Algebra II Curriculum Framework - raymondleemath

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Algebra
I
I

Curriculum Framework



Sugge
sted

Pacin
g



Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Beginning of Year Review

20

days

Preparing for
Advanced
Algebra:



Representing Functions



FOIL



Factoring Polynomials



The Counting Principle



Permutations and
Combinations



Congruent and Similar
Figures



The Pythagorean
Theorem



Use the four
-
step problem
-
solving
plan



Identify the domain
and range of
functions



Use the FOIL method to multiply
binomials



Use various techniques to factor
polynomials



Use the Fundamental Counting
Principle to find outcomes involving
independent and dependent events



Solve problems involving
permutations and combi
nations



Identify and use congruent and similar
figures



Use the Pythagorean Theorem and its
converse



Diagnostic
assessment



Real world
connection
/example
s



Teach with TECH



Practice/review
activities



Problem solving
activities



Post
-
test




Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Response cards



Reciprocal teaching



Writing to Learn
strategies



Vocabulary notecards



Lesson summaries



Journal prompts



E
ntrance/e
xit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Algebra I
I

(2010) student and teacher editions



Research
-
Based Strategies:
Narrowing the Achievement Gap for
Under
-
Resourced Students
by Ruby
Payne, Ph.D.



Online teacher resources:
http://glencoe.mcgraw
-
hill.
com/sites/0078884829/student_vi
ew0/



Online student edition:
http://connected.mcgraw
-
hill.com/connected/login.do




Math websites (see attachment)



Personal Tutor



Virtual
manipulatives/calculator



Math journals


Sugge
sted

Pacin
g



Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Unit

1

40

days

Linear Relations and Functions


Equations and Inequalities



Expressions and Formulas



Properties of Real
Numbers



Solving Equations



Solving Absolute Value
Equations



Solving Inequalities



Solving Compound
and
Absolute Value
Inequalities


Linear Functions and Relations



Relations and Functions



Linear Relations and
Functions



Rate of Change and Slope



Writing Linear Equations



Scatter Plots and Lines of
Regression



Special Functions



Parent Functions and
Transforma
tions



Graphing Linear and
Absolute Value
Inequalities


Systems of Equations and
Inequalities



Solving Systems of
Equations by Graphing



Solving Systems of
Equations Algebraically



Solving Systems of
Inequalities by Graphing



Optimization with Linear
Programming

Equations and Inequa
lities



Use the properties of real numbers to
evaluate expressions and formulas



Classify real numbers



Use the properties of equality to solve
equations



Solve absolute value equations



Solve inequalities, compound
inequalities, and absolute value
inequalities


Linear Functions and Relations



Identify the mathematical domains
and ranges of functions and determine
reasonable domain and range values
for continuous and discrete situations



Identify and sketch graphs of parent
functions, including linear functions
(f(x)=x)
and absolute value functions
(f(x)=
׀
x
׀
)



Collect and organize data, make and
interpret scatter plots, fit the graph of
a function to the data, interpret the
results, and proceed to model, predict,
and make decisions and critical
judgments



Graph lin
ear and absolute value
inequalities


Systems of Equations and Inequalities



Analyze situations and formulate
systems of equations in two or more
unknowns to solve problems



Use algebraic methods, graphs, or
tables to solve systems of equations or
inequalitie
s



Interpret and determine the
reasonableness of solutions to systems
of equations for given contexts



Diagnostic
assessment



Real
-
world
connection
/example
s



Check your
understanding



Practice and
problem solving



H.O.T. problems



Watch Out!



Spiral review



Skills review



Standardized test
practice



Algebra L
ab



Graphing
Technology Lab



Spreadsheet Lab



Enrichment
activities



Mid
-
chapter q
uiz



Practice test



Chapter/Unit test



Chapte
r 1 Project:
Purchasing Power



Chapter 2 Project:
Up and Down the
Mountain



Chapter 3 Project:
Breaking Even



Chapter 4 Project:
Animation



Activate prior
knowledge



Scaffolding
questions



K
-
W
-
L



Cooperative learning



Reciprocal teaching



Peer tutoring



Writing to Learn
strategies



E
ntrance/e
xit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Algebra II
(2010) student and
teacher editions



Research
-
Based Strategies:
Narrowing the Achievement Gap for
Under
-
Resourced Students
by Ruby
Payne, Ph.D.



Online teacher resources:
http://glencoe.mcgraw
-
hill.com/sites/0078884829/student_vi
ew0/



Online student edition:
http://connected.mcgraw
-
hill.com/connected/login.do




Math websites (see attachment)



Personal Tutor



Virtual manipulatives/calculator



Math journals


Sugge
sted

Pacin
g



Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Unit

2

38

days

Quadratic, Polynomial, and
Radical
Functions and Relations


Quadratic Functions and
Relations



Graphing Quadratic
Functions



Solving Quadratic
Equations by Graphing



Solving Quadratic
Equations by Factoring



Complex Numbers



Completing the Square



The Quadratic Formula
and the Discriminant



Transformations with
Quadratic Functions



Quadratic Inequalities


Polynomials and Polynomial
Functions



Operations with
Polynomials



Dividing Polynomials



Polynomial Functions



Analyzing Graphs of
Polynomial Functions



Solving Polynomial
Equations



The Remainder
and
Factor Theorems



Roots and Zeros



Rational Zero Theorem


Inverses and Radical Functions
and Relations



Operations on Functions



Inverse Functions and
Relations

Quadratic Functions and Relations



Determine reasonable domain and
range values of quadratic functions



Analyze situations involving
quadratic functions and formulate
quadratic equations and inequalities
to
solve problems



Solve quadratic equations and
inequalities using graphs, tables, and
algebraic methods, including the
Quadratic Formula



Use complex numbers to describe the
solutions of quadratic equations



Determine a quadratic function and its
roots



Ide
ntify and sketch graphs of parent
functions, including quadratic
functions



Use the parent function to investigate,
describe, and predict the effects of
changes in
a, h,
and
k
on the graphs of
the
y+a(x
-
h)
²
+k

form of a function


Polynomial and Polynomial Fu
nctions



Use tools including factoring and
properties of exponents to simplify
expressions and to transform and
solve equations



Identify the mathematical domains
and ranges of functions



Determine the reasonable domain and
range values for continuous
situations


Inverses and Radical Functions and Relations



Relate representations of square root
functions



Connect inverses of square root
functions with quadratic functions

 Determine solutions of square root


Diagnostic
assessment



Real
-
world
connection
/example
s



Check your
understanding



Practice and
problem solving



H.O.T. problems



Watch Out!



Spiral review



Skills review



Standardized test
practice



Algebra L
ab



Graphing
Technology Lab



Enrichment
activities



Mid
-
chapter quiz



Practice test



Chapter/Unit test



Chapter 5 P
roject:
How High Will It
Go?



Chapt
er 6 Project:
Vehicles in Motion



Cha
pter 7 Project:
Saving for College




Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Response cards



Reciprocal teaching



Writing to Learn
strategies



E
ntrance/e
xit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Algebra II
(2010) student and teacher editions



Research
-
Based Strategies:
Narrowing the Achievement Gap for
Under
-
Resourced Students
by Ruby
Payne, Ph.D.



Online teacher resources:
http://glencoe.mcgraw
-
hill.c
om/sites/0078884829/student_vi
ew0/



Online student edition:
http://connected.mcgraw
-
hill.com/connected/login.do




Math websites (see attachment)



Personal Tutor



Virtual manipulatives/calcula
tor



Math journals


Sugge
sted

Pacin
g



Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Unit 3

37

days

Advanced Functions and
Relations


Exponential
and Logarithmic
Functions and Relations



Graphing Exponential
Functions



Solving Exponential
Equations and
Inequalities



Logarithms and
Logarithmic Functions



Solving Logarithmic
Equations and
Inequalities



Properties of Logarithms



Common Logarithms



Base
e

and Natural
Logarithms



Using Exponential and
Logarithmic Functions


Rational Functions and Relations



Multiplying and Dividing
Rational Expressions



Adding and Subtracting
Rational
Expressions



Graphing Reciprocal
Functions



Variation Functions



Solving Rational
Equations and
Inequalities


Conic Sections



Midpoints and Distance
Formulas



Parabolas



Circles

Exponential and Logarithmic Functions and
Relations



Analyze a situation modeled by an
exponential function, formulate an
equation or inequality, and solve the
problem



Develop the definition of logarithms
by exploring and describing the
relationships betwee
n exponential
functions and their inverses



Use parent functions to investigate,
describe, and predict the effects of
parameter changes on the graphs of
exponential and logarithmic functions,
describe limitations on the domains
and ranges, and examine asymp
totic
behavior



Determine solutions of exponential
and logarithmic equations using
graphs, tables, and algebraic methods



Interpret and determine the
reasonableness of solutions to
exponential and logarithmic equations
and inequalities


Rational Functions an
d Relations



Determine the properties of reciprocal
functions and graph their
transformations



Use quotients of polynomials to
describe the graphs of rational
functions, describe limitations on the
domains and ranges, and examine
asymptotic behavior



Determin
e the reasonable domain and
range values of rational functions and
determine the reasonableness of
solutions to rational equations and
inequalities



Analyze a situation modeled by


Diagnostic
assessment



Real
-
world
connection/example
s



Check your
under
standing



Practice and
problem solving



H.O.T. problems



Watch Out!



Spiral review



Skills review



Standardized test
practice



Algebra L
ab



Graphing
Technology Lab



Enrichment
activities



Mid
-
chapter quiz



Practice test



Chapter/Unit test



Chapter 8 Project:
Measuring

Sound



Chapter 9 Project:
A Plane Trip



Chapter 10 Project:
Celestial Orbits



Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Response cards



Reciprocal teaching



Writing to Learn
strategies



Entrance/exit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Algebra II
(2010) student and teacher editions



Research
-
Based Strategies:
Narrowing the Achievement Gap for
Under
-
Resourced Students
by Ruby
Payne, Ph.D.



Online teacher
resources:
http://glencoe.mcgraw
-
hill.com/sites/0078884829/student_vi
ew0/



Online student edition:
http://connected.mcgraw
-
hill.com/connected/login.do




Math websites (see attachment)



Pers
onal Tutor



Virtual manipulatives/calculator



Math journals


Sugge
sted

Pacin
g



Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Unit 4

24

days

Discrete Mathematics


Sequences and Series



Sequences as Functions



Arithmetic Sequences and
Series



Geometric Sequences and
Series



Infinite Geometric Series



Recursion and Iteration



The

Binomial Theorem



Proof by Mathematical
Induction


Probability and Statistics



Experiments, Surveys,
and Observational Studies



Statistical Analysis



Conditional Probability



Probability and
Probability Distributions



The Normal Distribution



Hypothesis Testing



Binomial Distributions


Sequences and Series



Relate arithmetic sequences to linear
functions and relate geometric
sequences to exponential functions



Find specific terms and sums of
arithmetic and geometric series



Find the sum of an infinite geometric
serie
s and write repeating decimals as
fractions



Recognize and use special sequences
and iterate functions



Use Pascal’s triangle and the
Binomial Theorem to expand powers
of binomials



Use mathematical induction to prove
statements


Probability and Statistics



Us
e combinations and permutations to
find probability and use them to solve
problems



Find probabilities of two independent
and two dependent events



Find the probability of mutually
exclusive and inclusive events



Use a measure of central tendency to
represent

a set of data and find
measures of variation for a set of data



Determine whether a sample is biased
and find margins of sampling and
error



Create and use graphs of probability
distributions



Solve problems involving normally
distributed data



Use binomial
expressions to find
probability



Identify and calculate conditional
probabilities



Diagnostic
assessment



Real
-
world
connection/example
s



Check your
understanding



Practice and
problem solving



H.O.T. problems



Watch Out!



Spiral review



Skills review



Standardize
d test
practice



Algebra Lab



Graphing
Technology Lab



Enrichment
activities



Mid
-
chapter quiz



Practice test



Chapter/Unit test



Chapter 11 Project:
Animal Populations



Chapter 12 Project:
Educational
Statistics



Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Response cards



Reciprocal teaching



Writing to Learn
strategies



Entrance/exit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Algebra II
(2010) student and teacher e
ditions



Research
-
Based Strategies:
Narrowing the Achievement Gap for
Under
-
Resourced Students
by Ruby
Payne, Ph.D.



Online teacher resources:
http://glencoe.mcgraw
-
hill.com/sites/0078884829/student_vi
ew0/



Online student edition:
http://connected.mcgraw
-
hill.com/connected/login.do




Math websites (see attachment)



Personal Tutor



Virtual manipulatives/calculator



Math journals


Sugge
sted

Pacin
g



Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Unit 5

23

days

Trigonometry


Trigonometric Functions



Trigonometric

Functions
in Right Angles



Angles and Angle
Measures



Trigonometric Functions
of General Angles



Law of Sines



Law of Cosines



Circular Functions



Translations of
Trigonometric Graphs



Inverse Trigonometric
Functions


Trigonometric Identities and
Equations



Trigonometric Identities



Verifying Trigonometric
Identities



Sum and Difference of
Angles Identities



Double
-
Angle and Half
-
Angle Identities



Solving Trigonometric
Equations

Trigonometric Functions



Explore trigonometric functions, first
in acute angles in sta
ndard form, and
also for points on the unit circle



Derive and use the Law of Sines and
the Law of Cosines as applications of
trigonometric functions



Develop inverses for the sine, cosine,
and tangent functions



Use the trigonometric functions to
explore amp
litude and period



Investigate phase shifts and vertical
shifts in the graphs of trigonometric
functions


Trigonometric Identities and Equations



Verify and use trigonometric
identities



Solve trigonometric identities



Solve trigonometric equations using
the
ideas of factoring, the zero
product property, trigonometric
inverses, and periodic behavior



Diagnostic
assessment



Real
-
world
connection/example
s



Check your
understanding



Practice and
problem solving



H.O.T. problems



Watch Out!



Spiral review



Skills review



S
tandardized test
practice



Algebra Lab



Graphing
Technology Lab



Spreadsheet Lab



Geometry Lab



Enrichment
activities



Mid
-
chapter quiz



Practice test



Chapter/Unit test



Chapter 13 Project:
On the Water



Chapter 14 Project:
Electronics
Professions



Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Response cards



Reciprocal teaching



Writing to Learn
strategies



Entrance/exit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Algebra

II
(2010) student and teacher editions



Research
-
Based Strategies:
Narrowing the Achievement Gap for
Under
-
Resourced Students
by Ruby
Payne, Ph.D.



Online teacher resources:
http://glencoe.mcgraw
-
hill.com/sites/0078884829/student_vi
ew0/



Online student edi
tion:
http://connected.mcgraw
-
hill.com/connected/login.do




Math websites (see attachment)



Personal Tutor



Virtual manipulatives/calculator



Math journals