Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
8/24/2011
Course: Algebra 2
1st Semester
Chapter
2nd Semester
Chapter
Chapter 3 (and 1.1) - Linear Models and Systems
Chapter 6 - Matrices and Linear Systems
# Teaching
Days
8 Chapter 7 - Quadratic and Other Polynomial Functions
5 Chapter 8 – Rational Functions
# Teaching
Days
17
6
Chapter 4 - Functions, Relations, and Transformations
12 Chapter 12 – Trigonometry
7
Chapter 5 (and 1.2) - Exponential, Power, and Logarithmic
Functions
Optional Chapter 5 Exploration - e and ln
15 Chapter 13 – Trigonometric Functions
10
Chapter 11 – Applications of Statistics
Total
O: Optional
4 Chapter 9 - Series
5
8 Chapter 10 - Probability
9
52 Total
S: A WA State Standard
T: On the End of Course
54
P: ISD Priority
Number of days are teaching days only and do not include optional days. Additional days will be needed for quizzes, reviews and tests.
The number of quizzes stated is only a suggestion.
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 3
8/24/2011
Linear Models and Systems
Big Ideas:





Explicit and recursive equations for arithmetic sequences.
Review slope, linear equations in intercept form.
Teach point-slope form, explore connections between arithmetic sequences and linear equations.
Find lines of fit for data sets that are approximately linear,
Algebraically and graphically solve and represent systems of linear equations
Lesson
1-1
Objective(s)
Defining and Writing Arithmetic Sequences
Recursively
3-1
Recognize Connections Between Explicit and
Recursive Formulas
1
3.2
Revisiting Slope
1
3-3
Fitting a Line to Data
2
A2.1.A, A2.8.B,
A2.8.C, A2.8.E,
A2.8.F, A2.8.H
3-6
Linear Systems
1
A2.1.A, A2.1.B,
A2.8.A, A2.8.B,
A2.8.E
3-7
Substitution and Elimination
2
2 Quizzes, Review, Test
Priority # of days
1
Notes
Pick up graphs from 1.4.
Standards
A2.1.A, A2.8.E,
A2.8.F, A2.8.H,
A2.1.A, A2.1.B,
A2.8.A, A2.8.B,
A2.8.E
Make sure to include parallel and perpendicular
slopes.
Vocabulary is not the main point of this section.
A2.8.C , A2.8.E,
A2.8.F, A2.8.H
A2.1.B
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 6
8/24/2011
Matrices and Linear Systems
Big Ideas:
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

Use matrices to organize information.
Add, subtract, and multiply matrices by hand.
Solve systems of linear equations, with matrices.
Lesson
6.1
Objective(s)
Defining the Matrix
6.2
Matrix Operations
6.3
Solving Systems with Inverse Matrices
Quiz
Priority # of days
1
Notes
Standards
A2.8.A, A2.8.E
2
Day 1: Add/subtract, scalar multiplication
Day 2: Multiply
A2.7.A, A2.8.E
2
Calculator heavy
A2.1.B, A2.8.D,
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 4
8/24/2011
Functions, Relations, and Transformations
^ For all parent functions and relations, students should be able to identify the x-intercept(s), y-intercept, domain, range, asymptote(s) and sketch the graph.
Big Ideas:






Determine if a relation given in different forms is a function or not.
Domain and range of relations.
Function notation.
Parent functions and relations: linear, quadratic, square root, absolute value, and circles
Apply transformations (translations, dilations and reflections) to the parent functions and relations.
Algebraically find the composition of two functions.
Lesson
4-1
Objective(s)
Interpreting Graphs
4-2
Function Notation
4-3
^ Lines in Motion
4-4
^ Translations of Quadratics
2
A2.1.C, A2.5.A,
A2.8.D
4-5
^ Reflections and the Square Root Family
2
A2.5.A, A2.5.B,
A2.8.D
4-6
^ Dilations and the Absolute-Value Family
2
A2.1.A, A2.1.C,
A2.5.A, A2.8.C
4-7
^ Transformations and the Circle Family
2
A2.5.A, A2.8.D
4-8
Compositions of Functions
2
2/3 Quizzes, Review, Test
Priority # of days
O
1
Notes
Optional
2
O
3
Standards
A2.8.E
A2.8.E
Optional if students clearly learned point-slope
form in unit 3
3 days if doing investigation
Focus on problems like #1 and #10
A2.5.A, A2.8.D
A2.5.A, A2.8.E
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 5
8/24/2011
Exponential, Power, and Logarithmic Functions
^ For all parent functions and relations, students should be able to identify the x-intercept(s), y-intercept, domain, range, asymptote(s) and sketch the graph.
Big Ideas:









Explicit and recursive equations for geometric sequences.
Properties of exponents.
Converting between roots and rational exponents.
Use exponential functions to model real-world growth and decay scenarios.
Learn how to find the algebraic inverse of functions.
Use and apply logarithms to solve problems.
Properties of logarithms.
New parent functions: exponential, power and logarithmic
Graph and transform exponential and logarithmic equations and graphs.
Lesson
1-2
Objective(s)
Defining Geometric Sequences and Writing
Recursive their Equations
Priority # of days
1
5-1
^ Exponential Functions
1
5-2
^ Properties of Exponents and Power Functions
2-3
Notes
Pick up graphs from 1.4
Standards
A2.1.A, A2.8.A,
A2.8.B, A2.8.C,
A2.8.F, A2.8.H
A2.1.D, A2.4.A,
A2.4.B, A2.4.C,
A2.8.E
Day 1: Exponents Properties
Days 2 and 3: Exponential and Power Functions
Make sure to include mini-investigation on
power functions
Need additional supplements on exponent
properties similar to pg. 262-263 and More
Practice Your Skills 5-2 WS
A2.2.B, A2.4.A,
A2.4.C, A2.8.G
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
8/24/2011
Look at Algebra 1 book unit 6 for additional
resources
5-3
Rational Exponents and Roots
3
Day 1: Roots and Fractional Exponents
Days 2 and 3: Simplifying Roots and Fractional
Exponents
A2.2.B, A2.4.A,
A2.4.C, A2.8.E
Make sure to teach and graph exponential
functions by hand using point-ratio form
Make sure to do an problems like the following
for SAT prep:
3
81x5  3x 3 3x2
Need additional supplements on simplifying
square roots
Look at Algebra 1 book unit 6 for additional
resources
5-4
^ Applications of Exponential and Power Equations
2
5-5
Building Inverses of Functions
2
5-6
^ Logarithmic Functions
2
5-7
Properties of Logarithms
2
5-8
Applications of Logarithms
2 Quizzes, Review, Test
O
2
Make sure to graph by hand exponential and
power functions
A2.1.A, A2.1.D,
A2.4.C, A2.6.E,
A2.8.A, A2.8.B,
A2.8.C, A2.8.F,
A2.8.H
Make sure to graph by hand logarithmic
functions
A2.1.D, A2.4.A,
A2.4.B, A2.4.C
A2.4.A, A2.4.C,
A2.8.G
Optional
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Optional Unit 5
8/24/2011
e/ln Exploration
^ For all parent functions and relations, students should be able to identify the x-intercept(s), y-intercept, domain, range, asymptote(s) and sketch the graph.
Big Idea:



Lesson
e
Discover the natural exponential and natural logarithm
Convert between natural exponential and natural logarithmic forms.
Use e and ln functions to graphically and algebraically model real-world growth and decay scenarios.
Objective
Natural exponential
Priority # of Days
O
1
Notes
Optional
Supplemental Worksheets for Exploration and
homework needed.
ln
Natural logarithm
O
1
Optional
Supplemental Worksheets for in class
investigation and homework needed.
Review, Quiz
Standards
A2.1.D, A2.4.A,
A2.4.B, A2.4.C,
A2.8.E
A2.1.A, A2.1.D,
A2.4.A, A2.4.C,
A2.6.E, A2.8.B,
A2.8.C, A2.8.F,
A2.8.H
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 2
8/24/2011
Describing Data
Big Ideas:



Create, interpret, and compare box plots and histograms of data sets.
Calculate the five-number summary to understand and interpret a data set.
Calculate measures of central tendency (mean, median and mode), percentile ranks and standard deviation
Unit 11
Applications of Statistics
Big Ideas:



Learn different ways to collect data as part of designing a study
Apply different methods for making predictions
Study populations distributions, fit functions to data and develop predictions
*Since these units are being combined, we need to determine if we want to use sample or population standard deviation.
Lesson
2-1, 2-2,
2-3
Objective
Box Plots, Standard Deviation, Histograms and
Percentile Ranks
Priority # of Days
2-3
Notes
Also cover five-point summary and be able to
explain an outlier.
Calculate standard deviation by hand for small
data sets given the equation
Could do as a team test or scavenger hunt.
11.2
Understand the Difference Between a Parameter
and a Statistics
1
Cover vocabulary on pg. 624
Lesson can be investigation pg. 625 where
students create a relative frequency histogram
and probability distribution
Assign problem #12
Standards
A2.6.F, A2.8.A,
A2.8.E, A2.8.F,
A2.8.H
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
11.3
Normal Distribution
3
8/24/2011
Could use #12 from 11.2 to explain normal
distribution, standard deviations as points of
inflection
A2.6.F
Introduce 68-95-99.7; may want to do
investigation for this
Fathom explorations can be a class demo
Dynamic Exploration from unit 13 in first edition
of book (see bottom of pg 634)
11.4
Z-Values and Confidence Interval
2
Students do not need to know or use the
equation for normal distribution
Could use a z-table instead of calculator
Great investigation
Students can be give the confidence interval
formula
Review, Test
A2.6.F, A2.6.G,
A2.8.H
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 7
8/24/2011
Quadratic and Other Polynomial Functions
Big Ideas:









lesson
7-1
Add, subtract and multiply polynomial expressions.
Find quadratic functions that fit a set of data.
Study quadratic functions and their graphs in general form, vertex form, and factored form.
Find roots of a quadratic equation by factoring and by using the quadratic formula
Define complex numbers and operations with them.
Identify features of the graphs of a polynomial functions including zeros, intercepts, end behavior, and local max/min.
Write equations from graphs of higher-degree polynomials
Sketch graphs of higher-degree polynomial equations
Use division to find roots of higher-degree polynomials.
Objective
Polynomial Degree and Finite Differences
Priority # of Days
2
Notes
Use one day to review factoring (need
supplements).
Determine the degree of a polynomial by using
finite differences.
Standards
A2.1.C, A2.3.C,
A2.6.E, A2.8.A,
A2.8.B, A2.8.C,
A2.8.D, A2.8.F,
A2.8.H
7-2
Equivalent Quadratic Forms
3
A2.1.C, A2.3.A,
A2.3.B, A2.3.C,
A2.6.E, A2.8.E,
A2.8.H
7-3
Completing the Square
2
A2.3.A, A2.3.C,
A.2.6.E
7-4
The Quadratic Formula
2
A2.1.C, A2.3.B,
A2.3.C, A2.6.E
7-5
Complex Numbers
2
A2.1.C, A2.2.A,
A2.3.B, A2.3.C
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
7-6
Factoring Polynomials
2
7-7
Higher-Degree Polynomials
2
8/24/2011
A2.1.C, A2.2.A,
A2.3.A, A2.3.C,
A2.5.D
Include double and triple roots (see miniinvestigation #6)
A2.5.D
Local minimums and maximums are found
graphically
7-8
More About Finding Solutions
2/3 Quizzes, Review, Test
2
A2.5.D, A2.8.H
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 8
8/24/2011
Rational Functions
^ For all parent functions and relations, students should be able to identify the x-intercept(s), y-intercept, domain, range, asymptote(s) and sketch the graph.
Big Ideas:
1
1
and 2 and their transformations
x
x

Parent functions


Study rational functions and determine their properties of their graphs and equations.
Add, subtract, multiply, and divide rational expressions.
Lesson
8-6
Objective(s)
^ Introduction to Rational Functions
8.7
^ Graphs of Rational Function
2
8.8
Operations with Rational Expressions
2
Review, Test
Priority # of days
2
Notes
Graph and transform
1
x
Graph and transform
1
x2
Standards
A2.1.A, A2.1.E,
A2.5.C
A2.2.C
A2.2.C
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 12
8/24/2011
Trigonometry
Big ideas:
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


Use sine, cosine, and tangent
Use the Laws of Sines and Cosines
Properties of special right triangles
Reference Angles
Lesson
12.1
Objective
Right Triangle Trigonometry
12.2
Law of Sines
2
12.3
Law of Cosines
2
12.4
Reference Angles, Beginning of the Unit Circle
1
Review, Test
Priority # of Days
2
Notes
Cosecant, secant, and cotangent are optional
(13-6)
Ambiguous case is optional
Standards
A2.8.E
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 13
8/24/2011
Trigonometric Functions
^ For all parent functions and relations, students should be able to identify the x-intercept(s), y-intercept, domain, range, asymptote(s) and sketch the graph.
Big ideas:








Coterminal angles
Parents functions: sine and cosine
Basic modeling of the sine and cosine functions
Converting between radians and degrees.
Write out the unit circle.
Use the unit circle to find values of sine and cosine
Find angle values given sine and cosine values.
Transformations of trigonometric function graphs.
Lesson
13-1
Objective
Intro to Circular Functions and the Unit Circle
13-2
Radians
Priority # of Days
2
2
Notes
Coterminal angles worksheet
Standards
Do not include area of sectors and arc length
A2.8.E
Add Unit Circle
13-3
^ Graphing Trigonometric Functions
4
Supplemental worksheets, breaking down the
transformations.
A2.1.A, A2.8.D,
A2.8.E
Optional exploration to graph tangent function
13-5
Modeling Trigonometric Functions
2
Keep it basic and may be embedded in earlier
sections
Use supplemental worksheets
2/3 Quizzes, Review, Test
A2.8.A, A2.8.B,
A2.8.C, A2.8.F,
A2.8.H
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 9
8/24/2011
Series
Big Idea:




Lesson
9-1
Distinguish between arithmetic and geometric series
Write explicit formulas for series with sigma notation.
Find the sum of a finite numbers of terms of an arithmetic or geometric series.
Determine when an infinite geometric series has a sum and find the sum if it exists
Objective(s)
Arithmetic Series
Priority # of days
1
Notes
Be prepared to refresh arithmetic and geometric
sequences and writing them recursively and
explicitly
Standards
A2.7.B, A2.8.G
Do sigma notation worksheet.
9-2
Infinite Geometric Series
2
A2.7.B, A2.8.G
9-3
Partial Sums of Geometric Series
2
A2.7.B, A2.8.G
Algebra 2 Pacing Guide developed during the 2010-11 school year with comments from the summer 2011 workgroup
Unit 10
8/24/2011
Probability
Big Idea:
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






Count numbers of possibilities to determine probabilities.
Distinguish between theoretical and experimental probabilities
Tree diagrams and Venn diagrams
Permutations vs. Combinations
Binomial theorem
Pascal’s triangle to expand binomials and find combinations
Calculate binomial probabilities
Mutually exclusive and conditional probability
Lesson
10-1
Objective(s)
Randomness and Probability
10-2
Counting and Tree Diagrams
2
A2.6.A, A2.6.B,
A2.8.B
10-3
Mutually Exclusive Events
1
A2.6.A, A2.6.B
10-5
Permutations
1
A2.6.A, A2.6.C,
A2.8.E
10-6
Combinations
2
A2.6.A, A2.6.C
A2.8.E
10-7
Binomial Theorem and Pascal’s Triangle
2
A2.6.C, A2.6.D
2 Quizzes, Review, Test
Priority
# of days
1
Notes
Standards