Williamsport Area School District
Mathematics
Grade(s): 10/11
Course Title:
Academic Algebra II
Unit
Unit Title
1
Operations with Complex Numbers
2
Non-Linear Expressions
3
Factoring Polynomials
4
Non-Linear Expressions Involving
Polynomials
5
Solving and Applying Quadratic
Equations
6
Solving Equations Involving Rational
and Radical Expressions
Duration
(Days)
Algebra 2
Williamsport Area School District
Unit 1: Operations with Complex Numbers
Days:
Big Idea: Complex Numbers
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 2
Williamsport Area School District
Concept 1.1
Simplify square roots in terms of i
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do we simplify square roots in terms of i?
Square roots, cube roots, radical, radicand, index
Descriptor
Eligible
Content
1.1.A
Simplifying square roots expressions (not
involving i)
A2.1.1.1.1
1.1.B
Simplifying cube roots expressions (not
involving i)
A2.1.1.1.1
1.1.C
Simplifying all radical expressions
A2.1.1.1.1
1.1.D
Simplify radicals involving fractions
A2.1.1.1.1
Days
Resources:
Assessment Sources:
Notes:
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
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 2
Williamsport Area School District
Concept 1.2
Simplify expressions involving powers of i
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I simplify expressions involving powers of i?
Imaginary number, power, exponent, base
Descriptor
Eligible
Content
1.2.A
Simplifying powers of i
A2.1.1.1.2
1.2B
Multiplying powers of i
A2.1.1.1.2
Days
Resources:
Assessment Sources:
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Notes:
Page 4
Algebra 2
Williamsport Area School District
Concept 1.3
Add/Subtract complex numbers
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I add and subtract complex numbers?
Complex numbers, like terms, monomial, binomial
Descriptor
Eligible
Content
1.3.A
Adding complex numbers
A2.1.1.2.1
1.3.B
Subtracting Complex numbers
A2.1.1.2.1
Days
Resources:
Assessment Sources:
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Notes:
Page 5
Algebra 2
Williamsport Area School District
Concept 1.4
Multiply/Divide complex numbers
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I multiply and divide complex numbers?
Complex numbers, conjugate, binomial conjugate, rationalize
Descriptor
Eligible
Content
A2.1.1.2.2
1.4.A Multiplying Complex Numbers
1.4.B
Dividing Complex Numbers
Days
A2.1.1.2.2
Resources:
Assessment Sources:
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Notes:
Page 6
Algebra 2
Williamsport Area School District
Unit 2: Non-Linear Expressions
Days:
Big Idea: Non-Linear Expressions
Unit Essential Question:
How do I perform operations involving rational exponents?
Concept
Concept Title
2.1
Represent rational numbers using exponential
expressions
2.2
Simplify expressions involving exponents
2.3
Simplify Rational Exponent expressions
involving exponent rules
Duration
(Days)
Algebra 2
Williamsport Area School District
Concept 2.1
Represent rational numbers using exponential expressions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I represent rational numbers using exponential expressions?
Exponent, base, rational exponent, index, radicand, radical, power
Descriptor
Eligible
Content
A2.1.2.1.1
2.1.A Re-Writing Radical Expressions as
Rational Exponents and Simplify
2.1.B
Re-Writing Rational Exponents as
Radical Expressions and Simplify
A2.1.2.1.1
2.1.C
Simplifying negative rational exponents
A2.1.2.1.1
Days
Resources:
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Notes:
Page 8
Algebra 2
Williamsport Area School District
Concept 2.2
Simplify expressions involving exponents
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I simplify expressions involving exponents?
Exponent, power, base, rational exponent, reciprocal
Descriptor
Eligible
Content
2.2.A
Negative and Zero Exponent Rule
A2.1.2.1.1
2.2.B
Product and Quotient Rule
A2.1.2.1.1
2.2.C
Power of Powers
A2.1.2.1.1
2.2.D
Power of Products
A2.1.2.1.1
2.2.E
Power of Quotients
A2.1.2.1.1
Days
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Notes:
Page 9
Algebra 2
Williamsport Area School District
Concept 2.3
Simplify rational exponents involving exponent rules
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I simplify rational exponents involving exponent rules?
Descriptor
Eligible
Content
A2.1.2.1.1
2.3.A
Multiply and Divide Rational Exponents
2.3.B
Power of Power With Rational Exponents A2.1.2.1.1
2.3.C
Power of Product With Rational
Exponents
2.3.D
Days
A2.1.2.1.1
A2.1.2.1.1
Power of Quotient With Rational
Exponents
Resources:
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Notes:
Page 10
Algebra 2
Williamsport Area School District
Unit 3: Factoring Polynomials
Days:
Big Idea: Factoring Polynomials
Unit Essential Question:
How do factor polynomials?
Concept
Concept Title
3.1
Factoring polynomials involving a GCF
3.2
Factoring Polynomials when a=1
3.3
Factoring Special Cases
3.4
Factoring Polynomials when a>1
Duration
(Days)
Page 11
Algebra 2
Williamsport Area School District
Concept 3.1
Factoring polynomials involving a GCF
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do you factor a polynomial involving a GCF?
Polynomial, term, factor, coefficient, GCF
Descriptor
Eligible
Content
3.1.A
Find the GCF
A2.1.2.2.1
3.1.B
Factor out the GCF
A2.1.2.2.1
Days
Resources:
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Notes:
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Page 12
Algebra 2
Williamsport Area School District
Concept 3.2
Factoring Polynomials where a=1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I factor polynomials where a=1?
Definition of division, reciprocals, rational
Descriptor
Eligible
Content
3.2.A
Determine sign rules for factoring
A2.1.2.2.1
3.2.B
Factoring Polynomials where a=1
A2.1.2.2.1
3.2C
Factoring Polynomials where a=1 after
factoring out the GCF
A2.1.2.2.1
Days
Resources:
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Notes:
Page 13
Algebra 2
Williamsport Area School District
Concept 3.3
Factoring Special Cases
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I factor special cases?
Difference of squares, sum and difference of cubes
Descriptor
Eligible
Content
Days
A2.1.2.2.1
3.3.A
Factoring difference of squares
3.3.B
Factoring Sum and Difference of Cubes
A2.1.2.2.1
3.3.C
Factoring special cases involving a GCF
A2.1.2.2.1
Resources:
Assessment Sources:
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Notes:
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Page 14
Algebra 2
Williamsport Area School District
Concept 3.4
Factoring Polynomials When a>1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I factor polynomials when a>1?
GCF, a value, trinomial, binomial, factor
Descriptor
Eligible
Content
3.4.A
Factoring by grouping
A2.1.2.2.1
3.4.B
Factoring polynomials when a>1
A2.1.2.2.1
3.4.C
Factoring polynomials when a>1 and
there is a GCF involved
A2.1.2.2.1
Days
Resources:
Assessment Sources:
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Notes:
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Page 15
Algebra 2
Williamsport Area School District
Unit 4: Non-Linear Expressions-involving polynomials
Days:
Big Idea: Simplify expressions involving polynomials.
Unit Essential Question:
How do you simplify expressions involving polynomials?
Concept
Concept Title
4.1
Simplifying Rational Expressions
4.2
Multiplying and Dividing Rational
Expressions
4.3
Add and Subtract Rational Expressions
Duration
(Days)
Page 16
Algebra 2
Williamsport Area School District
Concept 4.1
Simplifying Rational Expressions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do you simplify rational expressions?
Rational Expressions, term, factor, simplify
Descriptor
Eligible
Content
4.1.A
Term vs. Factor
A2.1.2.2.2
4.1.B
Simplifying Monomial Rational
Expressions
A2.1.2.2.2
4.1.C
Simplifying Binomial Rational
Expressions
A2.1.2.2.2
Days
A2.1.2.2.2
4.1.D
Simplifying Trinomial Rational
Expressions
Resources:
Assessment Sources:
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Notes:
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Page 17
Algebra 2
Williamsport Area School District
Concept 4.2
Multiplying and Dividing Rational Expressions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I multiply and dividing rational expressions?
Rational expression, factor, term, reciprocal
Descriptor
Eligible
Content
4.2.A
Multiplying Rational Expressions
A2.1.2.2.2
4.2.B
Dividing Rational Expressions
A2.1.2.2.2
Days
Resources:
Assessment Sources:
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Notes:
Page 18
Algebra 2
Williamsport Area School District
Concept 4.3
Adding and Subtracting Rational Expressions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I add and subtract rational expressions?
Rational expression, factor, term, LCD
Descriptor
Eligible
Content
4.3.A
Adding and Subtracting Rational
Expressions With Like Denominators
A2.1.2.2.2
4.3.B
Finding the LCD of rational expressions
A2.1.2.2.2
4.3 C
Adding and Subtracting Rational
Expressions with Unlike Denominators
A2.1.2.2.2
Days
Resources:
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Notes:
Page 19
Algebra 2
Williamsport Area School District
Unit 5: Solving and Applying Quadratic Equations
Days:
Big Idea: Solving Quadratic Equations
Unit Essential Question:
How do I solve and apply quadratic equations to real life?
Concept
Concept Title
5.1
Solving Quadratics By Graphing
5.2
Solving Quadratics By Factoring
5.3
Solving Quadratics By Completing the
Square
5.4
Solving Quadratics Using the Quadratic
Formula
Duration
(Days)
Page 20
Algebra 2
Williamsport Area School District
Concept 5.1
Solving Quadratics by Graphing
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I solve quadratics by graphing?
Solutions, roots, zero’s, vertex, line of symmetry, max/min
Descriptor
Eligible
Content
A2.1.3.1.1
5.1.A Parts of a Quadratic
5.1.B
Real Life Applications
A2.1.3.1.1
5.1.C
Solving Quadratics by Graphing
A2.1.3.1.1
Days
Resources:
Assessment Sources:
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Notes:
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Page 21
Algebra 2
Williamsport Area School District
Concept 5.2
Solving Quadratics By Factoring
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I solve quadratics by factoring?
Solutions, roots, zero’s, vertex, line of symmetry, max/min
Descriptor
Eligible
Content
A2.1.3.1.1
5.2.A Solving quadratics by factoring where
a=1
A2.1.3.1.1
5.2.B
Solving quadratics by factoring involving
special cases
A2.1.3.1.1
5.2.C
Solving quadratics by factoring where
a>1
Days
Resources:
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Notes:
Page 22
Algebra 2
Williamsport Area School District
Concept 5.3
Solving Quadratics by Completing the Square When a=1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I solve quadratics by completing the square?
Solutions, roots, zero’s, vertex, line of symmetry, max/min
Descriptor
Eligible
Content
A2.1.3.1.1
5.3.A Solving Quadratics Using Square Roots
5.3.B
Find the C-Value of a quadratics
A2.1.3.1.1
5.3.C
Solving Quadratics by Completing the
Square
A2.1.3.1.1
Days
Resources:
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Notes:
Page 23
Algebra 2
Williamsport Area School District
Concept 5.4
Solving Quadratics Using The Quadratic Formula
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I solve quadratics using the quadratic formula?
Solutions, roots, zero’s, vertex, line of symmetry, max/min
Descriptor
Eligible
Content
A2.1.3.1.1
5.4.A Finding the discriminant and use it to
determine the nature of the solutions
5.4.B
Derive the quadratic formula
A2.1.3.1.1
5.4.C
Use the quadratic formula to solve
quadratic equations
A2.1.3.1.1
Days
Resources:
Assessment Sources:
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Notes:
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Page 24
Algebra 2
Williamsport Area School District
Unit 6: Solving Equations Involving Rational and Radical Expressions Days:
Big Idea: Solve equations involving rational and radical expressions
Unit Essential Question:
How do I solve equations involving rational and radical expressions?
Concept
Concept Title
6.1
Solving Rational Equations Using Cross
Multiplication
6.2
Solving Rational Equations Multiplying by the
LCD
6.3
Solving Radical Equations
Duration
(Days)
Page 25
Algebra 2
Williamsport Area School District
Concept 6.1
Solving Rational Equations Using Cross Multiplication
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I solve rational equations using cross multiplication?
Cross multiplication, quadratic, like terms, solutions
Descriptor
Eligible
Content
6.1.A
Solve Rational Equations Using Cross
Multiplication
A2.1.3.1.2
6.1.B
Identifying Extraneous Solutions
A2.1.3.1.2
6.1.C
Solve Rational Equations Using Cross
Multiplication
A2.1.3.1.2
Days
Resources:
Assessment Sources:
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Notes:
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Page 26
Algebra 2
Williamsport Area School District
Concept 6.2
Solving Rational Equations Multiplying by the LCD
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I solve rational equations with more than one rational
expression on each side?
Rational equations, LCD, Monomial, binomial
Descriptor
Eligible
Content
A2.1.3.1.2
6.2.A Find the LCD
6.2B
Monomials in the denominator
A2.1.3.1.2
6.2C
Binomials in the denominator
A2.1.3.1.2
Days
Resources:
Assessment Sources:
Notes:
Page 27
Algebra 2
Williamsport Area School District
Concept 6.3
Solving Radical Equations
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do I solve radical equations?
Radical equations, like terms, extraneous solution
Descriptor
Eligible
Content
6.3.A
Solving one-step radical equations
A2.1.3.1.2
6.3.B
Solving multi-step radical equations
A2.1.3.1.2
6.3.C
Solving radical equations involving
quadratics
A2.1.3.1.2
Days
Resources:
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Notes:
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Page 28