Williamsport Area School District
Mathematics
Grade(s): 9
Course Title:
Algebra 2 Honors
Unit
Unit Title
Duration
(Days)
1
Operations with Complex Numbers
25
2
Non-Linear Expressions
25
3
Non-Linear Expressions-involving
polynomials
25
4
Non-Linear Equations
30
5
Patterns, Relations and Functions
25
6
Applications of Functions
25
7
Data Analysis
25
Algebra I
Williamsport Area School District
Unit 1: Operations with Complex Numbers
Days: 25
Big Idea: What is a complex number?
Unit Essential Question:
How do I perform operations with complex numbers?
Concept
Concept Title
1.1
Simplify square roots in terms of i
1.2
Simplify expressions involving powers of i
1.3
Add/Subtract complex numbers
1.4
Multiply/Divide complex numbers
Duration
(Days)
Algebra I
Williamsport Area School District
Concept 1.1
Simplify square roots in terms of i
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I perform operations with complex numbers?
See unit preview document
Descriptor
1.1.A
Simplifying square roots expressions (not
involving i)
1.1.B
Simplifying cube roots expressions (not
involving i)
A2.1.1
1.1.C
Simplifying all radical expressions
A2.1.1
1.1.D
Simplify radicals involving fractions
A2.1.1
Resources:
Unit 1 Binder and files
Assessment Sources:
Add
Notes:
Eligible
Content
A2.1.1
Days

Drill perfect square and perfect cube factors (students should have
perfect squares and cubes memorized up to 12)

Only touch on the definition i = -1 . (Do not go further with
exponents on i)
Page 3
Algebra I
Williamsport Area School District
Concept 1.2
Simplify expressions involving powers of i
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I perform operations with complex numbers?
See Unit 1 Preview document
Descriptor
1.2.A
Simplify powers of i.
1.2.B
Multiply monomials involving powers of i.
Resources:
Unit 1 Binder and files
Assessment Sources:
Add
Eligible
Content
A2.1.1
Days
A2.1.1
Notes:
Page 4
Algebra I
Williamsport Area School District
Concept 1.3
Add/Subtract complex numbers
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I perform operations with complex numbers?
See Unit 1 Preview document
Descriptor
1.3.A
Add & subtract complex numbers (using i).
1.3.B
Add & subtract complex numbers when radicals
are not simplified (including a negative under the
square root)
Resources:
Unit 1 Binder and files
Assessment Sources:
Add
Eligible
Content
A2.1.1
Days
A2.1.1
Notes:
Page 5
Algebra I
Williamsport Area School District
Concept 1.4
Multiply/Divide complex numbers
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I perform operations with complex numbers?
See Unit 1 Preview document
Descriptor
1.4.A
Multiply & divide complex numbers (using i).
Eligible
Content
A2.1.1
1.4.B
Multiply & divide complex numbers when
radicals are not simplified (including a negative
under the square root).
A2.1.1
Resources:
Unit 1 binder and files
Assessment Sources:
Add
Days
Notes:
Page 6
Algebra I
Williamsport Area School District
Unit 2: Non-Linear Expressions
Days: 25
Big Idea: How do I simplify non-linear expressions?
Unit Essential Question:
How do I simplify non-linear expressions using exponent and logarithmic properties?
Concept
Concept Title
2.1
Represent rational numbers using exponential
expressions
2.2
Simplify expressions involving
exponents(numeric and algebraic)
2.3
Simplify expressions involving logarithms
Duration
(Days)
Algebra 2
Williamsport Area School District
Concept 2.1
Represent rational numbers using exponential expressions
Lesson Essential
Question(s):
How do I simplify non-linear expressions using exponent and logarithmic
properties?
Vocabulary:
Learning Goals:
See Unit 2 preview document
Descriptor
2.1.A
Convert expressions between radical and
exponential form
2.1.B
Simplify and evaluate exponential
expressions involving rational exponents
and negative exponents.
Resources:
Unit 2 binder and files
Assessment Sources:
Add
Eligible
Content
A2.1.2
Days
A2.1.2
Notes:
Page 8
Algebra 2
Williamsport Area School District
Concept 2.2
Simplify expressions involving exponents
Lesson Essential
Question(s):
How do I simplify non-linear expressions using exponent and logarithmic
properties?
Vocabulary:
Learning Goals:
See unit 2 preview document
Descriptor
2.2.A
Simplify expressions involving all
exponent rules (positive, negative and
rational)
2.2.B
Simplify numerical expressions involving
exponents(positive, negative and rational)
2.2C
Resources:
Simplify algebraic expressions involving
exponents (positive, negative and
rational)
Unit 2 binder and files
Assessment Sources:
Add
Eligible
Content
A2.1.2
Days
A2.1.2
A2.1.2
Notes:
Page 9
Algebra 2
Williamsport Area School District
Concept 2.3
Simplify expressions involving exponent rules
Lesson Essential
Question(s):
How do I simplify non-linear expressions using exponent and logarithmic
properties?
Vocabulary:
Learning Goals:
See unit 2 preview document
Descriptor
2.3.A
Convert from exponential to log notation
2.3.B
Simplify and evaluate numerical
expressions involving logarithms (ex.
Simplify
,
Eligible
Content
A2.1.2
Days
A2.1.2
) inverse
properties and 1 to 1 properties
2.3.C
Condense or expand algebraic
expressions involving logarithms
Resources:
Unit 2 binder and files
Assessment Sources:
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A2.1.2
Notes:
Page 10
Algebra 2
Williamsport Area School District
Unit 3: Non-Linear Expressions-involving polynomials
Days: 25
Big Idea: Simplify expressions involving polynomials.
Unit Essential Question:
How do you simplify expressions involving polynomials?
Concept
Concept Title
3.1
Factoring polynomials
3.2
Multiply/Divide rational expressions
3.3
Add/Subtract rational expressions
3.4
Simplify Complex fractions
Duration
(Days)
Page 11
Algebra 2
Williamsport Area School District
Concept 3.1
Factoring polynomials
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do you indentify the appropriate factoring method?
Polynomial, term, factor, coefficient, perfect square, degree, linear factor
Descriptor
Eligible
Days
Content
3.1.A Factoring Quadratics
A2.1.2
3.1.B
Factoring nth degree polynomials
Resources:
Unit 3 binder and files
Assessment Sources:
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Notes:
Add
A2.1.2
Page 12
Algebra 2
Williamsport Area School District
Concept 3.2
Multiply/Divide rational expressions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How can you apply basic rules of fractions to multiplying and dividing
rational expressions?
Definition of division, reciprocals, rational
Descriptor
Eligible
Days
Content
3.2.A Multiply rational expressions
A2.1.2
3.2.B
Divide rational expressions
Resources:
Unit 3 binder and files
Assessment Sources:
Add
A2.1.2
Notes:
Page 13
Algebra 2
Williamsport Area School District
Concept 3.3
Add/Subtract rational expressions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How can you apply basic rules of fractions to adding and subtracting
rational expressions?
Descriptor
Eligible
Content
A2.1.2
3.3.A
Finding a common denominator
(including factoring)
3.3.B
Adding rational expressions
A2.1.2
3.3.C
Subtracting rational expressions
A2.1.2
Resources:
Unit 3 binder and files
Assessment Sources:
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Notes:
Add
Days
Page 14
Algebra 2
Williamsport Area School District
Concept 3.4
Simplify Complex Fractions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do you apply the rules for dividing fractions in order to simplify
complex, equivalent fractions?
Descriptor
Eligible
Content
A2.1.2
3.3.A
Simplify complex fractions (monomials
only)
3.3.B
Involving just factoring
A2.1.2
3.3.C
Involving addition/ subtraction and
factoring
A2.1.2
Resources:
Unit 3 binder and files
Assessment Sources:
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Notes:
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Days
Page 15
Algebra 2
Williamsport Area School District
Unit 4: Non-Linear Equations
Days: 30
Big Idea: How do I solve non-linear equations?
Unit Essential Question:
What are the solutions to non-linear equations and how do I determine if they are extraneous?
Concept
Concept Title
4.1
Write and Solve Quadratics
4.2
Solve equations involving rational and
radical expressions
4.3
Write and solve simple exponential or
logarithmic equations
4.4
Write and solve linear or exponential growth
or decay applications
Duration
(Days)
Page 16
Algebra 2
Williamsport Area School District
Concept 4.1
Solve Quadratics
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How can you find the solutions to a quadratic equation?
Zero, solutions, x-intercepts, roots, discriminant, zero product property
Descriptor
Eligible
Days
Content
4.1.A Graphing
A2.1.3
4.1.B
Factoring
A2.1.3
4.1.C
Completing the square
A2.1.3
4.1.D
Quadratic Formula
A2.1.3
Resources:
Unit 4 binder and files
Assessment Sources:
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Notes:
Add
Page 17
Algebra 2
Williamsport Area School District
Concept 4.2
Solve equations involving rational and radical expressions
Lesson Essential
Question(s):
What are the solutions to non-linear equations and how do I determine if
they are extraneous?
Vocabulary:
Learning Goals:
Rational equation, extraneous solutions
Descriptor
Eligible
Content
A2.1.3.1
4.2.A
Solve rational equations (cross multiply
and set equal to zero)
4.2.B
Multiply by LCD (rational equations)
A2.1.3.1
4.2.C
Radical Equations
A2.1.3.1
Resources:
Unit 4 binder and resources
Assessment Sources:
Add
Days
Notes:
Page 18
Algebra 2
Williamsport Area School District
Concept 4.3
Solve simple exponential or logarithmic equations
Lesson Essential
Question(s):
What are the solutions to non-linear equations and how do I determine if
they are extraneous?
Vocabulary:
Exponential equations, logarithmic equation, extraneous solutions, 1-to-1
properties, condense, expand
Descriptor
Eligible
Days
Content
4.3.A Exponential---1 to 1 property
A2.1.3.1
Learning Goals:
4.3.B
Exponential--- Using log rules
A2.1.3.1
4.3.C
Logarithmic—1 to 1 properties
A2.1.3.1
4.3.D
Logarithmic—Using exponential rules
A2.1.3.1
Resources:
Unit 4 binder and files
Assessment Sources:
Add
Notes:
Page 19
Algebra 2
Williamsport Area School District
Concept 4.4
Write and solve linear or exponential growth or decay
applications
Lesson Essential
Question(s):
What are the solutions to non-linear equations and how do I determine if
they are extraneous?
Vocabulary:
Exponential growth and decay, simple interest, compound interest,
continuous growth, half-life, double or triple time
Descriptor
Eligible
Content
4.4.A Growth
A2.1.3.1
Learning Goals:
4.4.B
Decay
A2.1.3.1
4.4.C
Compound interest
A2.1.3.1
Resources:
Unit 4 binder and files
Assessment Sources:
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Notes:
Add
Days
Page 20
Algebra 2
Williamsport Area School District
Unit 5: Patterns, Relations and Functions
Days: 25
Big Idea: How do I analyze information from patterns, relations and functions?
Unit Essential Question:
How do I analyze information from data and functions for specific characteristics such as domain, range,
and intervals?
Concept
Concept Title
5.1
Analyze data to represent algebraic patterns
5.2
Identify/extend arithmetic or geometric
sequences
Domain, range and inverse of a function
5.3
5.4
Duration
(Days)
Identify characteristic of non-linear
functions
Page 21
Algebra 2
Williamsport Area School District
Concept 5.1
Analyze data to represent algebraic patterns
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I analyze information from data and functions for specific
characteristics such as domain, range, and intervals.
Arithmetic and geometric sequence, common ratio, common difference
Descriptor
Eligible
Days
Content
5.1.A Write an algebraic expression to model a pattern. (pg
A2.2.1.1.1
794 section 12.1)
5.1.B
Write a rule and extend and arithmetic sequence (pg
802 section 12.2)
A2.2.1.1.2
Write a rule and extend and geometric sequence (pg
810 section 12.3)
5.1.C
Resources:
Unit 5 binder and files
Assessment Sources:
Add
Notes:
Add
A2.2.1.1.2
Page 22
Algebra 2
Williamsport Area School District
Concept 5.2
Identify/extend arithmetic or geometric sequences
Lesson Essential
Question(s):
Vocabulary:
How do I analyze information from data and functions for specific
characteristics such as domain, range, and intervals.
Parent functions, domain, range, increase, decrease and constant intervals,
horizontal and vertical asymptote
Descriptor
Eligible
Days
Content
5.2.A Recognizing parent function by their graph or equation
A2.2.1.1.3
Learning Goals:
(Supplement)
Domain and Range of parent functions. (Supplement)
5.2.B
5.2.C
State increasing or decreasing intervals, local Max,
Local Min, horizontal asymptotes, and(or) vertical
asymptotes for parent functions. (Supplement)
A2.2.1.1.3
A2.2.1.1.4
Resources:
Assessment Sources:
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Notes:
Page 23
Algebra 2
Williamsport Area School District
Concept 5.3
Domain, range and inverse of a function
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I analyze information from data and functions for specific
characteristics such as domain, range, and intervals.
Inverse functions
Descriptor
Eligible
Content
5.3.A State the domain and range of a function given the
A2.2.1.1.4
Days
graph. (Supplement
5.3.B
Write the inverse equation for a given function. State
the domain and range. (Supplement)
Resources:
Unit 5 binder and files
Assessment Sources:
Add
A2.2.1.1.3
Notes:
Page 24
Algebra 2
Williamsport Area School District
Concept 5.4
Identify characteristic of non-linear functions
Lesson Essential
Question(s):
Vocabulary:
How do I analyze information from data and functions for specific
characteristics such as domain, range, and intervals.
Polynomial, zeros, roots, factors, solutions, relative maximum, relative
minimum
Descriptor
Eligible
Days
Content
5.4.A Identify the characteristics of a polynomial function.
A2.2.1.1.4
Learning Goals:
(pg 337 section 5.2)
5.4.B
5.4.C
Identify the characteristics of radical functions (pg 446
section 6.5)
Identify the characteristics of exponential and
logarithmic functions (Pg 478 section 4.1 and 4.2, pg
499 section 4.4)
A2.2.1.1.3
A2.2.2.1.2
Identify the characteristics of rational functions. (Pg
558 section 8.2, pg 565 section 8.3)
5.4D
Resources:
Unit 5 binder and files
Assessment Sources:
Add
Notes:
Add
A2.2.2.1.2
Page 25
Algebra 2
Williamsport Area School District
Unit 6: Applications of Functions
Days: 25
Big Idea: Mastering the characteristics of the family of functions: absolute value, quadratic, cubic,
square roots, rational, logarithmic and exponential.
Unit Essential Question:
Students should be able to describe the changes of family of functions through graphs, tables and equations
Concept
Concept Title
6.1
Create and interpret graphs/tables/equations of
polynomial functions
6.2
Create and interpret graphs/tables/equations of
exponential and logarithmic functions
6.3
Describe the effect of changing parameters
within family of functions
Duration
(Days)
Page 26
Algebra 2
Williamsport Area School District
Page 27
Algebra 2
Williamsport Area School District
Concept 6.1
Create and interpret graphs/tables/equations of polynomial
functions
Lesson Essential
Question(s):
Vocabulary:
Can I describe the changes of family of functions through graphs, tables and equations
Learning Goals:
Zeros, factors, solutions, roots, zeros, max, min and asymptotes, end
behavior, domain, range
Descriptor
Eligible
Days
Content
6.1.A Graphing polynomial functions
A2.2.2.1
6.1.B
Identify values, zeros, max, min and
asymptotes, end behavior
A2.2.2.1
6.1.C
Determine zeros of functions given a
table
A2.2.2.1
Resources:
Unit 6 binder and files
Assessment Sources:
Add
Notes:
Add
Page 28
Algebra 2
Williamsport Area School District
Concept 6.2
Create and interpret graphs/tables/equations of exponential
and logarithmic functions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Can I describe the changes of family of functions through graphs, tables and equations
Asymptotes, domain, range
Descriptor
6.2.A
Graphing logarithmic/exponential
functions
6.2.B
Determine the domain, range and
asymptotes of logarithmic and
exponential functions
Eligible
Content
A2.2.2.1
Days
A2.2.2.1
Resources:
Assessment Sources:
Notes:
Page 29
Algebra 2
Williamsport Area School District
Concept 6.3
Describe the effect of changing parameters within family of
functions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Can I describe the changes of family of functions through graphs, tables and equations
Transformations, functions, shifts
Descriptor
Eligible
Content
A2.2.2.2
6.3.A
Determine the different types of
transformations of a function
6.3.B
Compare and contrast graphs of a
function given the transformations
A2.2.2.1
6.3.C
Identify functions given a table or a graph
A2.2.2.1
Resources:
Unit 6 binder and files
Assessment Sources:
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Notes:
Add
Days
Page 30
Algebra 2
Williamsport Area School District
Unit 7: Data Analysis
Days: 25
Big Idea: How do you interpret and extrapolate data in order to predict future outcomes?
Unit Essential Question:
Can I interpret and analyze data to determine the best model of representation.
Concept
Concept Title
7.1
Draw/interpret scatterplots
7.2
Apply probability to practical situations
Duration
(Days)
Page 31
Algebra 2
Williamsport Area School District
Concept 7.1
Draw/interpret scatter plots
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Can I interpret and analyze data to determine the best model of representation.
Line of fit, regression, extrapolate
Descriptor
7.1.A
Draw/write the lines and curves of best fit
7.1B
Gather data represented by non-linear models and write
the equation to fit using the ti-84+
7.1C
Use the regression model
to predict future outcomes.
Resources:
Unit 7 binder and files
Assessment Sources:
Add
Eligible
Content
A2.2.3.1
Days
A2.2.3.1
A2.2.3.1
Notes:
Page 32
Algebra 2
Williamsport Area School District
Concept 7.2
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Apply probability to practical situations
Can I interpret and analyze data to determine the best model of representation.
Probability, odds, independent, dependent, and compound events,
Fundamental Counting Principle, combinations and permutations
Descriptor
Eligible
Content
7.2.A Use odds and probability to define odds
A2.2.3.2
and probability
7.2B
Determine probability of independent,
dependent, and compound events to
predict outcomes
A2.2.3.2
7.2C
Use the Fundamental Counting Principle
to solve problems involving probability
A2.2.3.2
Use combinations and permutations to
solve problems involving probability
A2.2.3.1
7.2D
Resources:
Days
Unit 7 binder and files
Assessment Sources:
Notes:
Page 33
Algebra 2
Concept 7.3
Williamsport Area School District
Apply probability to practical situations
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Descriptor
7.3.A
Use odds and probability to define odds
and probability
7.3.B
Determine probability of independent,
dependent, and compound events to
predict outcomes
7.3.C
Use the Fundamental Counting Principle
to solve problems involving probability
7.3.D
Use combinations and permutations to
solve problems involving probability
Eligible
Content
Days
Resources:
Assessment Sources:
Add
Notes:
Add
Page 34