Download Algebra 2 A 1st Semester Timeline: 1st Semester 2 Weeks

Algebra 2 A
1st Semester
Unit 1: Sequences and Series
Activities:
Timeline:
1st Semester
2 Weeks
Vocabulary:
Arithmetic Mean
Arithmetic Sequence
Arithmetic Series
Common Difference
Common Ratio
Explicit Formula
Geometric Mean
Recursive Formula
Sequence
Series
Term
Summation Notation
Infinite Series
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New State Standards:
A-SSE Seeing Structure in Expressions
1. Interpret expressions that represent a quantity in terms of its context.★
a.
Interpret parts of an expression, such as terms, factors, and coefficients.
4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1),
and use the formula to solve problems. For example, calculate mortgage payments.★
F-IF Interpreting Functions
3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a
subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1)
= 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
7. Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases.★
F-BF Building Functions
1. Write a function that describes a relationship between two quantities.★
a.
Determine an explicit expression, a recursive process, or steps for calculation from a
context.
2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use
them to model situations, and translate between the two forms.★
F-LE Linear, Quadratic and Exponential Models
2. Construct linear and exponential functions, including arithmetic and geometric sequences,
given a graph, a description of a relationship, or two input-output pairs (include reading these
from a table).
College Readiness:
Range (13-15) Basic Operations & Applications: Perform one-operation computation with
whole numbers and decimals
Range (13-15) Basic Operations & Applications: Solve problems in one or two steps using
whole numbers
Range (16-19) Basic Operations & Applications: Solve routine one-step arithmetic problems
(using whole numbers, fractions, and decimals) such as single step percent
Range (16-19) Basic Operations & Applications: Solve some routine two-step arithmetic
problems
Range (20-23) Numbers: Concepts & Properties: Exhibit knowledge of elementary number
concepts including rounding, the ordering of decimals, pattern identification, absolute value,
primes, and
greatest common factor
Range (33-36) Numbers: Concepts & Properties: Draw conclusions based on number concepts,
Resources:
Concepts and Skills:
Students will:
 Generate a sequence
 Use a recursive formula
 Identify an arithmetic
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sequence
Use an arithmetic mean
Identify a geometric
sequence
Use a geometric mean
Write and evaluate
arithmetic and geometric
series
Write a series in
summation notation
Find the sum of a finite
arithmetic series
Find the sum of a finite
geometric series
Find the sum of an infinite
arithmetic series
Find the sum of an infinite
geometric series
Unit Learning
Targets
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I can use the
fundamental
counting
principle to
count the
number of
ways an event
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Algebra II textbook: Larson,
Boswell, Kanold, Stiff
CH: 8
Internet Research
Infinite Algebra 1
Infinite Geometry
Infinite Algebra 2
Edmodo
Quality Core
Infinite Algebra II
Discovery Education
www.Khanacademy.org
brightstorm.com/math/algebra2/
Strategies:
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Graphing calculator
applications
Exit slips
ADP activities
Enrichment activities
ACT/SAT integration
Real World Applications
Vocabulary Builders
algebraic properties, and/or relationships between expressions and numbers
Range (13-15) Expressions, Equations, & Inequalities: Exhibit knowledge of basic expressions
(e.g., identify an expression for a total as b + g)
Range (13-15) Expressions, Equations, & Inequalities: Solve equations in the form x + a = b,
where a and b are whole numbers or decimals
Range (16-19) Expressions, Equations, & Inequalities: Solve one-step equations having integer
or decimal answers
Range (20-23) Expressions, Equations, & Inequalities: Evaluate algebraic expressions by
substituting integers for unknown quantities
Range (20-23) Expressions, Equations, & Inequalities: Solve routine first-degree equations
Range (28-32) Expressions, Equations, & Inequalities: Manipulate expressions and equations
Range (33-36) Expressions, Equations, & Inequalities: Write expressions that require planning
and/or manipulating to accurately model a situation
NCTM:
Numbers & Operations
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use number-theory arguments to justify relationships involving whole numbers.
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judge the reasonableness of numerical computations and their results
Algebra
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generalize patterns using explicitly defined and recursively defined functions
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understand relations and functions and select, convert flexibly among, and use
various representations for them
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use a variety of symbolic representations, including recursive and parametric
equations, for functions and relations
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use symbolic algebra to represent and explain mathematical relationships
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use symbolic expressions, including iterative and recursive forms, to represent
relationships arising from various contexts
Quality Core
A1A: Identify properties of real numbers and use them and the correct order of operations to
simplify expressions
A1D: Solve single-step and multistep equations and inequalities in one variable
A1J: Use inductive reasoning to make conjectures and deductive reasoning to arrive at valid
conclusions
B1: Mathematical processes learned in the context of increasingly complex mathematical and
real-world problems
H2A: Find the nth term of an arithmetic or geometric sequence
H2B: Find the position of a given term of an arithmetic or geometric sequence
H2C: Find sums of a finite arithmetic or geometric series
H2D: Use sequences and series to solve real-world problems
H2E: Use sigma notation to express sums
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can happen.
I can use
permutations
to count the
number of
ways an event
can happen.
I can
combination
to count the
number of
ways can
happen.
I can use the
binomial
theorem to
expand a
binomial that
is raised to
power.
I can find the
theoretical
and
experimental
probabilities.
I can find
geometric
probabilities.
I can find
probabilities
of unions and
intersections
of two events.
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I can use the
compliments
to find the
probability of
an event.
I can find the
probability of
independent
events.
I can find the
probability of
dependent
events.
I can find the
binomial
probabilities
and analyze
binomial
distributions.
I can test the
hypothesis.
I can
calculate
probabilities
using normal
distributions.
I can use
normal
distributions
to
approximate
binomial
distributions.
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Timeline:
1st Semester
Unit 2: Inequalities
Unit 3: Systems of Inequalities and Linear Programming
New State Standards:
2 weeks
Linear Inequalities
A-SSE Seeing Structure in Expressions
Interpret the structure of expressions
1. Interpret expressions that represent a quantity in terms of its context.
a) Interpret parts of an expression, such as terms, factors, and coefficients.
2 weeks
System of
Inequalities/
Linear
Programming
Vocabulary:
Inequalities
Expressions
Equations
Substitution
One step equations
Two step equations
Like terms
Terms
Factors
Coefficients
Degree
Distributive
Closure
Commutative
Associative
Identities
Inverse Properties
Leading Coefficient
Literal Equation
Constraints
Linear Programming
Objective Function
Feasible Region
A-CED Creating Equations
Create equations that describe numbers or relationships
1. Create equations and inequalities in one variable and use them to solve problems
3. Represent constraints by equations or inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or non-viable options in a modeling context. For
example, represent inequalities describing nutritional and cost constraints on combinations of
different foods.
4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving
equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
A-REI Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning
1. Explain each step in solving a simple equation as following from the equality of numbers
asserted at the previous step, starting from the assumption that the original equation has a
solution. Construct a viable argument to justify a solution method.
Solve equations and inequalities in one variable
3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
Represent and solve equations and inequalities graphically
11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y
= g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately,
e.g., using technology to graph the functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute
value, exponential, and logarithmic functions.★
I can find
expected
values of
collections of
outcomes.
Activities:
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Concepts and Skills:
Students will:
 Find distance and
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midpoint
Solve equations and
inequalities for word
problems
Write and solve equations
and inequalities for word
problems
Simplify expressions and
interpret their parts
Identify and use algebraic
properties of equality
Solve literal equations (for
a specified variable)
Solve system of equation
and inequalities using
various methods
(including graphing)
Solve linear programming
problems
Solve absolute value
inequalities
Multiple forms for linear
equations including point
slope
Learning Targets
College Readiness:
(Range 13-15) Basic Operations and Applications: Perform one-operation computation with
whole numbers and decimals
(Range 13-15) Basic Operations and Applications: Solve problems in one or two steps
Resources:
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I can evaluate
algebraic
expressions.
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Algebra II textbook: Larson,
Boswell, Kanold, Stiff
CH: 8
Internet Research
Infinite Algebra 1
Infinite Geometry
Infinite Algebra 2
Edmodo
Quality Core
Infinite Algebra II
Discovery Education
www.Khanacademy.org
brightstorm.com/math/algebra2/
Strategies:
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Graphing calculator
applications
Exit slips
ADP activities
Enrichment activities
ACT/SAT integration
Real World Applications
Vocabulary Builders
Vertices
Optimization
Maximum
Minimum
Compound Inequality
Absolute Value
Intersection
Interval Notation
Set Notation
using whole numbers
(Range 16-19) Basic Operations and Applications: Solve some routine two-step arithmetic
problems
(Range 30-36) Numbers: Concepts & Properties: Draw conclusions based on number concepts,
algebraic properties, and/or relationships between expressions and numbers
(Range 20-23) Numbers: Concepts & Properties: Exhibit knowledge of elementary number
concepts including rounding, the ordering of decimals, pattern identification, absolute value,
primes, and greatest common factor
(Range 13-15) Expressions, Equations, & Inequalities: Exhibit knowledge of basic expressions
(e.g., identify an expression for a total as b + g)
(Range 13-15) Expressions, Equations, & Inequalities: Solve equations in the form x + a = b,
where a and b are whole numbers or decimals
(Range 16-19) Expressions, Equations, & Inequalities: Substitute whole numbers for unknown
quantities to evaluate expressions
(Range 16-19) Expressions, Equations, & Inequalities: Solve one-step equations having integer
or decimal answers
(Range 16-19) Expressions, Equations, & Inequalities: Combine like terms (e.g., 2x + 5x)
(Range 20-23) Expressions, Equations, & Inequalities: Evaluate algebraic expressions by
substituting integers for unknown quantities
(Range 20-23) Expressions, Equations, & Inequalities: Add and subtract simple algebraic
expressions
(Range 20-23) Expressions, Equations, & Inequalities: Solve routine first-degree equations
(Range 20-23) Expressions, Equations, & Inequalities: Perform straightforward word-tosymbol translations
(Range 24-27) Expressions, Equations, & Inequalities: Solve real-world problems using first
degree
Equations
(Range 24-27) Expressions, Equations, & Inequalities: Write expressions, equations, or
inequalities with a single variable for common pre-algebra settings (e.g., rate and distance
problems and problems that can be solved by using proportions)
(Range 24-27) Expressions, Equations, & Inequalities: Solve first-degree inequalities that do
not require reversing the inequality sign
(Range 28-32) Expressions, Equations, & Inequalities: Manipulate expressions and equations
(Range 28-32) Expressions, Equations, & Inequalities: Write expressions, equations, and
inequalities for common algebra settings
(Range 28-32) Expressions, Equations, & Inequalities: Solve linear inequalities that require
reversing the inequality sign
(Range 33-36) Expressions, Equations, & Inequalities: Write expressions that require planning
and/or manipulating to accurately model a situation
(Range 33-36) Expressions, Equations, & Inequalities: Write equations and inequalities that
require planning, manipulating, and/or solving
NCTM:
Number and Operations:
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Develop a deeper understanding of very large and very small numbers and of various
representations of them;
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Use number-theory arguments to justify relationships involving whole numbers.
Algebra:
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understand the meaning of equivalent forms of expressions, equations, inequalities,
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I can simplify
algebraic
expressions
by combining
like terms.
I can solve
linear
equations
I can use
linear
equations to
solve real
world
problems.
I can rewrite
equations
with more
than one
variable
I can rewrite
common
formulas
I can solve
simple
inequalities
I can solve
compound
inequalities
I can solve
absolute
value
equations and
inequalities.
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and relations;
write equivalent forms of equations, inequalities, and systems of equations and solve
them with fluency—mentally or with paper and pencil in simple cases and using
technology in all cases;
Use symbolic algebra to represent and explain mathematical relationships
judge the meaning, utility, and reasonableness of the results of symbol manipulations,
including those carried out by technology.
Draw reasonable conclusions about a situation being modeled
Quality Core:
A1D: Solve single-step and multistep equations and inequalities in one variable
A1F: Write linear equations in standard form and slope-intercept form when given two points, a
point and the slope, or the graph of the equation
A1G: Graph a linear equation using a table of values, x- and y-intercepts, or slope-intercept
form
A1H: Find the distance and midpoint between two points in the coordinate plane
A1J: Use inductive reasoning to make conjectures and deductive reasoning to arrive at valid
conclusions
B1: Mathematical processes learned in the context of increasingly complex mathematical and
real-world problems
D1A: Solve linear inequalities containing absolute value
D1B: Solve compound inequalities containing “and” and “or” and graph the solution set
D2A: Graph a system of linear inequalities in two variables with and without technology to find
the solution set to the system
D2B: Solve linear programming problems by finding maximum and minimum values of a
function over a region defined by linear inequalities
Timeline:
Unit 4: Matrices
I can use
absolute
value
equations and
inequalities
to solve real
world
problems.
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Activities:
1st Semester
2 Weeks
Vocabulary:
New State Standards:
N-VM Vector & Matrix Quantities
6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence
relationships in a network
7. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a
game are doubled.
8. (+) Add, subtract, and multiply matrices of appropriate dimensions.
Resources:
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Concepts and Skills:
Students will:
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Write the dimensions of a
matrix
Identify a matrix element
Use identity and inverse
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Algebra II textbook: Larson,
Boswell, Kanold, Stiff
CH: 8
Internet Research
Infinite Algebra 1
Infinite Geometry
Infinite Algebra 2
Augmented Matrix
Determinant
Equal Matrices
Matrix
Matrix Addition
Matrix Element
Matrix Equation
Matrix Multiplication
Row Operations
Scalar Multiplication
Variable Matrix
Zero Matrix
Square Matrix
Inverse Matrix
9. (+) Understand that, unlike multiplication of numbers, matrix multiplication for square
matrices is not a commutative operation, but still satisfies the associative and distributive
properties.
10. (+) Understand that the zero and identity matrices play a role in matrix addition and
multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square
matrix is nonzero if and only if the matrix has a multiplicative inverse.
A-REI Reasoning with Equations & Inequalities
1. Explain each step in solving a simple equation as following from the equality of numbers
asserted at the previous step, starting from the assumption that the original equation has a
solution. Construct a viable argument to justify a solution method.
5. Prove that, given a system of two equations in two variables, replacing one equation by the
sum of that equation and a multiple of the other produces a system with the same solutions.
8. (+) Represent a system of linear equations as a single matrix equation in a vector variable.
9. (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations
(using technology for matrices of dimension 3 × 3 or greater).
College Readiness:
(Range 13-15) Basic Operations & Applications: Perform one-operation computation with
whole numbers and decimals
(Range 13-15) Basic Operations & Applications: Solve problems in one or two steps using
whole numbers
(Range 16-19) Basic Operations & Applications: Solve routine one-step arithmetic problems
(using whole numbers, fractions, and decimals) such as single step percent
(Range 16-19) Basic Operations & Applications: Solve some routine two-step arithmetic
problems
(Range 33-36) Numbers: Concepts &Properties: Draw conclusions based on number concepts,
algebraic properties, and/or relationships between expressions and numbers
(Range 13-15) Numbers: Concepts &Properties: Perform one-operation computation with whole
numbers and decimals
(Range 13-15) Expressions, Equations, &Inequalities: Exhibit knowledge of basic expressions
(e.g., identify an expression for a total as b + g)
(Range 13-15) Expressions, Equations, &Inequalities: Solve equations in the form x + a = b,
where a and b are whole numbers or decimals
(Range 16-19) Expressions, Equations, &Inequalities: Solve one-step equations having integer
or decimal answers
(Range 20-23) Expressions, Equations, &Inequalities: Add and subtract simple algebraic
expressions
(Range 20-23) Expressions, Equations, &Inequalities: Solve routine first-degree equations
(Range 28-32) Expressions, Equations, &Inequalities: Manipulate expressions and equations
(Range 28-32) Expressions, Equations, &Inequalities: Find solutions to systems of linear
equations
NCTM:
Numbers & Operations
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understand vectors and matrices as systems that have some of the properties of the
real-number system
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matrices
Subtract matrices
Determine equal matrices
Find unknown matrix
elements
Use scalar products
Solve matrix equations
with scalars
Multiply matrices
Determine if matrix
multiplication is defined
Verify matrix inverses
Evaluate determinant of
2X2 matrix
Find an inverse matrix
Solve a matrix equation
Evaluate determinant of
3X3 matrix
Use technology to solve
matrix problems
Write a system as a matrix
equation
Solve a system of two
equations
Solve a system of three
equations
Use Cramer’s Rule
Write an augmented
matrix
Write a system from and
augmented matrix
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Edmodo
Quality Core
Infinite Algebra II
Discovery Education
www.Khanacademy.org
brightstorm.com/math/algebra2/
Strategies:
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Graphing calculator
applications
Exit slips
ADP activities
Enrichment activities
ACT/SAT integration
Real World Applications
Vocabulary Builders
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judge the effects of such operations as multiplication, division, and computing
powers and roots on the magnitudes of quantities
develop an understanding of properties of, and representations for, the addition and
multiplication of vectors and matrices
develop fluency in operations with real numbers, vectors, and matrices, using mental
computation or paper-and-pencil calculations for simple cases and technology for
more-complicated cases
judge the reasonableness of numerical computations and their results
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Algebra:
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understand relations and functions and select, convert flexibly among, and use
various representations for them

interpret representations of functions of two variables

understand the meaning of equivalent forms of expressions, equations, inequalities,
and relations

write equivalent forms of equations, inequalities, and systems of equations and solve
them with fluency—mentally or with paper and pencil in simple cases and using
technology in all cases

judge the meaning, utility, and reasonableness of the results of symbol manipulations,
including those carried out by technology.
Quality Core:
A1A: Identify properties of real numbers and use them and the correct order of operations to
simplify expressions
A1D: Solve single-step and multistep equations and inequalities in one variable
A1E: Solve systems of two linear equations using various methods, including elimination,
substitution, and graphing
B1: Mathematical processes learned in the context of increasingly complex mathematical and
real-world problems
D1C: Solve algebraically a system containing three variables
F1A: Evaluate and simplify polynomial expressions and equations
I1A: Add, subtract, and multiply matrices
I1B: Use addition, subtraction, and multiplication of matrices to solve real-world problems
I1C: Calculate the determinant of 2 × 2 and 3 × 3 matrices
I1D: Find the inverse of a 2 × 2 matrix
I1E: Solve systems of equations by using inverses of matrices and determinants
I1F: Use technology to perform operations on matrices, find determinants, and find inverses
Timeline:
Unit 5: Factoring Quadratics and Complex Numbers
Activities:
2nd Semester
New State Standards:
4 weeks
Vocabulary:
A-SSE Seeing Structure in Expressions
Interpret the structure of expressions
1. Interpret expressions that represent a quantity in terms of its context. ★
a.
Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single
entity. For example, interpret P(1+r)n as the product of P and a factor not depending
on P.
Resources:
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Concepts and Skills:
Students will:
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Define parts of a
quadratic function
Find greatest common
factors
Factor quadratics
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Algebra II textbook: Larson,
Boswell, Kanold, Stiff
CH: 8
Internet Research
Infinite Algebra 1
Infinite Geometry
Infinite Algebra 2
Edmodo
Quadratic Function
Factor
GCF
Monomial
Binomial
Trinomial
Perfect Square Trinomial
Difference of Squares
2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as
(x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 +
y2).
College Readiness:
(Range 16-19) Number Concepts and Properties: Recognize one-digit factors of a number
(Range 24-27) Number Concepts and Properties: Work with numerical factors
(Range 28-32) Number Concepts and Properties: Apply number properties involving prime
factorization
(Range 28-32) Number Concepts and Properties: Apply number properties involving even/odd
numbers and factors/multiples
(Range 20-23) Expressions, Equations, and Inequalities: Multiply two binomials*
(Range 24-27) Expressions, Equations, and Inequalities: Factor simple quadratics (e.g., the
difference of squares and perfect square trinomials) *
(Range 28-32) Expressions, Equations, and Inequalities: Manipulate expressions and equations
NCTM:
Algebra:

Understand the meaning of equivalent forms of expressions

Use symbolic algebra to represent and explain mathematical relationships
Quality Core:
B1: Mathematical processes learned in the context of increasingly complex mathematical and
real-world problems
C1A: Identify complex numbers and write their conjugates
C1C: Simplify quotients of complex numbers
F1B: Factor polynomials using a variety of methods (e.g., factor theorem, synthetic division, long
division, sums and differences of cubes, grouping)
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Include graphical
representations of
factoring
Students will:
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Solve by factoring
Solve by finding square
roots
Solving by graphing
Simplify radicals using i
Perform operations on
complex numbers
(including rationalize the
denominator)
Factor using imaginary
numbers
Finding complex
solutions
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Quality Core
Infinite Algebra II
Discovery Education
www.Khanacademy.org
brightstorm.com/math/algebra2/
Strategies:
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
Graphing calculator
applications
Exit slips
ADP activities
Enrichment activities
ACT/SAT integration
Real World Applications
Vocabulary Builders