Download Module 1: Topic A: Polynomials

Suggested Timeline for the Common Core Algebra II Course
Note: Textbook pages are for reference only. You will have to use additional resources since
the text does not follow the modules completely.
Module 1: Topic A: Polynomials
Lesson
1
Title
Monomials
Content
Addition, Subtraction, Multiplication, Division
Include Review of Exponent Rules
Module/Textbook Pages
Textbook Pgs. 303-309
2-3
Polynomials
Define: Coefficient, Constant, Degree of Polynomial
Addition, Subtraction, Multiplication of polynomials
[Go over Tabular Method]
Module 1 Lesson 5
Pg. 56
Textbook Pgs. 305-308
4-5
Polynomials
Division by Long Division and Synthetic Division
Include examples with and without a remainder
Module 1 Lesson 6
Pg. 65
Module 1 Lesson 7
Pg. 75
Textbook Pgs. 311-315
6
Operations
Involving Radicals
Simplify, Addition, Subtraction, Multiplication,
Division, Rational Denominator
Module 1 Lesson 9
Pg. 98
Textbook Pgs. 407-420
*
Finding
Pythagorean Triples
Group activity in module
Module 1 Lesson 10
Pg. 108
7-8
Factor Polynomials/
Solve Polynomial
Equations
Greatest Common Factor, Difference of Two Perfect
Squares, Trinomials With and Without Leading
Coefficient, Sum/Difference of Two Perfect Cubes
Textbook Pg. P8
Pgs. 238-244
Pgs. 342 -346
9
Factor/Solve
Polynomials Using
Completing The
Square Method
Review the process of completing the square
Explain the difference between rational and
irrational roots
Module 1 Lesson 12
Pg. 130
10
11
Review
Test
* Optional Topic
Textbook Pgs. 324-346
Pgs. 256-260
Module 1: Topic B: Polynomials
Lesson
1
Title
Zeros of Polynomials
Content
Define: x-intercepts, Roots, Zeros, Multiplicity
Find all of the above using graphs
Module/Textbook Pages
Module 1 Lesson
Pg. 117
Textbook Pg. 75
2
Graph Polynomials
Major emphasis is to go over different functions on
the graphing calculator: x-intercepts, y-intercepts,
Zeros, Relative Maximums, Relative Minimums,
Windows, Interval where Function is Increasing or
Decreasing, Points of tangency on the x-axis
“Roller Coaster Question in Module”
Module 1 Lesson 14
Pg. 149 Question 1
3-4
Graph Polynomials
when Given in
Factored
and Standard Form
Find the zeros, solutions of 𝑓(𝑥) = 0, x-intercepts,
and degree of the polynomial. Be able to graph the
function including the x- and y-intercepts, relative
maximums and minimums. Describe end behavior
based upon the degree of the polynomial.
Evaluate end behavior of functions based on even
degree or odd degree. Define even and odd
functions.
Textbook Pgs. 322-335
Applications
Transition between verbal, numerical, algebraic,
and graphical thinking in analyzing applied
polynomial problems.
Module 1 Lessons 16
Pg. 178
Module 1 Lesson 17
Pg. 185
Remainder Theorem
Know and apply the Remainder Theorem and
understand the role zeros play in the theorem.
Use the Remainder Theorem to find all additional
factors and zeros of the polynomial function.
Apply the Rational Root Theorem to find all
possible rational roots and to find all rational
zeros.
Textbook Pgs. 352-356
5
6-7
8
9
Review
Test
Module 1: Topic C: Rational Expressions
Lesson
1
Title
Rational Expressions
Content
When is a fraction undefined, Simplify,
Negative 1 Rule
Module/Textbook Pages
Textbook Pgs. 529-535
2
Comparing Rational
Expressions
Extend comparisons of rational numbers to
comparing rational expressions and using
numerical, graphical, and algebraic analysis.
Module 1 Lesson 23
Pg. 249
3
Multiplication/Division
Multiply and divide rational expressions and
simplify using equivalent expressions.
Module 1 Lesson 24
Pg. 261
Textbook Pgs. 529-535
4
Addition/Subtraction
Addition and subtraction of rational expressions by Module 1 Lesson 25
converting to equivalent rational expressions with Pg. 272
a common denominator.
Textbook Pgs. 538-542
5
Complex Fractions
Remind students that the fraction bar represents
division, so a complex fraction represents division
between rational expressions. Rewrite complex
fractions in simplest form.
Module 1 Lesson 25
Pg. 272
Solve fractional equations and explain the
meaning of extraneous roots.
Module 1 Lesson 26
Pg. 283
6
Solve Fractional
Equations
Textbook Pgs. 538-542
Textbook Pgs. 570-577
7
Applications
“Word Problems”
Solve word problems using models that involve
rational expressions.
Module 1 Lesson 27
Pg. 293
Textbook Pgs. 570-577
8
9
Review
Test
Module 1: Topic D: Radicals And Imaginary Numbers
Lesson
1-2
Title
Solve Radical
Equations
Content
Solve Single and Double Radical Equations,
Solve Radical equations Involving Cube Roots and
Fourth Roots
Module/Textbook Pages
Module 1 Lesson 28
Pg. 304
Module 1 Lesson 29
Pg. 313
Textbook Pgs. 429-433
3-4
5
Imaginary Numbers/
Complex Numbers
Quadratic Equations
with Imaginary Roots
Define an Imaginary Number, Simplify,
Powers of i, Define a Complex Number,
Graph complex numbers, Addition, Subtraction,
Multiplication, and Division of complex numbers.
Find the values of a and b given an equation.
Module 1 Lesson 37
Pg. 418
Using the quadratic equation solve a quadratic
equation with imaginary roots. Go over the
discriminant rules.
Module 1 Lesson 38
Pg. 431
Textbook Pgs. 246-254
Textbook Pgs. 264-270
6-7
Polynomial Equations
with Imaginary Zeros
Using factoring, long division, synthetic division,
the remainder theorem, and the rational root
theorem, to find the zeros of polynomial
equations.
Fundamental Theorem of Algebra {Be able to
explain what types of roots a polynomial function
might have}. Write the equation of a polynomial
equation give the zeros.
Might want to mention sum of roots is
product of roots is
8
9
Review
Test
c
.
a
b
and
a
Module 1 Lesson 39
Pg. 445
Module 1 Lesson 40
Pg. 455
Textbook Pgs. 358-364
Module 1: Topic E: Systems of Equations
Lesson
1
Title
Linear Systems with
Three Variables
Content
Solve linear systems in three variables
algebraically.
Module/Textbook Pages
Module 1 Lesson 30
Pg. 320
Textbook Pgs. 161-165
2-3
4-6
7
8
Solve System of
Linear/
Quadratic Equations
Parabolas
Review
Test
Systems of equations that represent a line and a
circle and systems that represent a line and a
parabola, and make conjectures as to how many
points of intersection there can be in a given
system of equations. Solve algebraically and
graphically.
Module 1 Lesson 31
Pg. 329
Module 1 Lesson 32
Pg. 341
Model the locus of points at equal distance
between a point (focus) and a line (directrix).
Construct a parabola and understand this
geometric definition of the curve. Use algebraic
techniques to derive the analytic equation of the
parabola. Learn the vertex form of the equation of
a parabola and how it arises from the definition of
a parabola
[𝑦 = 𝑎(𝑥 − ℎ) + 𝑘] . Apply the geometric
transformation of dilation to show that all
parabolas are similar.
Module 1 Lesson 33
Pg. 352
Module 1 Lesson 34
Pg. 369
Module 1 Lesson 35
Pg. 388
Textbook Pgs. 640-643
Textbook Pgs. 599-600
Module 3: Topic A: Exponents
Lesson
1-2
Title
Integer Exponents
*Covered in Topic A
Might not want to go
over again
Rational Exponents
Content
To fully understand exponential functions and their use
in modeling real-world situations, students must be able
to extend the properties of integer exponents to
rational and real numbers.
Convert fractional exponents to radicals and vice
versa include positive and negative exponents.
Solve fractional equations.
Module/Textbook Pages
Module 3 Lesson 1
Pg. 14
Module 3 Lesson 3
Pg. 43
Module 3 Lesson 4
Pg. 62
Textbook Pgs. 303-308
Textbook Pgs. 422-428
3
Solve equations
involving Exponents
Exponential equations [match bases and set
exponents equal to each other]
Module 3 Lesson 7
Pg. 105
Textbook Pgs. 461-465
4
The number “e”
Derive the number e. Go over properties of e.
Module 3 Lesson 6
Pg. 86
Textbook Pgs. 501-506
5
Graphs of Exponential
Functions
Include Domain, Range, Intercepts, Asymptotes,
Intervals of increasing, Decreasing or Constant,
Relative Minimums or Maximums, Symmetry, and
Even, Odd or Neither. Include rate of change
questions. Do some basic transformations of
graphs
[Right, Left, Up and Down]. Be able to write
equation of the image after the transformation.
Textbook Pgs. 451-457
7
Applications
“Growth & Decay”
Banking/Interest [ 𝐴 = 𝑃(1  𝑟)𝑡, 𝐴 = 𝑃𝑒𝑟𝑡,
and
Textbook Pgs. 464-465


r
n
nt
A = 1  . Growth and Decay
8
9
Review
Test
Module 3: Topic B: Logarithms
Lesson
1
Title
Introduction of
Logarithms
Content
Calculate a simple logarithm using the definition.
“The module has a great lesson on this”
Module/Textbook Pages
Module 3 Lesson 8
Pg. 116
Textbook Pg. 472
2-3
Development of Laws
of Logarithms
Stress Bases of 2, 10, e
Construct a table of logarithms base 10 and
observe patterns that indicate properties of
logarithms.
Use logarithmic properties to rewrite logarithmic
expressions. Evaluate log expressions without the
use of a calculator. Justify properties of logarithms
using the definition and properties.
Module 3 Lesson 10
Pg. 137
Module 3 Lesson 11
Pg. 149
Module 3 Lesson 12
Pg. 160
Textbook Pgs. 485-490
4
5
Change of Base
Formula/Properties of
Logs with other bases
Exponential Equations
Understand how to change logarithms from one
base to another. Calculate logarithms with any
base using a calculator that computes only
logarithms base 10 and base 𝑒.
Module 3 Lesson 13
Pg. 175
Solve exponential equations by applying the
appropriate logarithm.
Module 3 Lesson 13
Pg. 175
Textbook Pgs. 494-495
Textbook Pgs. 492-496
Pg. 505
6
Logarithmic Equations
Solve logarithmic equations using the definition of
logarithm and logarithmic properties.
Module 3 Lesson 14
Pg. 193
Module 3 Lesson 15
Pg. 207
Textbook Pgs. 499-500
Pgs. 501-505
7
8
9
Quadratic, Exponential
and Logarithmic
Regression
Review
Test
Generate equations from a set of data values.
Use examgen questions
Textbook Pg. 476
Pg. 228
Module 3: Topic C: Graphing of Exponential and Logarithmic Functions
Lesson
1
2
Title
Inverses Graph
Logarithmic Functions
[Use Exponential
Function to assist
graphing Logs]
Inverses Graph
Content
Include: Domain, Range, Intercepts, Asymptotes,
Intervals of increasing, Decreasing or Constant,
Relative Minimums or Maximums, Symmetry, and
Even, Odd or Neither. Include rate of change
questions. Do some basic transformations of
graphs
[Right, Left, Up and Down]. Be able to write
equation of the image after the transformation.
Module/Textbook Pages
Module 3 Lesson 17
Pg. 262
Module 3 Lesson 18
Pg. 280
Define inverse. Find inverse algebraically and
graphically. Reflection over the line 𝑦 = 𝑥.
Module 3 Lesson 19
Pg. 262
Textbook Pgs. 478-482
Textbook Pgs. 393-398
Pgs. 478-482
3
4
Transformations
Graph natural
Logarithms
5
Choosing a Model
{Linear, Quadratic,
Exponential,
Logarithmic}
6
7
Review
Test
Midterm Review and Midterm
Study transformations of the graphs of exponential
and logarithmic functions and write equation of
image.
Use properties of logarithms and exponents to
produce equivalent forms of exponential and
logarithmic expressions. In particular, they notice
that different types of transformations can
produce the same graph due to these properties.
General Form: 𝑦 = 𝑘 + 𝑎 𝑙𝑜𝑔( 𝑥 − ℎ)
Module 3 Lesson 20
Pg. 312
Graph the natural logarithm function and
understand its relationship to other base 𝑏
logarithm functions. Apply transformations to
sketch the graph of natural logarithm functions by
hand
Module 3 Lesson 21
Pg. 334
Analyze data and real-world situations and find a
function to use as a model. Study properties of
linear, quadratic, exponential and logarithmic
functions. [Do sinusoidal functions at a later time]
Module 3 Lesson 22
Pg. 349
Textbook Pgs. 468-474
Textbook Pgs. 501-506
Module 3: Topic D and E: Sequences, Series and Applications of Logarithms
Lesson
1-2
Title
Sequences
Content
Review Arithmetic and Geometric Sequences
[Covered in CC Algebra I]
Find common difference and common ratio,
write sequences in Explicit and Recursive forms,
find nth term of a sequence
Module/Textbook Pages
Textbook Pgs. 659-678
Pgs. 692-695
3-4
Series
Sigma Notation, arithmetic series,
sum of finite and infinite series
Textbook Pgs. 659-678
Pgs. 683-687
5-10
Applications of
Logarithms
Growth and Decay, Compound Interest,
Continuous Interest, Car Loans, Population,
Credit Cards, Buying a House
Module 3 Lessons 26-33
Pgs. 419
Textbook throughout
Chapter 7 Pgs. 449-517
11
12
Review
Test
Module 2: Topic A: Trigonometry
Lesson
1
Title
Trig functions in right
triangles
Content
Define the 6 trig functions, go over the basic 30o,
45o, and 60o special values using right triangles.
Review Quotient and Reciprocal Identities from
geometry and use to simplify basic trig identities.
Module/Textbook Pages
Textbook Pgs. 790 - 796
2-3
Angles and Angle
Measure
Draw angles in standard position, initial side,
terminal side, clockwise and counter clockwise
rotations, coterminal angles in both degree and
radian measure. [Go over radian measure from
geometry include converting radian to degree and
vice versa, and the s =  r formula.]
Textbook Pgs. 799 - 805
4-7
Unit circle, Quadrantal
Angles, Quadrants, and
Reference Angles
Define the unit circle, “ASTC”, Find the values of
the quadrantal and first quadrant special angles
(30-45-60) in radian measure. Know ordered pair
(𝑥, 𝑦) is (𝑐𝑜𝑠  , 𝑠𝑖𝑛  ). Find reference angles in all
quadrants stressing radian measure. Be able to
identify the name of the segments on the unit
circle using the 6 trig functions.
Textbook Pgs. 807 - 813
8
Find remaining trig
functions using
Pythagorean trig
identities.
Review Pythagorean trig identity from geometry.
Using sin2  + cos2  = 1 find the remaining values
of the additional trig functions. Prove some basic
trig identities.
Textbook Pgs. 873 - 883
9
10
Review
Test
Module 2: Topic B: Graphing Trigonometric Functions
Lesson
1
Title
Unwrapping of the
periodic function.
“Sine and Cosine”
Content
Ferris wheel question, pedals on a bicycle
question.
2-3
Introduce basic sine
and cosine graph
Graph basic sine and cosine graphs, define
amplitude, frequency, period, midline, domain,
range, and intercepts.
Textbook Pgs. 837 - 842
4
Graph remaining trig
functions
Overview of the tangent, cotangent, secant, and
cosecant graphs. Discuss Asymptotes, Domain,
Range, and Period.
Textbook Pgs. 837 - 842
5-7
Translations of Sine
and Cosine Graphs
Graph trig functions involving phase and vertical
shifts in the form of 𝑦 = 𝐴 𝑠𝑖𝑛 𝐵(𝑥 − 𝐶) + 𝐷 and
𝑦 = 𝐴 𝑐𝑜𝑠 𝐵(𝑥 − 𝐶) + 𝐷.
Textbook Pgs. 845 - 851
8
Applications
Use trigonometry and trig graphs in a variety of
applications and word problems.
Textbook Pgs. 845 - 851
9
Choosing a Model
Analyze data and real-world situations and find a
function to use as a model. Study properties of
linear, quadratic, exponential, logarithmic and
sinusoidal functions.
Module 3 Lesson 22
Pg. 349
Textbook Pg. 830
More questions in
workbook
*Did much of this in Module 3 Topic C
10
11
Review
Test
Module/Textbook Pages
Module 2 Lesson 1 & 2
Module 4: Topic A: Probability
Lesson
1
Title
Probability
Content
Sample Space, Tree Diagrams, Outcomes, Events,
Theoretical vs. Empirical Probability,
Not (complement), Union (and), Intersection (or),
Use cards, spinners and dice to form probabilities
of single and compound events.
Module/Textbook Pages
Module 4 Lesson 1
Pg. 12
2-3
Two – Way Frequency
Tables
Conditional Probability, Complete and analyze two- Module 4 Lessons 2-4
way frequency tables
Pgs. 29
4-5
Venn Diagrams
Independent vs. Disjoint, Complement (and),
Union (and), Intersection (or),
Calculate probability using a Venn Diagram
Real World Applications
6-7
More Advanced
Probability Rules
Calculate the probability of the complement of an
Module 4 Lessons 6-7
event, the probability of an intersection when
Pgs. 81
events are independent, and conditional
probabilities. Calculate the probability of the union
of two events. The general form of the rule is
considered, as well as the special cases for disjoint
and independent events. The use of Venn diagrams
is encouraged throughout the lesson to illustrate
problems
8
9
Review
Test
Module 4 Lesson 5
Pg. 66
Module 4: Topic B: Modeling Data Distributions
Lesson
1
2
3
4-5
6
7
Title
Measures of Central
Tendency and
Variation
Content
Review of Algebra 1 Statistics including Mean,
Mode, Median, Range, Interquartile Range,
Standard Deviation and Variance from a data set
using technology.
Module/Textbook Pages
Textbook Pgs. P24-P28
Shapes of Distribution
Symmetric (Mound-shaped) vs. Skewed (left/right)
Spread of data – Approximating standard deviation
and mean from histograms
Using the normal curve distribution, discuss the
basic 68%, 95%, 99% questions. They will not be
using the curve to answer formal questions but
should have an understanding of the normal curve.
Module 4 Lesson 8
Pg. 107
A smooth curve is used to model a relative
frequency histogram, and the idea of an area
under the curve representing the approximate
proportion of data falling in a given interval is
introduced.
Basic shape of curve is symmetric and mound
shaped. Calculate z-scores and find the probability
under the curve using z-tables and technology.
Module 4 Lesson 9
Pg. 119
Using a curve to model
a data distribution
Normal Distribution
Review
Test
Textbook Pg. 733
Textbook Pg. 733
Module 4 Lessons 10-11
Textbook Pg. 760
Module 4: Topic C: Drawing Conclusions Using Data from a Sample
Lesson
1
Title
Types of Statistical
Studies
Content
Be able to identify the differences between an
observational study, a survey, and an experiment
Identify population, sample, treatment,
cause/effect, and any lurking variables in an
experiment
Bias vs. Unbiased
Identify random selection and random assignment
Module/Textbook Pages
Module 4 Lesson 12
Pg. 184
Textbook Pg. 723
2
Using sample data to
estimate a population
characteristic
Population vs. Sample
Characteristic vs. Statistic
How to generate a random sample from given
tables and from technology.
Module 4 Lesson 13
Pg. 195
3
Sampling Variability in
the Sample Mean
Students understand the term “sampling
variability” in the context of estimating a
population mean. Students understand that the
standard deviation of the sampling distribution of
the sample mean offers insight into the accuracy of
the sample mean as an estimate of the population
mean.
Module 4 Lesson 18-19
Pgs. 254
4
Margin of Error when
estimating a
Population Mean
Students use data from a random sample to
estimate a population mean. Students calculate
and interpret margin of error in context. Students
know the relationship between sample size and
margin of error in the context of estimating a
population mean.
Module 4 Lesson 20-21
Pgs. 276
5
Sampling Variability in
the Sample Proportion
Students understand the term “sampling
variability” in the context of estimating a
population proportion. Students understand that
the standard deviation of the sampling distribution
of the sample proportion offers insight into the
accuracy of the sample proportion as an estimate
of the population proportion.
Module 4 Lesson 14-15
Pgs. 207
6
Margin of Error when
estimating a
Population Proportion
Students use data from a random sample to
estimate a population proportion. Students
calculate and interpret margin of error in context.
Students know the relationship between sample
size and margin of error in the context of
estimating a population proportion.
Module 4 Lesson 16-17
Pgs. 229
7
8
Review
Test
Module 4: Topic D: Drawing Conclusions Using Data from an Experiment
Lesson
1
Title
Experiments and the
Role of Random
Assignment
Content
Given a description of a statistical experiment,
students identify the response variable and the
treatments. Students recognize the different
purposes of random selection and of random
assignment. Students recognize the importance of
random assignment in statistical experiments.
Module/Textbook Pages
Module 4 Lesson 23
Pg. 307
2
Differences Due to
Random Assignments
Students understand that when one group is
randomly divided into two groups, the two groups’
means will differ just by chance (a consequence of
the random division). Students understand that
when one group is randomly divided into two
groups, the distribution of the difference in the
two groups’ means can be described in terms of
shape, center, and spread.
Module 4 Lesson 24
Pg. 319
3-4
Ruling out Chance:
Randomization Testing
and Distribution
Given data from a statistical experiment with two
treatments, students create a randomization
distribution. Students use a randomization
distribution to determine if there is a significant
difference between two treatments.
Module 4 Lessons 25-27
Pg. 328
5-6
Drawing Conclusions
from an Experiment
Students carry out a statistical experiment to
compare two treatments. Given data from a
statistical experiment with two treatments,
students create a randomization distribution.
Students use a randomization distribution to
determine if there is a significant difference
between two treatments.
Module 4 Lessons 28-29
Pg. 367
7-8
Evaluating Reports
based on Data from an
Experiment
Students critique and evaluate statements in
published reports that involve determining if there
is a significant difference between two treatments
in a statistical experiment.
Module 4 Lesson 30
Pg. 379
9
10
Review
Test