment 2 will be
supplemented by a quiz to
demonstrate further student
understanding of quadratic
transformations in Lesson 11.
Connections to ACT: (Critical Content/Problem sets from wiki)
Lesson
Activity How does the lesson contribute to the EA
or End of Unit Assessment?

Describe translations of the parent
function f(x) = x2.

Given a translation of the
function f(x) = x2, write the
equation of the function.

Describe transformations of the
parent function f(x) = x2.

Given a transformation of the
function f(x) = x2, write the
equation of the function.

Write a quadratic function in vertex
form.

Use transformations to graph a
quadratic function in vertex form.
11-1
11-2
11-3
Pacing
Notes
1 day
Complete all. No omissions.
2 days
Complete all. No omissions.
1 day
Complete all. No omissions.
Connections to ACT: (Critical Content/Problem sets from wiki)
Embedded Assessment - __#3 Graphing Quadratic Functions and Solving Systems – The Green Monster (1 day)
What students need to be able to do
 Graph a parabola
 Maximum of a parabola
 Domain and range of quadratic functions
 Systems of equations with a linear equation and quadratic
equation
Vocabulary students need to understand
 Parabola
 Axis of symmetry
 Vertex
 Quadratic regression
 Vertex form
Pacing
Activity Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
Notes
12-1
12-2

Write a quadratic function from a
verbal description.

Identify and interpret key features
of the graph of a quadratic
function.

Write a quadratic function from a
verbal description.

Identify and interpret key features
of the graph of a quadratic
function.

Identify key features of a quadratic
function from an equation written
in standard form.

Use key features to graph a
quadratic function.

Use the discriminant to determine
the nature of the solutions of a
quadratic equation.

Use the discriminant to help graph
a quadratic function.

Graph a quadratic inequality in two
variables

Determine the solutions to a
quadratic inequality by graphing
12-3
12-4
12-5
2 days
Complete all. No omissions.
1 day
Complete all. No omissions.
2 days
Complete all. No omissions.
1 day
Complete all. No omissions.
1 day
Complete all. No omissions.
Pacing
Notes
Skip
Replace with Forming Quadratics
MDC
Skip
Replace with Forming Quadratics
MDC
Connections to ACT: (Critical Content/Problem sets from wiki)
Lesson
Activity How does the lesson contribute to the EA
or End of Unit Assessment?

Use graphing to solve a system
consisting of a linear and a
nonlinear equation.

Interpret the solutions of a system
of equations.
13-1

Use substitution to solve a system
consisting of a linear and nonlinear
equation.

Determine when a system consisting
13-2
of a linear and nonlinear equation has
no solution.
Connections to ACT: (Critical Content/Problem sets from wiki)
Unit Review and
Test
2 days
Course - Algebra II
Unit 3 - Polynomials
Number of Days - __________26_____________
Progression of Concepts and Skills Developed in this Unit
In this unit, students begin by writing and graphing a third-degree equation that represents a real-world situation. They perform
operations on polynomials; factor polynomials; identify the extrema, zeros, and roots of polynomials; and study the end behavior
of graphs of polynomial functions.
Academic Vocabulary/Math Terms
 Alternative
 Polynomial function
 Degree
 Standard form of a polynomial
 Relative maximum
 Relative minimum
 End behavior
 Even function
 Odd function
 Synthetic division
 Combination
 Factorial
 Summation notation
 Fundamental Theorem of Algebra
 Extreme
 Relative extrema
 Global extrema
MDC Lesson(s) for the Unit
Lesson:
Representing Polynomials (2 days)
Complete after Lesson 18
Skills/Reasoning addressed in the Lesson

Recognizing the connection between the zeros of
polynomials when suitable factorizations are
available, and graphs of the functions defined by
polynomials.

Recognizing the connection between
transformations of the graphs and transformations
of the functions obtained by replacing f(x) by f(x +
k), f(x) + k, -f(x), f(-x).
Skills Assessed in the Getting Ready
In which lesson is the skill first utilized
Rectangular prisms
Combining like terms
Factoring
 GCF
 Difference of squares
 Trinomials
Multiplying polynomials
Evaluating functions
x- and y- intercepts
Symmetry
Reading graphs
#1 14-1
#3 15-1
#3-4 17-1
#5
#6
#7
#8
#9
15-1
14-1
14-1
14-3
14-1
Embedded Assessment - _#1_Applications of Quadratic Functions and Equations – No Horsing Around (1 day)
What students need to be able to do
Vocabulary students need to understand
Polynomial functions
Operations with polynomials
Graphs of polynomials
Binomial expansion
Binomial theorem





Activity -14 Introduction to Polynomials
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
14-1
 Write a third-degree equation that
Polynomial function
Degree
Standard form of a polynomial
Relative maximum
Relative minimum
Pacing
Notes
1 day
Getting Ready #1, 6, 7, 9
Complete all. No omissions.
2 days
Complete all. No omissions.
1 day
Complete all. No omissions.
represents a real-world situation.
14-2
14-3

Graph a portion of this equation
and evaluate the meaning of a
relative maximum.

Sketch the graphs of cubic
functions.

Identify the end behavior of
polynomial functions.

Recognize even and odd functions
given an equation or graph.

Distinguish between even and odd
functions and even-degree and
odd-degree functions.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity – 15 Polynomial Operations
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
15-1
 Use a real-world scenario to
Pacing
Notes
1 day
Complete all. No omissions.
2 days
Getting Ready #2
Complete all. No omissions.
3 days
Complete all. No omissions.
Pacing
Notes
Complete if
time allows
Complete all if time allows. No
omissions.
Complete if
time allows
Complete all if time allows. No
omissions.
introduce polynomial addition and
subtraction.
15-2
15-3

Add and subtract polynomials.

Add, subtract, and multiply
polynomials.

Understand that polynomials are
closed under the operations of
addition, subtraction, and
multiplication.

Determine the quotient of two
polynomials.

Prove a polynomial identity and use it
to describe numerical relationships.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity – 16 Binomial theorem – Pascal’s Triangle
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
16-1
 Find the number of combinations of an
event.
16-2

Create Pascal’s triangle.

Know the Binomial Theorem.

Apply the Binomial Theorem to identify
the coefficients or terms of any
binomial expansion.
EA 1
Connections to ACT: (Critical Content/Problem sets from wiki)
1 day
Embedded Assessment - __#2 Factoring and Graphing Polynomials – Sketch Artist (1 day)
What students need to be able to do
Factoring polynomials
Graphing polynomials
Activity – Factors of Polynomials
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
17-1
 Determine the linear factors of
Vocabulary students need to understand
 Polynomial function
 Degree
 Even function
 Odd function
 Synthetic division
 X-intercept
 Y-intercept
Pacing
Notes
2 days
Getting Ready #3, #4
Skip 8, 9, Check Your Understanding
13, Practice 17 – difference of cubes
3 days
Getting Ready #5
Skip Try These A (d) and (f), Skip 7,
Check Your Understanding 2
Pacing
Notes
polynomial functions using
algebraic methods.
17-2

Determine the linear or quadratic
factors of polynomials by factoring
the sum or difference of two cubes
and factoring by grouping.

Know and apply the Fundamental
Theorem of Algebra.

Write polynomial functions, given
their degree and roots.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity – Graphs of Polynomials
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
18-1
18-2
18-3

Graph polynomial functions by
hand or using technology,
identifying zeros when suitable
factorizations are available, and
showing end behavior.

Recognize even and odd functions
from their algebraic expressions.

Know and apply the Rational Root
Theorem and Descartes’ Rule of
Signs.

Know and apply the Remainder
Theorem and the Factor Theorem.

Compare properties of two
functions each represented in a
different way.

Solve polynomial inequalities by
graphing.
EA2
2 days
Getting Ready #8
Complete all. No omissions.
3 days
Complete all. No omissions. Upon
completion of 18-2, complete
Representing Polynomials MDC.
1 day
Complete all. No omissions. EA2 –
2. sketch only – do not include sum
of cubes for root.
1 day
Connections to ACT: (Critical Content/Problem sets from wiki)
Unit Review and
Test
2 days
Course - Algebra II
Unit- 4 Series, Exponential and Logarithmic Functions
Number of Days - ___________32____________
Progression of Concepts and Skills Developed in this Unit
In this unit, students study arithmetic and geometric sequences and implicit and explicit rules for defining them. Then they
analyze exponential and logarithmic patterns and graphs as well as properties of logarithms. Finally, they solve exponential and
logarithmic equations
Academic Vocabulary/Math Terms
 Sequence
 Arithmetic sequence
 Common difference
 Recursive formula
 Explicit formula
 Series
 Partial sum
 Sigma notation
 Geometric sequence
 Common ratio

















Geometric series
Finite series
Infinite series
Sum of the infinite geometric series
Exponential function
Exponential decay factor
Exponential growth factor
Asymptote
Logarithm
Common logarithm
Logarithmic function
Natural logarithm
Change of base formula
Exponential equation
Compound interest
Logarithmic equation
Extraneous solution
MDC Lesson(s) for the Unit
Lesson:
Comparing Investments
Complete if time permits
Skills Assessed in the Getting Ready
Pattern recognition
Properties of exponents
Solving equations
Writing and graphing functions
Skills/Reasoning addressed in the Lesson

Translating between descriptive, algebraic and
tabular data, and graphical representation of the
functions.

Recognizing how, and why, a quantity changes per
unit interval.
In which lesson is the skill first utilized
#1-3 19-1
#4-6 20-1
#7 19-1
#8 19-1
Embedded Assessment - _#1 Sequence and Series – The Chessboard Problem (1 day)_
What students need to be able to do



Identifying terms in arithmetic and geometric sequences
Identify common differences and common ratios
Writing implicit and explicit rules for arithmetic and
geometric sequences.
Vocabulary students need to understand






Sequence
Arithmetic sequence
Common difference
Recursive formula
Explicit formula
Series








Activity – 19 Arithmetic Sequences and Series
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
19-1 Arithmetic  Determine whether a given sequence is
Sequences
arithmetic.

Find the common difference of an
arithmetic sequence.

Write an expression for an arithmetic
sequence, and calculate the nth term.
19-2 Arithmetic 
Series
19-3 Sigma
Notation
Write a formula for the nth partial sum of
an arithmetic series.

Calculate partial sums of an arithmetic
series.

Identify the index, lower and upper limits,
and general term in sigma notation.

Express the sum of a series using sigma
notation.

Find the sum of a series written in sigma
notation.
Partial sum
Sigma notation
Geometric sequence
Common ratio
Geometric series
Finite series
Infinite series
Sum of the infinite geometric series
Pacing
Notes
2 days
Getting Ready #1, 2, 3
Complete all. No omissions.
2 days
Complete all. No omissions.
1 day
Complete. No omissions.
Pacing
Notes
2 days
Complete all. No omissions.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity – 20 Geometric Sequences and Series
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
20-1 Geometric
 Determine whether a given
Sequences
sequence is geometric.

Find the common ratio of a
geometric sequence.

Write an expression for a
geometric sequence, and calculate
the nth term.

Derive the formula for the sum of a
finite geometric series.

Calculate the partial sums of a
geometric series.
20-3
Convergences of
Series

Determine if an infinite geometric
sum converges.

Find the sum of a convergent
geometric series.
EA1

20-2 Geometric
Series
2 days
Complete all. No omissions.
1 day (if time)
Complete all. No omissions. EA1 –
As is.
1 day
Connections to ACT: (Critical Content/Problem sets from wiki)
Embedded Assessment - __#2 Exponential Functions and Common Logarithms – Whether or Not (1 day)
What students need to be able to do
Vocabulary students need to understand
 Exponential function
 Exponential decay factor
 Exponential growth factor
 Asymptote
Examining exponential patterns and functions
Identifying and analyzing exponential graphs
Transforming exponential functions
Graphing and transforming natural base exponential functions
Examining common logarithmic functions
Understanding properties of logarithms
Activity -21 Exponential Functions and Graphs
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
21-1 Exploring
 Identify data that grow
Exponential
exponentially.
Patterns
21-2 Exponential
Functions

Compare the rates of change of
linear and exponential data.

Identify and write exponential
functions.

Determine the decay factor or
Pacing
Notes
1 day
Getting Ready, #7
Complete all. No omissions.
1 day
Complete all. No omissions.
growth factor of an exponential
function.
21-3 Exponential
Graphs and
Asymptotes
21-4 Transforming
Exponential
Functions
21-5 Natural Base
Exponential
Functions

Determine when an exponential
function is increasing or
decreasing.

Describe the end behavior of
exponential functions.

Identify asymptotes of exponential
functions.

Explore how changing parameters
affects the graph of an exponential
function.

Graph transformations of
exponential functions.

Graph the function f(x) = ex.

Graph transformations of f(x) = ex.
1 day
Complete all. No omissions.
1 day
Complete all. No omissions.
1 day
KUTA Software supplements for
base e and natural logarithms to
replace. Move to after EA2.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity – 22 Logarithms and their Properties
Lesson
How does the lesson
contribute to the EA or End
of Unit Assessment?
22-1
 Complete tables and
Exponential
plot points for
Data
exponential data.
22-2 Common
Logarithm
Function

Write and graph an
exponential function
for a given context.

Find the domain and
range of an
exponential function.

Use technology to
graph y = log x.

Evaluate a logarithm
using technology.
Pacing
Notes
Skip
Include Khan Academy Richter Scale video at this link and
add it to 22-2.
https://www.khanacademy.org/math/algebra2/logarithmstutorial/logarithm_properties/v/richter-scale
1 day
Complete all. No omissions.
22-3
Properties of
Logarithms
22-4 More
Properties of
Logarithms
EA2

Rewrite exponential
equations as their
corresponding
logarithmic
equations.

Rewrite logarithmic
equations as their
corresponding
exponential
equations.

Make conjectures
about properties of
logarithms.

Write and apply the
Product Property and
Quotient Property of
Logarithms.

Rewrite logarithmic
expressions by using
properties.

Make conjectures
about properties of
logarithms.

Write and apply the
Power Property of
Logarithms.

Rewrite logarithmic
expressions by using
their properties.

2 days
Getting Ready, #4, 5, 6
Complete entire lesson in one day. No omissions. Include
a second day of rigor and repetition from supplemental
resource.
1 day
Complete all. No omissions. EA2 – Complete all.
1 day
Connections to ACT: (Critical Content/Problem sets from wiki)
Embedded Assessment - __#3 Exponential and Logarithmic Equations – Evaluating Your Interest (1 day)
What students need to be able to do
 Solving exponential equations
 Solving logarithmic equations
 Solving real-world applications of exponential and
logarithmic functions
Vocabulary students need to understand
 Logarithm
 Common logarithm
 Logarithmic function






Activity -23
Lesson
23-1 Logarithms in
Other Bases
23-2 Properties of
Logarithms and
the Change of
Base Formula
23-3 Graphs of
Logarithmic
Functions
Natural logarithm
Change of base formula
Exponential equation
Compound interest
Logarithmic equation
Extraneous solution
Pacing
Notes
1 day
Complete all. No omissions.
1 day
Complete all. No omissions.
2 days
Complete all. No omissions.
Pacing
Notes
1 day
Getting Ready #8
Complete all. No omissions.
2 days
Complete all. No omissions.
How does the lesson contribute to the EA
or End of Unit Assessment?

Use composition to verify two
functions as inverse.

Define the logarithm of y with
base b.

Write the Inverse Properties for
logarithms.

Apply the properties of logarithms
in any base.

Compare and expand logarithmic
expressions.

Use the Change of Base Formula.

Find intercepts and asymptotes of
logarithmic functions.

Determine the domain and range
of a logarithmic function.

Write and graph transformations of
logarithmic functions.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity - 24
Lesson
24-1 Exponential
Equations
24-2 Solving
Equations by
Using Logarithms
How does the lesson contribute to the EA
or End of Unit Assessment?

Write exponential equations to
represent situations.

Solve exponential equations.

Solve exponential equations using
logarithms.

Estimate the solution to an
exponential equation.

Apply the compounded interest
formula.

Solve logarithmic equations.

Identify extraneous solutions to
logarithmic equations.

Use properties of logarithms to
rewrite logarithmic expressions
24-4 Exponential
and Logarithmic
Inequalities

Solve exponential inequalities.

Solve logarithmic inequalities.
EA

24-3 Logarithmic
Equations
2 days
Example D (optional). Spend 1 of
the days doing extended practice
Skip
Complete entire EA3
1 day
Connections to ACT: (Critical Content/Problem sets from wiki)
Unit Review and
Test
2 Day
Course - Algebra II
Unit – 5 Radical and Rational Functions
Number of Days - __________30_____________
Progression of Concepts and Skills Developed in this Unit
In this unit, you will extend your study of functions to radical, rational, and inverse functions. You will graph radical and
rational functions using transformations and by analyzing key features of the graph, and you will examine the domain and
range of the functions. You will solve rational equations and inequalities as well as equations with rational exponents. You
will also solve inverse and combined variation problems, average cost per unit problems, and work problems that are
modeled using rational functions.
Academic Vocabulary/Math Terms
 Square root regression
 One-to-one function
 Rational function
 Horizontal asymptote
 Vertical asymptote
 Inverse variation
 Constant of variation
 Combined variation
 Joint variation
 Complex fraction
 Discontinuity
 Removable point of discontinuity
MDC Lesson(s) for the Unit
Lesson:
Functions and Everyday Situations
Skills/Reasoning addressed in the Lesson
Complete if time allows.

Articulate verbally the relationships between
variables arising in everyday contexts.

Translate between everyday situations and sketch
graphs of relationships between variables.

Interpret algebraic functions in terms of the
contexts in which they arise.

Reflect on the domains of everyday functions and
in particular whether they should be discrete or
continuous.
Skills Assessed in the Getting Ready
In which lesson is the skill first utilized
Rewriting radical expressions in equivalent forms
Simplifying rational expressions
Simplifying monomials
Determining asymptotic restrictions
Factoring trinomials and difference of squares
binomials
Finding inverses of functions
Writing interval notation
Solving direct variation problems
#1
#2
#3
#4
#5
25-2
29-1
29-1
27-3
29-1
#6 26-1
#7 25-1
#8 28-1
Embedded Assessment - _#1 Radical Functions :Square roots, Cube Roots, and Their Inverses – How Big is That Ball? (1
day)_
What students need to be able to do
Vocabulary students need to understand


Square root functions
Cube root functions
Transformations of square root and cube root functions
Inverses of square root and cube root functions
Activity -25 – Square Root and Cube Root Functions
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
25-1 Square Root
 Graph and describe
Functions
transformations of the square root
function y=x√.
Square root regression
One-to-one function
Pacing
Notes
2 days
Getting Ready #1
Complete all. No omissions.

Interpret key features of a graph
that models a relationship between
two quantities.
25-2 Solving
Square Root
Equations

Solve square root equations.

Identify extraneous solutions.
25-3 Cube Root
Functions

Skip

Graph transformations of the cube
root function y=x√3.
Identify key features of a graph
that models a relationship between
two quantities.

Solve cube root equations.
1 day
Complete all. No omissions.

Check the reasonableness of
solutions.
Pacing
Notes
1 day
Getting Ready #6
Examples A and B and Try These A-B;
rest of section is optional.
1 day
Complete all. No omissions.
1 day
Complete all. No omissions. EA1 –
Complete 1 – 3, 4 (optional), 5
25-4 Solving Cube
Root Equations
2 days
Complete all. No omissions.
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity – 26- Inverse: Roots, Squares, and Cubes
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
26-1 Square Root
 Graph and write the inverse of
Factions and
square root functions.
Regressions

Find a square root model for a
given table of data.
26-2 Square Root
and Quadratic
Functions

Graph and write the inverse of
square root functions.

Find the inverse relations of
quadratic functions.
26-3 Cube Root
and Cubic
Functions

Graph and write the inverse of
cube root functions.

Find the inverse relations of cubic
functions.
Connections to ACT: (Critical Content/Problem sets from wiki)
*** Remember to add rows for MDC lessons to determine which lesson or activity they follow- include contribution,
pacing, and any notes.
Embedded Assessment - __#2 Rational Functions and Variations – A Condo for My Cat (1 day)
What students need to be able to do
 Rational functions
 Inverse variation
Activity How does the lesson contribute to the EA
or End of Unit Assessment?
27-1 Introduction
 Formulate rational equations that
to Rational
model real-world situations.
Functions
Notes

Graph equations on coordinate
axes.
27-2 Formulating
and Graphing
More Rational
Functions

Formulate rational equations that
model real-world situations.

Graph equations on coordinate
axes.
27-3 Identifying
Asymptotes

Determine the horizontal and
vertical asymptotes of a rational
function.

Graph a rational function on the
coordinate plane.
Vocabulary students need to understand
 Rational function
 Horizontal asymptote
 Vertical asymptote
 Inverse variation
 Constant of variation
 Combined variation
 Joint variation
 Complex fraction
Pacing
2 days
Complete all. No omissions.
2 days
Complete all. No omissions.
1 day
Complete all. No omissions.
Pacing
Notes
Connections to ACT: (Critical Content/Problem sets from wiki)
Lesson
Activity How does the lesson contribute to the EA
or End of Unit Assessment?
28-1 Inverse
Variation and
Combined
Variation

Create, solve, and graph an equation
involving inverse variation.

Solve an equation involving combined
variation.
28-2

Transformations
of the Parent

Rational Function
Describe transformations of the parent
function f(x)=1/x and sketch the graphs.
Identify the x-intercepts, y-intercepts, and
asymptotes of transformations of the
parent function f(x)=1/x.
Skip
Skip
EA2 – Skip 3 – 7. Can give 1 – 2 as
assessment or design a KUTA
Software quiz that covers topics in
Activity 27.
Connections to ACT: (Critical Content/Problem sets from wiki)
*** Remember to add rows for MDC lessons to determine which lesson or activity they follow- include contribution,
pacing, and any notes.
Embedded Assessment - __#3 Rational Expressions, Equations, and Inequalities – Work It Out! (1 day)
What students need to be able to do
 Rational expressions
 Rational equations
 Rational inequalities
Activity -29 Simplifying Rational Expressions
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
29-1
 Simplify rational expressions.
29-2
29-3

Multiply and divide rational
expressions.

Add and subtract rational
expressions.

Simplify complex fractions.

Identify the vertical asymptotes of
rational functions by finding the
domain values that make the
Vocabulary students need to understand
 Vertical asymptotes
 Non removable discontinuity
 X-intercept
 Y-intercept
 minimum
Pacing
Notes
2 days
Complete all. No omissions.
2 days
Example A – Try These B; Example C
– Try These C, a
1 day
Complete activity with emphasis on
horizontal asymptotes or create 1
day supplement in KUTA Software
functions undefined.
29-4

Use the degrees of the numerator
and denominator of rational
functions to identify the horizontal
asymptotes.

Analyze and graph rational
functions, identifying any
asymptotes, intercepts, and holes.

Analyze and graph rational
functions representing real-world
scenarios.
Skip
Connections to ACT: (Critical Content/Problem sets from wiki)
Activity -30 Rational Equations and Inequalities
Lesson
How does the lesson contribute to the EA
or End of Unit Assessment?
30-1
 Solve rational equations,
Pacing
Notes
2 days
Example A – 4; Check Your
Understanding
Omit 8 – 22; Supplement with KUTA
Software implementation
2 days
Complete all. No omissions.
Supplement with KUTA Software
handout implementation
identifying any extraneous
solutions.
30-2

Create and solve rational
equations that represent work
problems.

Solve rational inequalities by
graphing.

Solve rational inequalities by
finding the sign of the inequality on
either side of the numerator and
denominator zeros.
Connections to ACT: (Critical Content/Problem sets from wiki)
Unit Review and
Test
2 Days