Recurring Themes Throughout the Course
CLE:
CLE 3103.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.
CLE 3103.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness
of the solution.
CLE 3103.1.3 Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of
reasoning, logic, and intuition.
CLE 3103.1.4 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model
mathematical ideas, and to communicate solution strategies.
CLE 3103.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting
the solutions, mathematical ideas, and communication.
CLE 3103.1.6 Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between
mathematics and the real world.
CLE 3103.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.
CLE 3103.2.4 Understand the capabilities and limitations of technology when performing operations, graphing, and solving equations involving complex numbers.
Checks for
Understanding
3103.1.5 Determine the accuracy
and reliability of a mathematical
model.
3103.1.9 Translate the syntax of
technology to appropriate
mathematical notation for nonlinear and transcendental
functions.
3103.1.10 Interpret the results of
mathematical modeling in
various contexts to answer
questions.
3103.1.1 Create and analyze
scatter-plots of non-linear and
transcendental functions.
3103.1.2 Compare and contrast
sampling techniques and identify
the best technique for a given
situation.
1
State Performance
Indicators
SPI 3103.1.4 Use mathematical
language, symbols, definitions,
proofs and counterexamples
correctly and precisely to
effectively communicate
reasoning in the process of
solving problems via
mathematical modeling with
both linear and non-linear
functions.
SPI 3103.1.1 Move flexibly
between multiple representations
(contextual, physical, written,
verbal, conic/pictorial, graphical,
tabular, and symbolic) of nonlinear and transcendental
functions to solve problems, to
model mathematical ideas, and to
communicate solution strategies.
SPI 3103.1.2 Recognize and
describe errors in data collection
and analysis as well as
Assessments
Instructional
Resources
Connections
A classroom set of TI84s or TI-spires.
School-to-career Masters
http://www.algebra2.com/careers
or resource kit
kutasoftware.com has several
worksheets for various topics
Science and Mathematics Lab
Manual (Glencoe Resource Kit)
http://www.glencoe.com/se
c/math/algebra/algebra2/al
gebra2_05/extra_examples
/index.php4/tn
http://www.regentsprep.or
g/Regents/math/ALGEBR
A/mathALGEBRA.htm#Equations
_and_Inequalities__
http://education.ti.com/edu
cationportal/activityexchan
ge/activity_list.do?cid=us
http://glencoe.mcgrawhill.com/sites/007873830x/
3103.1.4 Identify the weaknesses
of calculators and other
technologies in representing
nonlinear data, such as graphs
approaching vertical asymptotes,
and use alternative techniques to
identify these issues and
correctly solve problems.
3103.1.3 Use calculators to
identify regression equations for
nonlinear data.
3103.1.5 Determine the accuracy
and reliability of a mathematical
model.
3103.1.9 Translate the syntax of
technology to appropriate
mathematical notation for nonlinear and transcendental
functions.
identifying representations of
data as being accurate or
misleading.
SPI 3103.1.3 Use technology
tools to identify and describe
patterns in data using non-linear
and transcendental functions that
approximate data as well as
using those functions to solve
contextual problems.
student_view0/chapter7/les
son7/personal_tutor.html
http://glencoe.mcgrawhill.com/sites/0078884829/
student_view0/chapter7/les
son1/personal_tutor.html
http://www.purplemath.co
m/modules/
http://www.onlinemathlear
ning.com/unit-circle.html
http://teachers.henrico.k12.
va.us/math/HCPSAlgebra2
/
www.Mathorama.com
http://www.fkss.ca/courses
/math/PMa12/index.html
Online Assessment with instant
feedback:
http://education.jlab.org/so
lquiz/index.html
Scavenger Hunt:
Tool to find resources, located in
each chapter of Glencoe Algebra
2
http://www.glencoe.com/sec/mat
h/algebra/algebra2/algebra2_05/p
dfs/Algebra2Scavenger.pdf
Reading to Learn Mathematics:
Vocabulary for each chapter of
Glencoe Algebra 2 (activity
sheets)
Reading & Writing in the
Mathematics Classroom
(Glencoe Resource Kit)
2
eGlossary-Math
http://www.glencoe.com/apps/e
Glossary612/landing.php
Online Algebra 2 Lessons:
http://yourteacher.com/browselessons
Teaching Mathematics with
Foldables, Dinah Zike
Resource CDs in kit: Alge2Pass
Tutorials, Electronic Text Book,
Worksheets and Enrichment
Vocabulary Help:
http://mathwords.com
CLE 3103.2.4
3103.2.11 Understand the
capabilities and limitations of
technology. Make estimations
without a calculator to detect
potential errors.
3
http://calculusapplets.com/graph
errors.html
Course: Algebra 2
1st Nine Weeks
Unit 1: Characteristics of Functions
CLE:
Curriculum Guide
Estimated Time: 4 Weeks
CLE 3103.3.2 Understand, analyze, transform and generalize mathematical patterns, relations and functions using properties and various representations.
CLE 3103.3.3 Analyze and apply various methods to solve equations, absolute values, inequalities, and systems of equations over complex numbers.
CLE 3103.3.5 Use mathematical models involving equations and systems of equations to represent,
interpret and analyze quantitative relationships, change in various contexts, and other real-world phenomena.
Essential Questions:
How do you use the characteristics of each family of functions to distinguish between absolute value, step, piece-wise, linear, or quadratic functions?
How would you determine the domain and range of a relation and how do they relate to the relation's inverse?
What methods would you use to solve contextual problems involving 2 and 3-variable systems of linear equations and inequalities?
Unit Academic Vocabulary:
Inverse of a relation, inverse function, piece-wise function, step function
Prerequisite Skills: Graph linear equations, solve linear equations
Checks for
State
Understanding
Performance Assessments
Indicators
CLE 3103.3.2
3103.3.3 Determine and
graph the inverse of a
function with and without
technology.
3103.3.4 Analyze the
effect of changing various
parameters on functions
and their graphs.
3103.3.5 Graph piece-wise
and step functions.
3103.3.11 Describe and
articulate the
characteristics and
parameters of a parent
function.
4
SPI 3103.3.5 Describe the
domain and range of
functions and articulate
restrictions imposed either
by the operations or by the
contextual situations
which the functions
represent.
SPI 3103.3.10 Identify
and/or graph a variety of
functions and their
translations
SPI 3103.3.7 Identify
whether a function has an
inverse, whether two
functions are inverses of
each other, and/or explain
why their graphs are
reflections over the line y
= x.
Daily formative
assessments
Unit test
School-based
common
assessments
District Benchmark
Assessment?
Instructional Resources
Domain Representations Activity
http://illuminations.nctm.org/LessonDetail.aspx?id=L6
21
Graphing Piecewise Functions(Calc):
http://www.tc3.edu/instruct/sbrown/ti83/funcpc.htm
Function Transformation Activities (Calc):
1. http://education.ti.com/educationportal/activi
tyexchange/Activity.do?cid=US&aId=9797
2.
http://education.ti.com/educationportal/activi
tyexchange/Activity.do?cid=US&aId=11930
Quadratic Function Transformations (Calc):
http://education.ti.com/educationportal/activityexchang
e/Activity.do?cid=US&aId=9795
How to Find an Inverse (TI)
http://education.ti.com/educationportal/activityexchang
e/Activity.do?cid=US&aId=8211
Connections
Cell Phone Plans (Step Functions)
Finance: Graphing Inequalities related to
dividend earnings, minimum projections,
share values or other related economics
topics
ACT Standards:

Read tables and graphs

Manipulate data from graphs

Solve real-world problems
using first-degree equations

Write equations and
inequalities that require
planning, manipulating, and/or
solving

Solve simple absolute value
inequalities

Analyze and draw conclusions
based on information from
graphs in the coordinate plane

Determine when an expression
is undefined
CLE 3103.3.3
3103.3.8 Solve a three by
three system of linear
equations algebraically and
by using inverse matrices
and determinants with and
without technology.
3103.3.18 Solve compound
inequalities involving
disjunction and
conjunction and linear
inequalities containing
absolute values.
3103.3.19 Solve linear
programming problems.
SPI 3103.3.8 Solve
systems of three linear
equations in three
variables.
Escape from the Tomb (Answers the question “When
am I ever going to use systems of equations?”
http://illuminations.nctm.org/LessonDetail.aspx?id=L6
98
SPI 3103.3.9 Graph the
solution set of two or three
linear or quadratic
inequalities.
Talk or Text (Application of Systems)
http://illuminations.nctm.org/LessonDetail.aspx?id=L7
80
Biology/Chemistry applications with
Linear Programming
Matrix Operations, Solving (Not Cramer's, Calc):
http://mathbits.com/mathbits/tisection/precalculus/matr
ices.htm
Cramer's Rule:
http://www.purplemath.com/modules/cramers.htm
Linear Programming:
http://teachers.henrico.k12.va.us/math/hcpsalgebra2/36.htm
Systems of Linear Equations:
http://teachers.henrico.k12.va.us/math/hcpsalgebra2/37.htm
Linear Programming—Dirt Bike Dilemma
http://illuminations.nctm.org/LessonDetail.aspx?id=L6
85
CLE 3103.3.5
SPI 3103.3.12 Interpret
graphs that depict realworld phenomena.
SPI 3103.3.13 Solve
contextual problems using
quadratic, rational, radical
and exponential equations,
finite geometric series or
systems of equations.
5
Contextual Quadratic Project:
http://www.glencoe.com/sec/math/algebra/algebra2/alg
ebra2_05/webquest/unit2/webquest.php4/ny
Social Studies
Course: Algebra 2
1st Nine Weeks
Unit 2: Algebraic Operations
CLE:
Curriculum Guide
Estimated Time: 4 Weeks
CLE 3103.3.1 Understand and apply properties of rational exponents and perform basic operations to simplify algebraic expressions.
CLE 3103.3.5 Use mathematical models involving equations and systems of equations to represent,
interpret and analyze quantitative relationships, change in various contexts, and other real-world phenomena.
Essential Questions:
How would you determine that a polynomial has been completely factored?
How do you properly simplify fractions that include radicals?
Unit Vocabulary:
complete the square, rational function
Prerequisite Skills: operations on rational numbers, properties of exponents, factor polynomials
Checks for
State
Understanding Performance Assessments
Instructional Resources
Indicators
CLE 3103.3.1
3103.3.1 Perform operations
on algebraic expressions and
justify the procedures.
3103.3.21 Factor
polynomials using a variety
of methods including the
factor theorem, synthetic
division, long division, sums
and differences of cubes,
and grouping.
6
SPI 3103.3.1 Add,
subtract and multiply
polynomials; divide a
polynomial by a lower
degree polynomial.
SPI 3103.3.3 Add,
subtract, multiply,
divide and simplify
rational expressions
including those with
rational and negative
exponents.
Daily formative
assessments
Polynomial operations:
http://teachers.henrico.k12.va.us/math/hcpsal
gebra2/5-1.htm
Unit test
Polynomial Modeling with Algebra Tiles
School-based common
assessments
District Benchmark
Assessment?
Use graphing calculator to compare factored
and un-factored forms to check for accuracy
Factoring/Multiplying Polynomials
Activity/Game
http://www.regentsprep.org/Regents/math/A
LGEBRA/AV3/GridPoly.htm
Connections
Cost Analyst Career Connection: Production Costs
and Factors
Medicine: Estimating populations during epidemics
with equations
Business
Entertainment
ACT Standards:

Find and use the least common multiple

Work with numerical factors

Work with scientific notation

Work with squares and square roots of
numbers

Work with problems involving positive
integer exponents

Work with cubes and cube roots of
numbers

Determine when an expression is
undefined

Add, subtract, and multiply polynomials

Draw conclusions based on number
concepts, algebraic properties, and/or
relationships between expressions and

CLE 3103.3.5
3103.3.6 Simplify
expressions and solve
equations containing
radicals.
7
SPI 3103.3.12
Interpret graphs that
depict real-world
phenomena.
Interpreting Graphs (with or without Tech):
http://www.glencoe.com/sec/math/algebra/al
gebra2/algebra2_05/usa_today/index.php4/n
y
numbers
Write expressions that require planning
and/or manipulating to accurately model a
situation
Economics
Social Studies