LHS Curriculum
Lakeview High School
Algebra II
Curriculum Alignment Document
“Home of the Wildcats”
Revised May, 2010
LHS Curriculum
Lakeview Community Schools
High School Mathematics Power Standards
Algebra 1, Algebra 2, Trigonometry & Pre-Calculus
Representation: Given a graphic, tabular, or symbolic representation, students will be able to produce the other two
representations, describe the behavior, identify and interpret key features, evaluate, and find solutions.
Graph: Given a verbal, tabular, or symbolic representation, students will be able to create a graphical
representation. Further, students will be able to identify and interpret the key features of an equation, inequality, or
system from its graph (i.e zeros, intercepts, trends, end behavior); solve/evaluate functions using the graphical
representation.
Table: Given a verbal, graphical, or symbolic representation, students will be able to generate a tabular
representation. Further, students will be able to read and interpret the key features (i.e. zeros, intercepts, trends, end
behavior) of a function from its table.
Symbolic: Given a verbal, tabular, or graphical representation of a function(s), students will be able to write an
expression, equation, inequality, or system. Further, students will be able to identify and interpret the key features
of a function from its equation (i.e zeros, intercepts, trends, end behavior); solve/evaluate functions using the
symbolic representation.
Manipulation: Through the manipulation of real numbers and/or algebraic expressions, students will distinguish
between and perform the processes of evaluating, simplifying, solving, and justifying.
Transformation: Given a parent function, students will be able to identify and model applicable changes numerically,
symbolically and graphically.
Analysis & Prediction: In a given real-world situation, students will be able to analyze data to draw reasonable
conclusions and predict outcomes (i.e. end term behavior, domain/range, maximum/minimum, correlation/regression).
Notes:
These Power Standards were written by Deb Ferry and colleagues at Macomb Intermediate School District for Algebra
1 and Algebra 2. Refer to the original documents (http://mathematicspowerstandards.weebly.com/index.html)
For details of Lakeview Community Schools High School mathematics unit organization, refer to the following
curriculum document pages. In addition, each power standard included several HSCEs, and many HSCEs also repeat
in each power standard. Refer to the Power Standards Matrix (11x17) document for details.
LHS Curriculum
Algebra II
Quadratic Equations and Functions (With Complex Numbers)
4 Weeks
High School Content expectation(s) or related standard: A1.1.1, A1.1.3, A1.2.1,
A1.2.2, A1.2.3, A1.2.8, A2.1.1, A2.1.2, A2.1.3, A2.1.6, A2.1.7, A2.2.1, A2.2.2,
A2.2.3, A2.3.2, A2.3.3, A2.4.1, A2.4.2, A2.4.3, A3.3.1, A3.3.2, A3.3.4, A3.3.5,
L1.1.1, L1.1.2, L1.1.3, L1.2.1
Prior Knowledge: Working with Simple Square Roots, Working with Variables, Multiplying
Binomials, Factoring Trinomials, Working with Functions Graphically By Hand and With a
Graphing Calculator, Working with Geometric Translations, Manipulating Algebra Tiles,
Understanding Symmetry
Key Concepts/Vocabulary: Square Root, Principal Square Root, Radical Symbol, Imaginary
Unit, Imaginary Number, Complex Numbers with Real and Imaginary Parts, Parabola,
Quadratic Function, Vertex, Parent Function, Complete the Square, Quadratic Equation,
Standard Form, Roots, Zeros, Principle of Zero Products, Quadratic Formula, Discriminant,
Conjugate, Double Root
Teaching Focus/Objectives:
Suggested Activities
Assessments
(i.e. “The learner will”)
The learner will simplify
square root expressions
and examine mathematical
structures within the real
and complex numbers.
Chapter 4-3 Parts B and C Focus
on Advanced Algebra
Warm-Up Quizzes
Chapter 4 Test
The learner will understand
the relationship between
quadratic functions and
their graphs.
Chapter 5-1 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 5-1 Test
The learner will solve
quadratic equations multiple
ways.
Chapter 5-2 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 5-2 Test
Additional Resources:
More Practice with Conjugates: http://www.purplemath.com/modules/radicals4.htm and
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut41_rationalize.htm
Electronic Notes
More Practice with Quadratic Functions (Worksheets): http://edhelper.com/QuadraticEquations.htm
Math Tools: Grades 3-12 book.
Algebra for All CD
LHS Curriculum
Algebra II
Polynomial Expressions, Equations, and Functions (and Power Functions)
4 Weeks
High School Content expectation(s) or related standard: A1.1.1, A1.1.3, A1.1.4,
A1.1.5, A1.2.1, A1.2.2, A1.2.8, A2.1.1, A2.1.2, A2.1.3, A2.1.6, A2.1.7, A2.2.1,
A2.2.2, A2.2.3, A2.3.2, A2.3.3, A2.4.1, A2.4.2, A2.4.3, A3.5.1, A3.5.2, A3.5.3,
A3.4.1, A3.4.2, A3.4.3, L1.1.1, L1.1.2, L1.1.3, L1.2.1
Prior Knowledge: Understanding Descending Order, Working with Exponents, Using a
Graphing Calculator, Working with Variables, Defining Minimums and Maximums of
Functions, Understanding Zeros and Roots of Functions, Factoring Trinomials,
Understanding Complex Numbers, Understanding Long Division
Key Concepts/Vocabulary: Polynomial, Degree of the Polynomial, Leading Coefficient,
Constant Term, Polynomial Function, Cubic Function, Quartic Function, Continuous, Absolute
Maximum, Relative Maximum, Absolute Minimum, Relative Minimum, Polynomial Equation,
Remainder Theorem, Factor Theorem, Rational Roots Theorem, Fundamental Theorem of
Algebra
Teaching Focus/Objectives:
(i.e. “The learner will”)
The learner will solve and
understand the properties
of polynomial functions.
The learner will solve
polynomial functions by
graphing and using division
to factor.
The learner will analyze
and interpret polynomial
models and results.
Suggested Activities
Assessments
Chapter 8-1 Focus on Advanced
Algebra
Algebra for All Building Polynomial
Functions Activity
Warm-Up Quizzes
Chapter 8-1 Test
Chapter 8-2 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 8-2 Test
Chapter 8-2 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 8-2 Test
Additional Resources:
More Practice With Polynomial Function Division: http://edhelper.com/polynomials.htm
Electronic Notes
Math Tools: Grades 3-12 book.
Algebra for All CD
LHS Curriculum
Algebra II
Rational Expressions, Equations, and Functions
2 Weeks
High School Content expectation(s) or related standard: A1.1.1, A1.1.3, A1.2.1,
A1.2.2, A1.2.3, A1.2.8, A2.1.1, A2.1.2, A2.1.3, A2.1.6, A2.1.7, A2.2.1, A2.2.2,
A2.2.3, A2.3.2, A2.3.3, A2.4.1, A2.4.2, A2.4.3, A3.6.1, A3.6.3, L1.1.1, L1.1.2,
L1.1.3, L2.1.4, L2.1.5
Prior Knowledge: Factoring Trinomials, Dividing Polynomials, Least Common Denominator
Concept, Multiplying Binomials and Polynomials
Key Concepts/Vocabulary: Rational Expressions, Least Common Denominator with
Polynomials, Asymptote, Discontinuous, Rational Function, Vertical Asymptote, Rational
Equation
Teaching Focus/Objectives:
(i.e. “The learner will”)
Suggested Activities
Assessments
The learner will write,
evaluate, multiply, divide,
and simplify rational
expressions.
Chapter 8-3 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 8-3 Test
The learner will simplify
sums and differences of
rational expressions.
Chapter 8-3 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 8-3 Test
Chapter 8-3 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 8-3 Test
The learner will solve
equations involving rational
expressions.
Additional Resources:
More Practice with Polynomials: http://edhelper.com/polynomials.htm
Math Tools: Grades 3-12 book.
Electronic Notes
Algebra for All CD
LHS Curriculum
Algebra II
Sequence and Series
2 Weeks
High School Content expectation(s) or related standard: A1.1.1, A1.1.3, A1.2.1,
A1.2.2, A1.2.3, A1.2.8, A2.1.1, A2.1.2, A2.1.3, A2.1.6, A2.1.7, A2.2.2, A2.2.3,
A2.3.2, A2.3.3, A2.4.1, A2.4.2, A2.4.3, L1.1.1, L1.1.2, L1.1.3, L2.1.4, L2.1.5,
L2.2.1, L2.2.2, L2.2.3
Prior Knowledge: Pattern Recognition, Modeling, Understanding Slope, Recognizing Linear
Functions Vs. Exponential Functions
Key Concepts/Vocabulary: Sequences, Terms, General Term, nth Term, Infinite Sequence,
Recursive Definition, Inductive Reasoning, Arithmetic Series, Partial Sum, Sigma Notation,
Geometric Sequence, Common Ratio, Geometric Series, Converge, Limit, Formulas for
Arithmetic and Geometric Series
Teaching Focus/Objectives:
(i.e. “The learner will”)
The learner will recognize,
represent, and generate
arithmetic sequences.
Suggested Activities
Chapter 4-1 Focus on Advanced
Algebra
The learner will find partial Chapter 4-1 Focus on Advanced
sums of arithmetic series
Algebra
and write them using sigma
notation.
The learner will recognize,
represent, and generate
geometric sequences.
Assessments
Warm-Up Quizzes
Chapter 4-1 Test
Warm-Up Quizzes
Chapter 4-1 Test
Chapter 4-2 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 4-2 Test
The learner will find the
partial sums of geometric
series.
Chapter 4-2 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 4-2 Test
The learner will investigate
the convergence of infinite
geometric series.
Chapter 4-2 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 4-2 Test
LHS Curriculum
Additional Resources:
4-1 A Lab (Explore) Exercise from the Focus on Advanced Algebra CD-Rom
4-2 A Lab (Explore) Exercise from the Focus on Advanced Algebra CD-Rom
More Practice Worksheets for Arithmetic and Geometric Sequences and Series:
http://www.kutasoftware.com/freeia2.html
Math Tools: Grades 3-12 book.
Electronic Notes
Algebra for All CD
LHS Curriculum
Algebra II
Exponential Functions and Logarithmic Functions
6 Weeks
High School Content expectation(s) or related standard: A1.1.1, A1.1.3, A1.2.1,
A1.2.2, A1.2.3, A1.2.8, A2.1.1, A2.1.2, A2.1.3, A2.1.6, A2.1.7, A2.1.8, A2.2.1,
A2.2.2, A2.2.3, A2.3.2, A2.3.3, A2.4.1, A2.4.2, A2.4.3, A3.2.1, A3.2.2, A3.2.3,
A3.2.4, A3.2.5, L1.1.1, L1.1.2, L1.1.3, L1.2.1, L2.1.4, L2.1.5
Prior Knowledge: Understanding Some of the Basic Properties of Exponents, Recognizing
Linear and Quadratic Graphs and Functions, Working with a Graphing Calculator, Using the
Distributive Property
Key Concepts/Vocabulary: Combined Variation, Inverse Variation, Joint Variation,
Rectangular Hyperbola, Point Symmetry, Base, Exponent, Exponential Notation, Power,
Scientific Notation, Exponential Equation, Exponential Function, Exponential Decay,
Exponential Growth, e (Number)
LHS Curriculum
Teaching Focus/Objectives:
(i.e. “The learner will”)
The learner will identify
inverse, combined, and
joint variation.
The learner will investigate
properties of graphs of
exponential functions.
The learner will recognize
and apply the properties of
exponents.
Suggested Activities
Chapter 7-1 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 7 Test
Chapter 7-1 Focus on Advanced
Algebra
Algebra for All Exponential
Functions Graphing Activity
Warm-Up Quizzes
Chapter 7 Test
Chapter 7-1 Focus on Advanced
Algebra
The learner will use
Chapter 7-2 Focus on Advanced
rational-number powers and
Algebra
explore the relationship
between radicals and
exponents.
The learner will solve
radical equations.
The learner will explore
exponential functions and
their graphs.
The learner will use
exponential functions to
model exponential growth
and decay.
The learner will explore
and understand the number
e and one of its uses.
Assessments
Chapter 7-2 Focus on Advanced
Algebra
Chapter 9-1 Focus on Advanced
Algebra
Chapter 9-1 Focus on Advanced
Algebra
Algebra for All Module 1: Nuclear
Energy: Exponential Growth and
Decay Activity
Algebra for All Discovering Growth
Patterns Activity
Chapter 9-1 Focus on Advanced
Algebra
The learner will understand
the inverse relationship
between exponential and
logarithmic functions.
Chapter 9-2 Focus on Advanced
Algebra
The learner will use
Chapter 9-2 Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 7 Test
Warm-Up Quizzes
Chapter 7 Test
Warm-Up Quizzes
Chapter 7 Test
Warm-Up Quizzes
Chapter 9 Test
Warm-Up Quizzes
Chapter 9-1 Test
Warm-Up Quizzes
Chapter 9-1 Test
Warm-Up Quizzes
Chapter 9-2 Test
Warm-Up Quizzes
LHS Curriculum
logarithms and their
properties to solve
exponential equations.
Chapter 9-2 Test
Additional Resources:
Make a Flip-Chart (Foldable) For Exponential Properties and Logarithmic Properties (Look in Literacy Foldable
for Examples)
9-2 C Lab (Explore) Exercise from the Focus on Advanced Algebra CD-Rom
More Practice Worksheets for Logarithms: http://edhelper.com/algebra.htm and
http://www.ma.utexas.edu/users/asalerno/worksheets.html
Math Tools: Grades 3-12 book.
Electronic Notes
Algebra for All CD
LHS Curriculum
Algebra II
Conic Sections
2 Weeks
High School Content expectation(s) or related standard: A1.1.1, A1.1.3, A1.2.1,
A1.2.2, A1.2.3, A1.2.8, A2.1.1, A2.1.2, A2.1.3, A2.1.6, A2.1.7, A2.2.1, A2.2.2,
A2.2.3, A2.3.2, A2.3.3, A2.4.1, A2.4.2, A2.4.3, G1.7.1, G1.7.2, G1.7.3, L1.1.1,
L1.1.2, L1.1.3, L1.2.1, L2.1.4, L2.1.5
Prior Knowledge: Working with Quadratic and Linear Functions and Their Graphs,
Completing the Square, Cartesian Coordinates, Linear Equations
Key Concepts/Vocabulary: Center, Circle, Conic Sections, Radius, Standard Form, Ellipse,
Foci, Major Axis, Minor Axis, Vertices, Asymptotes, Branches, Center, Foci, Hyperbola
Teaching Focus/Objectives:
Suggested Activities
Assessments
(i.e. “The learner will”)
The learner will develop
the standard form of the
equation of a circle and
graph circles.
Chapter 5-3 A Focus on Advanced
Algebra
Warm-Up Quizzes
Chapter 5 Test
The learner will develop
the standard form of the
equation of an ellipse and
graph ellipses.
Chapter 5-3 B Focus on Advanced
Algebra
Creating an Ellipse with Cardboard,
Floss, and Thumb Tacks and
Labeling It (Explore Activity)
Warm-Up Quizzes
Chapter 5 Test
The learner will develop
the standard form of the
equation of a hyperbola and
graph hyperbolas.
Chapter 5-3 C Focus on Advanced
Algebra
Graphic Organizer Activity for
Different Types of Conics with
Their Equations
Warm-Up Quizzes
Chapter 5 Test
Additional Resources:
More Practice with Conics: http://edhelper.com/conics.htm
Conic Section Worksheet from Math Tools: Grades 3-12. Worksheet and Activity Explained on Pg 153.
Electronic Notes
Algebra for All CD