Honors
Algebra II
Curriculum
1
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Reading this document:
1. Power Standards
a. Power Standards have been outlined in BOLD text. These are the
understandings and skills that all students must become proficient in
upon exiting the course. These will therefore become the pre-requisite
understandings and skills for the next sequential course (Algebra I,
Algebra II, Advanced Algebra).
b. We must instruct and assess the entire curriculum not just the
identified power standards. These other “nice to know” standards are
still important in the understanding of the curriculum.
c. Power Standards will be assessed:
i. Through Trimester Benchmark Assessments
ii. Through School-based benchmark assessment which lead to
the Trimester Benchmark Assessment
iii. Multiple times; students will have multiple attempts to
demonstrate proficiency in each of the identified Power
Standards
2. Level of Bloom is identified numerically in the “as evidence by” column of the
curriculum. An outline of the “new” Bloom Taxonomy is below.
Level
1
2
Remember Understand
3
Apply
4
Analyze
5
Evaluate
6
Create
The
Knowledge
Dimension
Factual
Knowledge
Conceptual
Knowledge
Procedural
Knowledge
Metacognitive
Knowledge
2
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
A Vision for School Mathematics:
Imagine a classroom, a school, or a school district where all students have access to
high-quality, engaging mathematics instruction. There are ambitious expectations for
all, with accommodation for those who need it. Knowledgeable teacher have adequate
resources to support their work and are continually growing as professionals. The
curriculum is mathematically rich, offering student opportunities to learn important
mathematical concepts and procedures with understanding. Technology is an essential
component of the environment. Students confidently engage in complex mathematical
tasks chosen carefully by teachers. They draw on knowledge from a wide variety of
mathematical topics, sometime approaching the same problem from different
mathematical perspectives or representing the mathematics in different ways until they
find methods that enable them to make progress. Teacher help students make, refine, and
explore conjectures on the basis of evidence and use a variety of reasoning and proof
techniques to confirm or disprove those conjectures. Students are flexible and
resourceful problem solvers. Alone or in groups and with access to technology, they
work productively and reflectively, with the skilled guidance of their teachers. Orally
and in writing, students communicate their ideas and results effectively. They value
mathematics and engage actively in learning it.
Principles and Standards for School Mathematics
NCTM 2000
3
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Pacing Recommendations
Honors Algebra II
1) Trimester One Benchmark Assessment
2) Trimester Two Benchmark Assessment
3) Trimester Three Benchmark Assessment
Unwrapped Connecticut Mathematical Frameworks:
Standard 1: Algebraic Reasoning
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Understands and Describes patterns
Represent quantitative relationships
Analyze quantitative relationships
Uses operations, properties and algebraic symbols
Standard 2: Numerical and Proportional Reasoning

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Understands numerical representation
Describes quantitative relationships
Computes numbers flexibly and fluently
Estimates measure and quantities
Standard 3: Geometry and Measurement

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Uses geometric theorems
Describes relationships
Communicates ideas
Develops and applies an understanding of units and formulas
Solves problems in one, two and three dimensions
Standard 4: Working with Data

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Uses Data (collects, organizes, displays and analyzes)
Forms hypotheses and makes predictions
4
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Honors Pathway at a Glance
Honors Algebra I
1) Trimester One
a) Goal 1: Understanding Linear
Equations and Inequalities in One
Variable
b) Goal 2: Graph and Interpret Linear
Equations and Inequlaities
2) Trimester Two
a) Goal 3: Solve Systems of Linear
Equations and Inequalities
b) Goal 4: Simplify expressions
involving integer exponents
3) Trimester Three
a) Goal 5: Polynomial Operations
b) Goal 6: Quadratic functions,
equations and inequalities
c) Goal 7: Applying the Pythagorean
Theorem
Honors Geometry
1. Trimester One:
Honors Algebra II
1. Trimester One:
a. Goal 1: Linear equation and
inequalities
b. Goal 2: Quadratic functions,
equations and inequalities
2. Trimester Two:
a. Goal 3: Polynomials and
Polynomial Functions
b. Goal 4: Exponential Functions
c. Goal 5: Rational Expressions and
Equations
3. Trimester Three
a. Goal 6: Radicals and Rational
Exponents
b. Trigonometric Functions
Enrichment: Sequences and Series
Honors Pre-Calculus
1) Trimester One
a) Goal 1: Review the concepts of a
function
b) Goal 2: Analyze and problem solve
using Polynomial and Rational
Functions
2) Trimester Two
a) Goal 3: Analyze and Problem solve
using Exponential and Logarithmic
Functions
b) Goal 4: Use Trigonometry to
evaluation, graph and problem
solve
3) Trimester Three
a) Goal 5: Introduce Limits as a
fundamental concept of calculus
2. Trimester Two:
3. Trimester Three:
5
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Goal 1: To use systems of linear equations and inequalities.
Chapter 3
Big Idea (s):
1. Solutions are not always unique.
2. Multiple methods can be used to solve problems.
3. Sometimes, more than one function is needed to solve some problems.
Essential Question (s):
1. How do you determine when more than one equation is needed to solve a
problem?
2. What are the different methods of solving systems of equations? How do you
determine the best method to apply?
3. What are the different possible solution set of a system of linear equations?
Learning Outcomes
Students will:
1. Solve systems of linear
equations
1.1. Graphing Method
1.1.1. Manually
1.1.2. Graphing calculator
1.2. Algebraic Method
1.2.1. Linear combination
1.2.2. Substitution
As evidenced by:

(3)Solving systems of equations by graphing
method, at the proficient level
o Manually constructing a graph of a system
to estimate the solution and checking
through substitution
o Using the graphing calculator to
determine the solution
 (3)Solving system of equations by algebraic
methods, at the proficient level
o Substitution method
o Linear Combination
o Identify the strength and weaknesses of
each method
6
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
2. Solve systems of linear
inequalities
2.1. Graphing Method
2.1.1. Manually
2.1.2. Graphing calculator
2.2. Algebraic Method
2.2.1. Linear combination
2.2.2. Substitution

3. Problem-solve using systems
3.1. Write a system from
words
3.2. Solve systems

(4)Solving authentic problems using method
of choice, at the proficient level

(5)Writing and solving authentic problems
involving two linear equations, at the
proficient level

(5)Writing and solving authentic problems
involving two linear inequalities, at the
proficient level

(4)Representing solutions in different modes
(Rule of 4: verbally, data (ordered pair),
graphically and symbolically), at the
proficient level

(4) Identifying the domain and range in the
context of the problem

(3)Identifying “feasible” region; region for
solution set, at the proficient level
(3)Identifying “optimal solution” (maximum
and minimum), at the proficient level
(4)Solving authentic problems, at the
proficient level
(4) Identifying the domain and range in the
context of the problem
4. Problem-solve using linear
programming
(4)Solving systems of equations by graphing
method, at the proficient level
o Manually constructing a graph of a system
to estimate the solution and checking
through substitution
o Using the graphing calculator to
determine the solution
 (4)Solving system of equations by algebraic
methods, at the proficient level
o Substitution method
o Linear Combination
o Identify the strength and weaknesses of
each method
 (4) Identifying the domain and range of the
solution to the system



Implementation Guide
7
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Goal 2: To use quadratic functions, equations and inequalities.
Chapter 5
Big Idea (s):
1. Multiple methods can be used to solve problems.
2. Not all functions are linear.
3. Functions have different characteristics.
Essential Question (s):
1. What are the different methods of solving quadratic functions and equations, and how
do you determine the best method to apply?
2. How are the different functions that you have studied similar and different?
a. Linear
b. Quadratic
c. Absolute Value
3. How do quadratic functions help model and solve problem in the real world?
Learning Outcomes
Students will:
1. Graph quadratic equations
and inequalities
As evidenced by:



(3)Manually creating graphs (at the
proficient level) of quadratic functions
o By making a table of values
o Labeling the vertex and axis of symmetry
(3)Graphing quadratic functions using the
graphing calculator, at the proficient level
(3) Determine the shaded region of a quadratic
inequality
8
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
2. Solve quadratic equations and
inequalities by:
2.1. Finding the square root
(single variable)
2.2. Quadratic Formula
2.3. Finding x-intercepts (two
variable equations)
2.3.1. square roots
2.3.2. factoring from
standard form
2.3.3. completing the square
3. Determine the number of
solutions of a quadratic
equations

(1)Memorizing of the quadratic formula

(3)Applying the quadratic formula and
calculating the solution(s), at the proficient
level

(2) Using Radical Notation for the solutions
to quadratic equations/inequalities

(3) Solving quadratic equations involving
complex numbers

(5)Analyzing equations and determining the
most appropriate method to apply when solving
quadratic equation/inequalities, at the proficient
level.

(5) Using appropriate methods to graph the
quadratic equation/inequalities

(2) Determining the number of solutions to a
quadratic equation
o Using the discriminant
o From a graph
4. Write quadratic equations
given:
4.1. the graph of the function
4.2. a set of data


(5) Analyzing the information on the graph
(points) to determine the most appropriate form
of the equation

Vertex Form

Intercept Form
(3)Using technology to determine the
quadratic model (regression equation)
Implementation Guide
9
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Goal 3: To use polynomials and polynomial functions.
Chapter 6.1-6.5
Big Idea (s):
1. Functions have different characteristics.
2. The four basic operations of mathematics (add, subtract, multiply and divide) can
be applied to algebraic expressions.
Essential Question (s):
1. How are the different functions that you have studied similar and different?
a. Linear
b. Quadratic
c. Absolute
d. Polynomials
2. How can you determine the characteristics and behavior of polynomial functions?
a. Graphically
b. Symbolically
3. What are the properties of exponents? How do you apply them to polynomial
operations?
Learning Outcomes
Students will:
1. Use the properties of exponents
1.1. Evaluate expressions
1.2. Simplify expressions
As evidenced by:


(2)Applying the properties of exponents to
evaluate expressions, at a proficient level
(2)Applying the properties of exponents to
simplify expressions, at the proficient level
10
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
2. Examine polynomial functions
2.1. Evaluate polynomials
2.2. Define polynomial
functions
2.3. Graph polynomial
functions
2.4. Describe

(2)Applying the order of operations to
evaluate polynomial functions, at the
proficient level

(5)Determine whether a function is a
polynomial function, at the proficient level
o Symbolically
o Graphically

(2-4)Graphing polynomial functions, at the
proficient level
o Without technology
o With the graphing calculator
o Using the concept of domain and range to set
appropriate window values of the graphing
calculator

(4)Describe polynomial functions in words, at
the proficient level
o End behavior (even/odd)
o Effect of leading coefficient
o Maximums and Minimums
o Zeros/roots
3. Apply basic operations to
polynomials
3.1. Add, subtract, multiply
and divide polynomials
3.2. Use properties of
exponents

(2)Applying the properties of exponents on
polynomial expressions, at the proficient level
o Addition and Subtraction
o Multiplication
o Division
11
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
4. Factor polynomial expressions

(3)Factoring polynomial expressions, at the
proficient level
o Sum or difference of cubes
o Grouping
o Quadratic Form
o Polynomial expressions

(3)Demonstrating the inverse relationships, at
the proficient level, between:
o Adding and Subtracting
o Multiplying and Dividing
5. Find solutions to Polynomial
Equations

(3)Demonstrating that factoring is a form of
division, at the proficient level

(3)Solving polynomial equations, at the
proficient level
o Symbolically using factoring
o Graphically using the graphing calculator

(4)Identifying special patterns
Implementation Guide
12
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Goal 4: To use exponential functions.
Chapter 8.1-8.3
Big Idea (s):
1. Some functions have restricted domain and range.
2. Functions have different characteristics and purposes.
Essential Question (s):
1) How are the different functions that you have studied similar and different?
a) Linear
b) Quadratic
c) Exponential
2) How do exponential functions help model and solve problem in the real world?
Learning Outcomes
Students will:
1. Use exponential growth and
decay functions
As evidenced by:



2. Use exponential functions with
base e
(2)Identify the domain and range
o From the graph of the function
o From the symbolic representation of the
function
(2)Graph exponential growth and decay
functions
(4)Problem solve using exponential growth
and decay
o Write exponential growth and decay models

(2)Apply the laws of exponents to base e
exponential expressions

(3)Graph base e exponential functions

(3)Identify the domain and range of
exponential functions with base e

(2)Evaluate exponential functions with
base e
Implementation Guide
13
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Goal 5: Rational Expressions and Equations
Chapter 9.4-9.6
Big Idea (s):
1. Algebraic operations can be applied to rational expressions and equations.
2.
Essential Question (s):
1. How are the properties of algebra used to simplify and solve rational
expressions/equations?
2.
Learning Outcomes
Students will:
As evidenced by:
1. Simplify rational expressions
1.1. multiply
1.2. divide

2. Simplify rational expressions
2.1. add
2.2. subtract


(3) Identifying common factors by factoring
polynomials
(3) Applying the rules of adding and
subtracting fractions to rational expressions
3. Solve Rational Equation

(3) checking for extraneous solutions

(3) Identifying common factors by factoring
polynomials
(3) Applying the rules of multiplying and
dividing fractions to rational expressions
Implementation Guide
14
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Goal 6: To use radicals and rational exponents, expressions and equations.
Chapter 7.1-7.3 and 7.6
Big Idea (s):
1. Some functions have restrictions on domain and range.
2. Algebraic operations can be applied to roots and radicals.
3. Some real-word phenomena can be modeled by radical functions.
Essential Question (s):
1. How do we extend the concept of the square root to other types of roots?
2. How are the properties of algebra used to simplify and solve radical/rational
expressions and equations?
3. How can you determine the characteristics of radical functions?
a. Graphically
b. Symbolically
c. Numerically
Learning Outcomes
Students will:
As evidenced by:

1. Calculate the “nth root” of real
numbers
(2)Defining the “nth root” in words and through
the use of algebraic symbols.
 (3)Calculate the “nth root” by applying
mathematical reasoning.
o Evaluating expressions with rational
exponents
o Solve equations with rational exponents
o Use the graphing calculator to estimate “nth
roots”
 (2)Using both radical and rational notation
interchangeably
1.1
2. Use the properties of rational
exponents

(2)Applying the properties of rational
exponents to simplify expressions

(2)Applying the properties of rational
exponents to evaluate expressions

(3)Applying the properties of rational
exponents to:
o Add and subtract
o Multiply and divide
o composition
15
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
3. Solve radical equation
3.1. Simple radicals
3.2. Rational exponents
3.3. Equations with more than
one radical
Implementation Guide

(3)Appling the properties of rational
exponents to solve radical equations

(3) checking for extraneous solutions
16
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Goal 7: To use trigonometric functions
Chapter 13
Big Idea (s):
1. Triangles can be used to solve varied problems.
2. Trigonometric Functions can be used to find a missing side or angle measure of right
triangles.
Essential Question (s):
1. What are the six trigonometric ratios and how are the sides of a triangle used to form
these ratios?
2. How is the Pythagorean Theorem used to develop trigonometric ratios?
Learning Outcomes
Students will:
1. Evaluate trigonometric functions
for acute angles
1.1. Sine, Cosine, Tangent
1.2. Cosecant, Secant, Cotangent
As evidenced by:



2. Use degree and radian angle
measure

(3)Calculate missing side length of right
triangles
(3)Calculate missing angle measures of right
triangles
(4)Apply understanding of trigonometric
functions to solve authentic problems
(2)Draw angles with given measure in standard
form
o Degree
o Radian
3. Evaluate trigonometric functions
for any angle
3.1. Sine, Cosine, Tangent
3.2. cosecant, secant, cotangent

(2)Find positive and negative coterminal angles

(2)Convert between degree and radian measure

(3)Calculate arc length

(3)Calculate area of sectors

(2)Evaluate trigonometric functions given a
point

(2)Evaluate trigonometric functions of any
angle

(3)Evaluate trigonometric angles by using
reference angles

(3)Use trigonometric functions to solve
authentic problems
17
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
4. Use inverse trigonometric
functions
5. Use the Law of Sines
6. Law of Cosines

(1)Define inverse Trigonometric Functions

(3)Calculate angles measure of Inverse
Trigonometric Functions

(3)Relate inverse operations to inverse
trigonometric function to solve trigonometric
equations

(4)Write and solve authentic problems that
involve trigonometry

(4)Calculate missing sides and angles of a
triangle given at least one side and two other
parts of the triangle

(4)Calculate the area of any triangle by using
the appropriate formula

(3)Calculate missing sides and angles of a
triangle when
o two sides and the included angle of a
triangle are given
o three sides are given
6. Solve problems involving
6.1. parametric equations
6.2. projectile motion

(4)Write and use Heron’s Laws to find the
areas of a triangle

(2)Graph Parametric Equations

(3)Write and solve parametric equations

(4)Solve authentic problems using parametric
equations and projectile motion
18
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
Implementation Guide
Enrichment: To use sequences and series.
Big Idea (s):
1. Patterns exist and mathematics can explain some patterns.
2. Patterns lead to solutions.
Essential Question (s):
1. What are patterns? How do they help us solve problems?
2. What are the similarities and differences between Geometric Sequences and
Arithmetic Sequences (Series)?
Learning Outcomes
Students will:
1. Investigate Sequences
 Finite
 Infinite
As evidenced by:





2. Investigate Series
 Finite
 Infinite
(1)Defining finite and infinite sequences
(3)Calculating the first n-terms of a sequence,
at the proficient level
(3)Calculating the n-th term of an infinite
sequence, at the proficient level
(4) Identifying patterns and write the rule for
the sequence, at the proficient level
(2)Graphing sequences

(1)Defining finite and infinite series

(1)Writing series using the ∑ (summation)
symbol
19
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008
3. Investigate Arithmetic
Sequences and Series
 Finite and Infinite
 Common Differences

(1)Defining Arithmetic Sequences

(4)Calculating the common differences, at
the proficient level

(3)Writing the rule for arithmetic sequences
and series, at the proficient level

(3)Calculating the “n-th” term, at the
proficient level, given:
o A term and the common difference
o Two terms
4. Investigate Geometric
Sequences and Series
 Common Ratio
 Finite and Infinite

(3)Calculating the sum of a finite arithmetic
series, at the proficient level

(4)Applying arithmetic sequences and series
to solve authentic problems, at the proficient
level

(4)Calculating the common ratio, at the
proficient level
(4)Writing the rule for geometric sequences
and series, at the proficient level
(3)Calculating the “n-th” term, at the
proficient level, given:
o A term and the common ratio
o Two terms
(4)Applying geometric sequences and series
to solve authentic problems, at the proficient
level



Implementation Guide
20
Connecticut Technical High Schools
Honors Algebra II
August 7, 2008