Download Algebra 2 - Mathematics Curriculum MPS Unit Plan # 1 Title

Algebra 2 - Mathematics Curriculum MPS
Unit Plan # 1
Title: Quadratic Functions & Factoring
Subject: Algebra 2
Length of Time: 3 weeks
Unit Summary: Students will learn how to graph quadratic functions written in standard form, vertex form,
or intercept form, how to graph and use graph of quadratic inequality to solve it. Students will learn how to
factor binomials and trinomials and learn to solve equations by factoring, finding square roots, completing
the square, and using the quadratic formula. Students will also learn to use properties of radicals, how to
simplify radicals, and how to calculate with the imaginary unit I and perform operations with complex
numbers.
Learning Targets
Conceptual Category: Number and Quantity Domain – The Complex Number System
Cluster: Perform arithmetic operations with complex numbers
Standard#:
CC.9-12.NCN2
Standard:
Use the relation i 2 = -1 and the commutative, associative, and distributive properties to add, subtract, and
multiply complex numbers.
Conceptual Category: Algebra Domain: Seeing Structure in Expressions
Cluster: Write expressions in equivalent forms to solve problems
Standard#:
CC.9-12.ASSE.3A
Standard:
Factor a quadratic expression to reveal the zeros of the function it defines.
Conceptual Category: Algebra Domain: Reasoning with Equations and Inequalities
Cluster: Solve equations and inequalities in one variable
Standard#:
CC.9-12.AREI.4A
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x
– p)2 = q that has the same solutions. Derive the quadratic formula from this form.
Standard:
CC.9.12-AREI.4B
Solve quadratic equations by inspection (e.g., for x2 = 49) taking square roots, completing the square, the
quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic
formula gives complex solutions and write them as a + bi for real numbers a and b.
Conceptual Category: Mathematics Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard#:
CC.9-12.F.IF.7
Standard:
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases. A. Graph linear and quadratic functions and show intercepts, maxima,
and minima.
Unit Essential Question:
 How do we use properties to add, subtract, and
multiply complex numbers?
 How do we factor quadratic expressions?
 How do we use the method of completing the
square to transform any quadratic equation?
Unit Enduring Understandings:
 Relation, Communicative, Associative,
Distributive Properties
 Quadratic Equations
 Quadratic Functions
 Linear Functions
 How can we solve quadratic equations by
inspection taking square roots, completing the
square, the quadratic formula and factoring?
 How can we recognize when the quadratic
formula gives complex solutions and write them as
a + bi for real numbers a and b?



Quadratic Factoring
Binomials and Trinomials
Square Roots
Unit Objectives:
 Students will learn how to graph quadratic functions written in standard form, vertex form, or
intercept form.
 Students will learn how to graph and use graph of quadratic inequality to solve it.
 Students will learn how to factor binomials and trinomials.
 Students will earn to solve equations by factoring, finding square roots, completing the square, and
using the quadratic formula.
 Students will also learn to use properties of radicals, how to simplify radicals, and how to calculate
with the imaginary unit I and perform operations with complex numbers.
Evidence of Learning
Formative Assessments:
 Quizzes, On Spot Checking for Understanding – Entry/Exit Tickets, Performance Series
Summative Assessment:
 Unit Test
Lesson Plans
Lessons
1.1 Graph Quadratic Functions in Standard Form
1.2 Graph Quadratic Functions in Vertex or
Intercept Form
1.3 Solve x2 x bx + c = 0 by Factoring
1.4 Solve ax2 x bx + c = 0 by Factoring
1.5 Solve Quadratic Equations by Finding Square
Roots
1.6 Perform Operations with Complex Numbers
1.7 Complete the Square
1.8 Use the Quadratic Formula and the
Discriminant
1.9 Graph and Solve Quadratic Inequalities
Curriculum Resources:
 Larson Algebra 2 – Teacher Resources
 www.njctl.org/courses/math/algebra2/
Timeframe
2 days
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Algebra 2 - Mathematics Curriculum MPS
Unit Plan # 2
Title: Polynomial Functions
Subject: Algebra 2
Length of Time: 3 weeks
Unit Summary: Students learn and apply properties of exponents as they simplify expressions involving
powers and add, subtract, and multiply polynomials. They learn methods to factor and solve polynomial
equations, including the Remainder and Factor Theorems. Using intercepts and other methods, students
will graph polynomial functions, classify the zeros of the functions, and find all real zeros. Students will also
write higher degree polynomial functions using intercepts and finite differences.
Learning Targets
Conceptual Category: Number and Quantity Domain: The Real Number System
Cluster: Extend the properties of exponents to rational exponents.
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer
CC.9-12.Nexponents to those values, allowing for a notation for radicals in terms of rational exponents (preparation for)
RN1
Conceptual Category: Number and Quantity Domain: The Complex Number System
Cluster: Use complex numbers in polynomial identities and equations.
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
CC.9-12.NCN.9(+)
Conceptual Category: Algebra Domain: Seeing the Structure in Expressions
Cluster: Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
CC.9-12.ASSE.2
Conceptual Category: Algebra Domain: Arithmetic with Polynomials and Rational Expressions
Cluster: Perform arithmetic operations on polynomials
Understand that polynomials form a system analogous to the integers, namely, they are closed under the
CC.9-12.Aoperations of addition, subtraction, and multiplications; add, subtract, and multiply polynomials.
APR.1
Know and apply the Remainder Theorem: for a polynomial p(x) and a number a, the remainder on division by x –
CC.9-12.A1 is p(a) = 0 if and only if (x – a) is a factor of p(x).
APR.2
Conceptual Category: Functions Domain: Interpreting Functions
Cluster: Analyze functions using different representations
CC.9-12.FIF.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases. C. graph polynomial functions, identifying zeros when suitable
factorizations are available, and showing end behavior.
Unit Essential Question:
 How do the characteristics of quadratics apply to
polynomials?
Unit Enduring Understandings:
 Like terms have the same bases with the
same degrees.
 Graphs of polynomials have end behaviors
dependent on the degree of the polynomial
 Division of Polynomials follow the rules of long

division
The total zeros (real and imaginary) total the
degree of the polynomial.
Unit Objectives:
 Students will be able to combine polynomial functions using operations of addition, subtraction,
multiplication, and division.
 Students will be to describe characteristics of polynomials given equations, tables, and graphs.
 Students will be able to find the zeros of a polynomial.
 Students will be able to apply the Fundamental Theorem of Algebra.
 Students will be able to analyze graphs of polynomial functions.
Evidence of Learning
Formative Assessments:
 Quizzes, On Spot Checking for Understanding – Entry/Exit Tickets, Performance Series
Summative Assessment:
 Unit Test
Lesson
Lessons
Timeframe
2.1 Use of Properties of Exponents
2.2 Evaluate and Graph Polynomial Functions
2.3 Add, Subtract, and Multiply Polynomials
2.4 Factor and solve Polynomial Equations
2.5 Apply the Factor and Remainder Theorems
2.6 Find Rational Zeros
2.7 Apply the Fundamental Theorem of Algebra
2.8 Analyze Graphs of Polynomial Functions
Curriculum Resources:
 Larson Algebra 2 – Teacher Resources
 www.njctl.org/courses/math/algebra2/
2 days
2 days
2 days
2 days
2 days
2 days
2 days
2 days
Algebra 2 Mathematics Curriculum MPS
Unit Plan # 3
Title: Rational and Exponents & Radical Functions
Subject: Algebra 2
Length of Time: 2 weeks
Unit Summary: Students will learn the meaning of nth roots and rational exponents, how to interchange
rational exponent notation and radical notation and how to apply the properties of rational exponents. Next,
they will perform function operations, including composition. Then, they will learn how to determine whether
a given function has an inverse that is also a function. Finally, students will graph square root and cube root
functions to solve radical equations.
Learning Targets
Conceptual Category: Number and Quantity Domain: The Real Number System
Cluster: Extend the properties of exponents to rational exponents
Standard#:
Standard:
CC.9.12.N.RN.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer
exponents to those values, allowing for a notation for radicals in terms of rational exposures.
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
CC.9.12.NRN.2
Conceptual Category: Algebra Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain
the reasoning
Standard#:
Standard:
Solve simple rational and radical equations in one variable, and give examples showing how extraneous
CC.9.12.Nsolutions may arise.
REI.2
Conceptual Category: Functions Domain: Interpreting Functions
Cluster: Analyze functions using different representations
CC.9-12.F.IF.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases. B. graph square root, cube root, and piecewise-defined functions,
including step functions and absolute value functions.
Conceptual Category: Functions Domain: Building Functions
Cluster: Build a function that models a relationship between two quantities
Write a function that describes a relationship between two quantities. B. combine standard function types using
CC.9-12.F.arithmetic operations. C. (+) compose functions.
BF.1
Conceptual Category: Functions Domain: Building Functions
Cluster: Build new functions from existing functions
CC.9-12.F.BF.4
Find inverse functions. A. solve an equation of the form f(x) = c for simple function f that has an inverse and write
an expression for the inverse. B. (+) verify by composition that one function is the inverse of another. C. (+) read
values of an inverse function from a graph or a table, given that the function has an inverse. D. (+) produce an
invertible function from a non-invertible function by restricting the domain.
Unit Essential Question:
 How are rational functions and their graphs similar
to linear functions? How are they different?
Unit Enduring Understandings:
 Denominator cannot equal zero
 Zeros of the denominator create discontinuities
at those points for the function at those values.
 To add or subtract rationals, need common
denominators.
 To solve a variation problem, one needs to find
constant of variation first.
 Solving a rational equation yields possible
solutions, substitute to check for extraneous
solutions.
Unit Objectives:
 Students will be able to simplify rational expressions.
 Students will be able to add, subtract, multiply, and divide rational expressions
 Students will be able to solve variation problems.
 Students will be able to graph rational equations, identify asymptotes, and removable
discontinuities.
 Students will be able to solve rational equations and identify if the solutions are feasible or
extraneous.
 Students will learn how to determine whether a given function has an inverse that is also a function.
 Students will graph square root and cube root functions to solve radical equations.
Evidence of Learning
Formative Assessments:
 Quizzes, On-Spot Checking for Understanding – Entry/Exit Tickets, Performance Series
Summative Assessment:
 Unit Test
Lesson Plans
Lessons
Timeframe
3.1 Evaluate nth Roots & Use Rational Exponents
3.2 Apply Properties of Rational Exponents
3.3 Perform Function Operations & Compositions
3.4 Use Inverse Functions
3.5 Graph Square Root & Cube Root Functions
3.6 Solve Radical Equations
Curriculum Resources:
 Larson Algebra 2 – Teacher Resources
 www.njctl.org/courses/math/algebra2/
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Algebra 2 - Mathematics Curriculum MPS
Unit Plan # 4
Title: Exponential & Logarithmic Functions
Subject: Algebra 2
Length of Time: 3 weeks
Unit Summary: Students learn to graph and use exponential growth and decay functions, evaluate and
graph logarithmic functions, use properties of logarithms to rewrite logarithms expressions, solve
exponential and logarithmic equations. Students will also learn to write and apply exponential and power
functions.
Learning Targets
Conceptual Category: Functions Domain: Interpreting Functions
Cluster: Analyze functions using different representations
CC.9-12.FIF.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases. C. graph polynomial functions, identifying zeros when suitable
factorizations are available, and showing end behavior.
Conceptual Category: Functions Domain: Building Functions
Cluster: Build new functions from existing functions
(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve
CC.9-12.Fproblems involving logarithms and exponents.
BF.5
Conceptual Category: Functions Domain: Linear, Quadratic and Exponential Models
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a
CC.9-12.Fdescription of a relationship, or two input-output pairs (include reading these from a table).
LE.2
For exponential models, express as a logarithm the solution to ab = d where a, c, and d are numbers and the
CC.9-12.Fbase b is 2, 10, or e; evaluate the logarithm using technology.
LE.4
Unit Essential Question:
Unit Enduring Understandings:
 What does the graph of an exponential growth
 Make sense of problems and solve them.
function look like?
 Reason abstractly and quantitatively by
evaluating logarithms, graphing logarithmic
 When is the natural base e useful?
functions, and writing/applying exponential and
 How do we rewrite exponential growth and decay
power functions.
functions to answer questions about the

Use appropriate tools strategically such as
functions?
using functions involving e, and when solving
 What is the relationship between exponential and
exponential and logarithmic inequalities.
logarithmic functions?
 Attend to precision by graphing exponential
 How can we use a calculator to evaluate a
growth functions
logarithm when the base is not 10 or e?
 Look for and make use of structure when
 Why do logarithmic equations sometimes have
graphing exponential growth functions and
extraneous solutions?
when graphing exponential decay functions.
 Look for and express regularity in repeated
 How do we determine whether a set of data fits an
reasoning such as when using functions
exponential pattern or a power pattern?
involving e and when applying properties of
logarithms.
Unit Objectives:


Students will make sense of problems and solve them.
Students will reason abstractly and quantitatively by evaluating logarithms, graphing logarithmic
functions, and writing/applying exponential and power functions.
 Students will use appropriate tools strategically such as using functions involving e, and when solving
exponential and logarithmic inequalities.
 Students will attend to precision by graphing exponential growth functions
 Students will look for and make use of structure when graphing exponential growth functions and
when graphing exponential decay functions.
 Students will look for and express regularity in repeated reasoning such as when using functions
involving e and when applying properties of logarithms.
Evidence of Learning
Formative Assessments:
 Quizzes, On Spot Checking for Understanding – Entry/Exit Tickets, Performance Series
Summative Assessment:
 Unit Test
Lesson
Lessons
Timeframe
4.1 Graph Exponential Growth Functions
4.2 Graph Exponential Decay Functions
4.3 Use Functions Involving e
4.4 Evaluate Logarithms & Graph Logarithmic
Functions
4.5 Apply Properties of Logarithms
4.6 Solve Exponential & Logarithmic Equations
4.7 Write & Apply Exponential & Power Functions
Curriculum Resources:
 Larson Algebra 2 – Teacher Resources
 www.njctl.org/courses/math/algebra2/
2 days
2 days
2 days
2 days
2 days
2 days
2 days
Algebra 2 Mathematics Curriculum MPS
Unit Plan # 5
Title: Rational Functions
Subject: Algebra 2
Length of Time: 3 weeks
Unit Summary: Students learn to write and use models for inverse and joint variation, graph rational
functions, multiply, divide, add, subtract rational expressions, and to simplify complex fractions, identify
characteristics of functions and compare properties of functions in represented in different ways.
Learning Targets
Conceptual Category: Algebra Domain: Arithmetic with Polynomials and Rational Expressions
Cluster: Rewrite rational expressions
Standard#:
CC.9-12.AAPR.7
Standard:
Understand that rational expressions form a system analogous to the rational numbers, closed under addition,
subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide
rational expressions.
Conceptual Category: Algebra Domain: Creating Equations
Cluster: Creating equations that describe numbers or relationships
Standard#:
Standard:
Create equations in two or more variables to represent relationships between quantities; graph equations on
CC.9-12.Acoordinate axes with labels and scales.
CED.2
Conceptual Category: Algebra Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain
the reasoning
Standard#:
Standard:
Solve simple rational and radical equations in one variable, and give examples showing how extraneous
CC.9-12.Asolutions may arise.
REI.2
Conceptual Category: Functions Domain: Interpreting Functions
Cluster: Analyze functions using different representations
CC.9-12.FIF.7D
CC.9-12.FIF.9
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions).
Unit Essential Question:
 What are the differences between direct, inverse,
and joint variation?
 What does the graph of the rational function
y=a/x-h + k look like?
 What are the steps for graphing a general rational
function?
 What are the steps for multiplying and dividing
rational expressions?
Unit Enduring Understandings:
 Use direct, inverse variation and joint variation
models to solve and categorize different kinds
of variation problems.
 Know the graph of the rational function y=a/x-h
+ k by translating graphs of the function y=a/x.
 Graphing the intercepts, asymptotes, and end
behavior of a rational function.
 Know the steps for multiplying and dividing
rational expressions.
 What are the steps for adding or subtracting
rational expressions with different denominators?
 What are the steps for solving rational equations?
 How do we compare functions represented in
different ways?



Know the steps for adding or subtracting
rational expressions with different
denominators.
Know the steps for solving rational equations.
Sketch a graph of different representations of
functions to compare/contrast characteristics
of functions
Unit Objectives:
 Students will be able to simplify rational expressions.
 Students will be able to add, subtract, multiply, and divide rational expressions
 Students will be able to solve variation problems.
 Students will be able to graph rational equations, identify asymptotes, and removable
discontinuities.
 Students will be able to solve rational equations and identify if the solutions are feasible or
extraneous.
 Students will graph different representations of functions to compare/contrast characteristics of
functions
Evidence of Learning
Formative Assessments:
 Quizzes, On-Spot Checking for Understanding – Entry/Exit Tickets, Performance Series
Summative Assessment:
 Unit Test
Lesson Plans
Lessons
Timeframe
5.1 Model Inverse and Joint Variation
5.2 Graph Simple Rational Functions
5.3 Graph General Rational Functions
5.4 Multiply & Divide Rational Functions
5.5 Add & Subtract Rational Expressions
5.6 Extension
5.7 Describe & Compare Function Characteristics
Curriculum Resources:
 Larson Algebra 2 – Teacher Resources
 www.njctl.org/courses/math/algebra2/
2 days
2 days
2 days
2 days
2 days
2 days
2 days
Algebra 2 - Mathematics Curriculum MPS
Unit Plan # 6
Title: Data Analysis & Statistics
Subject: Algebra 2
Length of Time: 3 weeks
Unit Summary: Students learn the formula for combinations, examine patterns found in Pascal’s triangle
and apply these patterns to binomial expansions, extend their understanding of probability distributions and
measures of central tendency to the study of normal distributions. Students will study sampling methods for
collecting data, how to identify biased samples, and how to calculate a margin of error.
Learning Targets
Conceptual Category: Algebra Domain – Arithmetic with Polynomials & Rational Expressions
Cluster: Use polynomial identifies to solve problems
Standard#:
CC.912.A.APR.5
Standard:
Know and apply the Binomial Theorem for the expansion of (x + y) n in powers of x and y for a positive integer n,
where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
Conceptual Category: Statistics & Probability Domain: Interpreting Categorical and Quantitative
Data
Cluster: Summarize, represent, and interpret data on a single count or measurement variable
Standard#:
CC.9-12.SID.4
Standard:
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population
percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators,
spreadsheets, and tables to estimate areas under the normal curve.
Conceptual Category: Statistics & Probability Domain: Making Inferences and Justifying
Conclusions
Cluster: Understand and evaluate random process underlying statistical experiments
Standard#:
CC.9-12.SIC.1
Standard:
Understand statistics as a process for making inferences about population parameters based on a random samle
from that population.
Conceptual Category: Statistics & Probability Domain: Making Inferences and Justifying
Conclusions
Cluster: Making inferences and justify conclusions from sample surveys, experiments, and
observational studies
Standard#:
CC.9.12.SIC.3
Standard:
Recognize the purposes of and differences among sample surveys, experiments, and observational studies;
explain how randomization relates to each.
Conceptual Category: Statistics & Probability Domain: Using Probability to Make Decisions
Cluster: Calculate expected values and use them to solve problems
Standard#:
CC.9.12.SMD.3
Standard:
Develop a probability distribution for a random variable defined for a sample space in which theoretical
probabilities can be calculated; find the expected value.
Unit Essential Question:
 How can we determine the value of nCr besides
applying the formula?
 What is a binomial distribution?
 Where can we find the values in a normal
distribution that rarely occur displayed on a normal
curve?
 What should be true of the sample when one
conducts a survey?
 How can we collect data that accurately
represents a population?
Unit Enduring Understandings:
 Pascal’s Triangle can be used to
determine combinations of a number of
objects taken r at a time.
 Know all possible outcomes of an event.
 Know how to calculate the probability of an
outcome.
 Areas under a normal curve can be
examined to find values that rarely occur
displayed on a normal curve.
 Samples should be unbiased and have a
limited margin of error.
 By conducting experiments and
observational studies, we can ensure that
our data better represents a population.
Unit Objectives:
 Students will learn that Pascal’s Triangle can be used to determine combinations of a number of
objects taken r at a time.
 Students will know all possible outcomes of an event.
 Students will know how to calculate the probability of an outcome.
 Students will examine areas under a normal curve to find values that rarely occur displayed on a
normal curve.
 Students will articulate that samples should be unbiased and have a limited margin of error.
 By conducting experiments and observational studies, students will ensure that our data better
represents a population.
Evidence of Learning
Formative Assessments:
 Quizzes, On Spot Checking for Understanding – Entry/Exit Tickets, Performance Series
Summative Assessment:
 Unit Test
Lesson Plans
Lessons
6.1 Use Combinations & the Binomial Theorem
6.2 Construct & Interpret Binomial Distributions
6.3 Use Normal Distributions
6.4 Select & Draw Conclusions from Samples
6.5 Compare Surveys, Experiments, and
Observational Studies
Curriculum Resources:
 Larson Algebra 2 – Teacher Resources
 www.njctl.org/courses/math/algebra2/
Timeframe
2 days
3 days
2 days
2 days
2 days
Algebra 2 - Mathematics Curriculum MPS
Unit Plan # 7
Title: Sequences and Series
Subject: Algebra 2
Length of Time: 2 weeks
Unit Summary: Students explore sequences and series, define explicit rules that generate number
sequences whose terms have a common ratio. Students use notation to represent and find the sum of the
terms of a series. They use rules for the sum of arithmetic series, finite and infinite geometric series.
Students define recursive rules for generating arithmetic and geometric sequences and investigate how to
use iteration to generate a sequence recursively given a function rule.
Learning Targets
Conceptual Category: Algebra Domain: Seeing Structure in Expressions
Cluster: Write expressions in equivalent forms to solve problems
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity
CC.9.12.Arepresented by the expression.
SSE.3
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula
CC.9.12.Ato solve problems.
SSE.4
Conceptual Category: Functions Domain: Intepreting Functions
Cluster: Understand the concept of a function and use function notation
CC.9.12.F-IF.3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the
integers.
Conceptual Category: Functions Domain: Building Functions
Cluster: Build a function that models a relationship between two quantities.
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model
CC.9.12.Fsituations, and translate between the two forms.
BF.2
Unit Essential Question:
Unit Enduring Understandings:
 How can you write an expression using
 An arithmetic sequence has a constant
summation notation?
difference between consecutive terms.

A geometric sequence has a constant ratio
 How can you tell that a sequence is arithmetic?
between consecutive terms.
 How can you find the sum of the terms of a

A series is the sum the terms of the related
geometric series?
sequence.
 What is the difference between a sequence and a
 An infinite series has a definite sum if the ratio
series?
between terms, r, is 0< |r| <1.
 What is the difference between geometric and
 Expressions for sums can be solved using
arithmetic sequences?
summation notation.
 When does an infinite geometric series have a
 Know the differences of consecutive terms of a
sum, and when does it not have a sum?
sequence.
 Know how to use the formula Sn=a1(1-r2/1-r)
 How do you write a recursive rule for an arithmetic
to find the sum of the terms of a geometric
sequence and for a geometric sequence?
series.

Determine the absolute value of the common
ratio of the series
Unit Objectives:
 Students will be able to identify the common difference in an arithmetic sequence.
 Students will be able to identify the common ratio in a geometric sequence.
 Students will be able to find the value missing term(s) in arithmetic and geometric sequences.
 Students will be able to find the sum of arithmetic, geometric, and infinite geometric series.
 Students will be able to identify special sequences, including Fibonacci Sequences.
Evidence of Learning
Formative Assessments:
 Quizzes, On Spot Checking for Understanding – Entry/Exit Tickets, Performance Series
Summative Assessment:
 Unit Test
Lesson
Lessons
Timeframe
7.1 Define & Use Sequences and Series
7.2 Analyze Arithmetic Sequences & Series
7.3 Analyze Geometric Sequences & Series
7.4 Find Sums of Infinte Geometric Series
7.5 Use Recursive Rules with Sequences &
Functions
Curriculum Resources:
 Larson Algebra 2 – Teacher Resources
 www.njctl.org/courses/math/algebra2/
2 days
2 days
2 days
2 days
2 days
Algebra 2 - Mathematics Curriculum MPS
Unit Plan # 8
Title: Quadratic Relations and Conic Sections
Subject: Algebra 2
Length of Time: 3 weeks
Unit Summary: This unit introduces students to properties and characteristics of conic sections. Students
will apply distance and midpoint formulas, graph and write equations for parabolas, circles, eclipses, and
hyperbolas, investigate translations of conic sections and methods for classifying conic sections based on
equations. Students use graphing, substitution, and elimination to solve quadratic systems.
Learning Targets
Conceptual Category: Algebra Domain: Reasoning with Equations and Inequalities
Cluster: Solve systems of equations
Solve a simple system of a linear equation and a quadratic equation in two variables algebraically and
CC.9-12.Agraphically.
REI.7
Conceptual Category: Geometry Domain: Expressing Geometric Properties with Equations
Cluster: Translate between the geometric description and the equation for a conic section
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square
CC.9-12.Gto find the center and radius of a circle given by an equation.
GPE.1
Derive the equation of a parabola given a focus and directrix.
CC.9-12.GGPE.2
Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of
CC.9-12.Gdistances from the foci is constant.
GPE.3
Cluster: Use coordinates to prove simple geometric theorems algebraically
Use coordinates to prove simple geometric theorems algebraically.
CC.9-12.GGPE.4
Unit Essential Question:
Unit Enduring Understandings:
 How can we find the position of an object at a
 Application of distance and midpoint formulas.
given time, including when it hits the ground?
 The graph of a quadratic is U-shaped and
called a parabola.
 Given the coordinates of the endpoints of the

Identification of the focus and directrix of a
diameter of a circle, how can we find the center
parabola.
and radius of a circle?

Identification of the standard form of an
 Which two features of a parabola are equidistant
equation of a circle with center (0,0).
from its vertex?
 Understanding that vertices, co-vertices, and
 What information is needed to write the equation
foci of an ellipse are related to an equation for
of a circle with center (0, 0)?
the ellipse.
 What points does one need to write an equation of
 Identification of the vertices and asymptotes of
an elipse?
a hyperbola.
 What kind of figure can be used to locate the
 Conics can be identified and graphed by
vertices and asymptotes of a hyperbola?
writing and analyzing equations of translated
conics.
 How can one identify and graph a conic if it is
translated from the general equation for that
 By solving quadratic systems, we can identify
conic?
the points of intersection of two distinct conics.
 A quadratic can have 0, 1, or 2 zeros.
 How can we identify the points of intersection of
 The x-intercepts of a quadratic can also be
two distinct conics?
called zeros or solutions.



The quadratic formula can be used to find
zeros
The discriminant of quadratic formula can tell
the number and nature of the roots
In the graph of 𝑓(𝑥) = 𝑎(𝑏(𝑥 + 𝑐))2 + 𝑑, a is a
vertical dilation or reflection, b is a horizontal
dilation or reflection, c is a horizontal slide, and
d is a vertical slide of 𝑓(𝑥) = 𝑥 2 .
Unit Objectives:
 Students will be able to graph quadratic equations.
 Students will be able to solve quadratic equations graphically and algebraically.
 Students will be able to state the number and nature of the roots of a quadratic using the
discriminant..
 Students will be able to graph quadratic inequalities.
 Students will be able to apply the techniques for finding zeros of a quadratic to real-world problems.
.
Evidence of Learning
Formative Assessments:
 Quizzes , On Spot Checking for Understanding – Entry/Exit Tickets, Performance Series
Summative Assessment:
 Unit Test
Lesson
Lessons
Timeframe
8.1 Apply the Distance & Midpoint Formulas
8.2 Graph & Write Equations of Parabolas
8.3 Graph & Write Equations of Circles
8.4 Graph & Write Equations of Ellipses
8.5 Graph & Write Equations of Hyperbolas
8.6 Translate & Classify Conic Sections
8.7 Solve Quadratic Systems
Curriculum Resources:
 Larson Algebra 2 – Teacher Resources
 www.njctl.org/courses/math/algebra2/
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Algebra 2 Mathematics Curriculum MPS
Unit Plan # 9
Title: Trigonometric Ratios & Functions
Subject: Algebra 2
Length of Time: 3 weeks
Unit Summary: Students will learn the right triangle definitions of six trigonometric functions and how to use
right triangle trigonometry. Students will learn to use radian measure to evaluate trigonometric functions of
any angle, learn to evaluate and use inverse trigonometric functions and apply law of sines and cosines to
solve triangles and applied problems.
Learning Targets
Conceptual Category: Functions Domain: Trigonometric Functions
Cluster: Extend the domain of trigonometric functions using the unit circle
Standard#:
Standard:
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
CC.9-12.FTF.1
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real
CC.9-12.Fnumbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
TF.2
Cluster: Model periodic phenomena with trigonometric functions
Understand that restricting a trigonometric function to a domain on which it is always increasing or always
CC.9-12.Fdecreasing allows its inverse to be constructed.
TF.6
Conceptual Category: Geometry Domain: Similarity, Right Triangles, and Trigonometry
Cluster: Define trigonometric ratios and solve problems involving right triangles
Standard#:
G-SRT.6
Standard:
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to
definitions of trigonometric ratios for acute angles.
Cluster: Apply trigonometry to general triangles
G-SRT.11
Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).
Unit Essential Question:
 How are trigonometric functions used in right
triangles?
 What is radian measure?
 How can you evaluate trigonometric functions of
any angle?
 What is the relationship between the sides and
angles of a triangle?
 How are inverse trigonometric functions used?
 Where can the law of sines be used to solve
triangles?
 In which cases can the law of cosines be used to
solve a triangle?
Unit Enduring Understandings:
 Solving of Right Triangles and trigonometric
equations.
 By working with angles related to central
angles of circles, radian measure will be
understood.
 Trig Ratios relate the sides and angles of a
right triangle
 The unit circle is relies on 30-60-90 and 45-4590 triangles
 Graphing trig functions is the set of points in
the form (θ, f(θ)) as oppose to the unit circle
which is (cos 𝜃, sin 𝜃)
 The law of sines and cosines are used for nonright triangles.
Unit Objectives:
 Students will be able to solve right triangles.
 Students will be able to convert radians to degrees and degrees to radians.
 Students will be able to graph trig functions
 Students will be able to apply the laws of sine and cosine to solve non-right triangles.
 Students will be able to prove trig equations by applying Pythagorean identities.
Evidence of Learning
Formative Assessments:
 Quizzes, On-Spot Checking for Understanding – Entry/Exit Tickets, Performance Series
Summative Assessment:
 Unit Test
Lesson Plans
Lessons
Timeframe
9.1 Use Trigonometry with Right Angles
9.2 Define General Angles & Use Radian Measure
9.3 Evaluate Trigonometric Functions of Any Angle
9.4 Evaluate Inverse Trigonometric Functions
9.5 Apply the Law of Sines
9.6 Apply the Law of Cosines
Curriculum Resources:
 Larson Algebra 2 – Teacher Resources
 www.njctl.org/courses/math/algebra2/
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2 days
2 days
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2 days