OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Content Area: Mathematics
Course Title: Algebra II
Grade Level: 11, 12
Unit Plan 1
Solving Equations and Inequalities
Pacing Guide
3 weeks
Unit Plan 2
Functions and Linear Models
Pacing Guide
3 weeks
Unit Plan 3
Systems of Equations in
Two and Three Variables
Pacing Guide
4 weeks
Unit Plan 4
Matrices and Matrix Operations
Pacing Guide
3 weeks
Unit Plan 5
Quadratic Functions
Pacing Guide
5 weeks
Unit Plan 6
Polynomial Functions
Pacing Guide
5 weeks
Unit Plan 7
Power, Roots and Radicals
Pacing Guide
4 weeks
Unit Plan 8
Exponential Functions
Pacing Guide
2 weeks
Unit Plan 9
Rational Functions
Pacing Guide
4 weeks
Date Created:
February 2012
Board Approved on:
March 14, 2012
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Solving Equations and Inequalities
Target Course/Grade Level: Algebra II / 11, 12
Unit Summary
Manipulating expressions, equations and inequalities algebraically to evaluate expressions and solve
equations and inequalities.
Primary interdisciplinary connections:
Infused within the unit are connection to the 2009 NJCCCS for Mathematics, Language Arts Literacy and
Technology.
21st century themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include:
Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership,
and cross cultural understanding and interpersonal communication.
Technology connections:
For further clarification refer to NJ Class Standard Introductions at:
http://www.corestandards.org/the-standards/mathematics
Learning Targets
Content Standards
Solve equations and inequalities in one variable
3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
Create equations that describe numbers or relationships
1. Create equations and inequalities in one variable and use them to solve problems. Include equations
arising from linear and quadratic functions, and simple rational and exponential functions.
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.
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.
Unit Essential Questions
• How do you translate real-life
situations into equations and
inequalities?
• How do you solve equations and
inequalities using algebra and other
strategies?
Unit Enduring Understandings
Students will understand that…
• Equation solving is working backward and undoing
operations.
• The solution to an inequality is a set, not just a single
solution.
• There is a connection between absolute value and linear
equations.
Unit Objectives
Students will know how to…
• Write algebraic expressions using
variables.
• Simplify expressions using order of
operations, the distributive property,
and combining like terms.
• Translate expressions and statements
into algebraic expressions, equations,
and inequalities.
• Evaluate variable expressions.
• Check solutions of equations and
inequalities.
• Use a process including properties of
equality and justification to solve
equations and inequalities.
• Learn the sign-change rule for
multiplying or dividing both sides of
a one-variable inequality by a
negative number.
• Solve literal equations for given
variable.
• Solve absolute value equations that
contain 0, 1, or 2 solutions.
Unit Objectives
Students will be able to…
• Solve a wide variety of equations and inequalities using
aforementioned skills.
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
•
•
Observation
Homework
Class participation
DO-NOW
Notebook
Summative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
Chapter/Unit Test
Quizzes
Presentations
•
•
Unit Projects
Quarterlies and Final Exams
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
Textbook (McDougal Littell Algebra II)
TI Graphing Calculator
Microsoft Excel
Teacher-made tests, worksheets, warm-ups, and quizzes
Computer software to support unit
Teacher Notes:
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Functions and Linear Models
Target Course/Grade Level: Algebra II / 11, 12
Unit Summary
Model real-world data by two-variable graphing. By using algebra skills, be able to predict outcomes or
estimate unknown data related to given data. Apply skills from linear equations to both inequalities and
absolute value graphs.
Primary interdisciplinary connections:
Infused within the unit are connection to the 2009 NJCCCS for Mathematics, Language Arts Literacy and
Technology.
21st century themes:
For further clarification refer to NJ Class Standard Introductions at:
http://www.corestandards.org/the-standards/mathematics
Learning Targets
Content Standards
Create equations that describe numbers or relationships
2. Create equations in two or more variables to represent relationships between quantities; graph equations
on coordinate axes with labels and scales.
3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and
interpret solutions as viable or nonviable options in a modeling context. For example, represent
inequalities describing nutritional and cost constraints on combinations of different foods.
Represent and solve equations and inequalities graphically
10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).
12. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the
case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as
the intersection of the corresponding half-planes.
Unit Essential Questions
• How can linear equations be used to
model real world data?
• How can linear graphing be used to
predict outcomes?
• When is it reasonable to estimate with
a line of best fit?
Unit Enduring Understandings
Students will understand that…
• The equation in multiple formats, and its application to
inequalities and absolute value.
• Line of fit will allow students to predict unknown values.
Unit Objectives
Students will know…
• Plot points & name coordinates of
points on the coordinate plane.
• Calculate slope of a line using the
slope formula.
• Identify the slope of a line from its
graph.
• Write the equation of a line given its
graph or two points on the line.
• Write an equation in slope intercept
form, point-slope form, and standard
form.
• Represent the solution of a twovariable equation as a linear graph.
• Graph real data as a scatter plot and
estimate line of best fit to predict an
outcome.
• Calculate linear regression with a
graphing calculator.
• Represent the solution of a twovariable inequality as a linear graph.
• Use the graphing calculator to graph
equations, inequalities, and system of
equations/inequalities.
• Graph Absolute value equations.
• Evaluate and graph piecewise
functions.
Unit Objectives
Students will be able to…
• Graph a wide variety of equations and inequalities using
aforementioned skills. Look at graphs and determine the
matching equation.
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
Observation
Homework
Class participation
•
•
DO-NOW
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.corestandards.org/the-standards/mathematics
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
Textbook (McDougal Littell Algebra II)
TI-84 Graphing Calculator
Microsoft Excel
Teacher-made tests, worksheets, warm-ups, and quizzes
Computer software to support unit
Teacher Notes:
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Systems of Equations in Two and Three Variables
Target Course/Grade Level: Algebra II / 11, 12
Unit Summary
Solve systems of equations and inequalities in two and three variables using a variety of methods.
Primary interdisciplinary connections:
Infused within the unit are connection to the 2009 NJCCCS for Mathematics, Language Arts Literacy and
Technology
21st century themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include:
Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership,
and cross cultural understanding and interpersonal communication
Technology connections:
For further clarification refer to NJ Class Standard Introductions at:
http://www.corestandards.org/the-standards/mathematics
Learning Targets
Content Standards
Solve systems of equations
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.
6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of
linear equations in two variables.
Represent and solve equations and inequalities graphically
12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in
the case of a strict inequality), and graph the solution set to a system of linear inequalities in two
variables as the intersection of the corresponding half-planes
Unit Essential Questions
• How to solve systems of equations
using graphing, substitution, and
elimination.
• Understand when each method is
appropriate.
• How to solve systems of inequalities
using graphing, and what the
intersecting region represents.
Unit Enduring Understandings
Students will understand that…
• That the intersection of two lines provides a solution to
the system.
• Solving systems by graphing has its limitations.
• Multiplying and entire equation by a non-zero constant
does not change the value of the equation.
• A real world solution to a system of equations has
significance in the real world.
Unit Objectives
Students will know…
• How to solve systems of linear
equations.
• Solve systems using substitution.
• Solve systems using elimination.
• Solve systems using graphing.
• Solve systems of linear inequalities.
Unit Objectives
Students will be able to…
• Solve systems using all methods and document their real
world meaning.
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
Observation
Homework
Class participation
•
•
DO-NOW
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.corestandards.org/the-standards/mathematics
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
Textbook (McDougal Littell Algebra II)
TI-84 Graphing Calculator
Microsoft Excel
Teacher-made tests, worksheets, warm-ups, and quizzes
Computer software to support unit
Teacher Notes:
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Matrices and Matrix Operations
Target Course/Grade Level: Algebra II / 11, 12
Unit Summary
Matrix operations including addition, subtraction, scalar multiplication, matrix multiplication, inverses and
determinants.
Use Cramer’s rule and inverse matrices to solve systems of linear equations.
Primary interdisciplinary connections:
Infused within the unit are connection to the 2009 NJCCCS for Mathematics, Language Arts Literacy and
Technology.
21st century themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include:
Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership,
and cross cultural understanding and interpersonal communication.
Learning Targets
Content Standards
N-VM.6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence
relationships in a network.
N-VM.7. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a
game are doubled.
N-VM.8. (+) Add, subtract, and multiply matrices of appropriate dimensions.
N-VM.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.
N-VM.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.
N-VM.11. (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable
dimensions to produce another vector. Work with matrices as transformations of vectors.
N-VM.12. (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value
of the determinant in terms of area.
Unit Essential Questions
• How can a system of equations be
used as a problem solving tool?
• How can matrices be used to organize
real life data?
Unit Enduring Understandings
Students will understand that…
• Matrices are a method for organizing data in rows and
columns.
• Matrices can be used to solve systems of linear equations.
Unit Objectives
Students will know…
• How to perform arithmetic with
matrices.
• How to find the inverse and
determinant of a matrix.
Unit Objectives
Students will be able to…
• Organize data in rows and columns in a matrix.
• Solve systems using matrix operations.
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
Observation
Homework
Class participation
•
•
DO-NOW
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.corestandards.org/the-standards/mathematics
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
Textbook (McDougal Littell Algebra II)
TI-84 Graphing Calculator
Microsoft Excel
Teacher-made tests, worksheets, warm-ups, and quizzes
Computer software to support unit
Teacher Notes:
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Quadratic Functions
Target Course/Grade Level: Algebra II / 11, 12
Unit Summary
Students will be able to graph quadratic functions in 3 (standard, vertex, intercept) different forms.
Students will be able to solve quadratic equations using 4 methods (factoring, square roots, quadratic
formula and completing the square).
Primary interdisciplinary connections:
Infused within the unit are connection to the 2009 NJCCCS for Mathematics, Language Arts Literacy and
Technology.
21st century themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include:
Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership,
and cross cultural understanding and interpersonal communication.
Learning Targets
Content Standards
Understand the relationship between zeros and factors of polynomials
3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a
rough graph of the function defined by the polynomial.
Analyze functions using different representations
7. 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.
c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing
end behavior.
Unit Essential Questions
• How can we model applications using
quadratic functions?
• How can we solve quadratic
equations using the quadratic formula,
factoring, completing the square, the
quadratic formula or the graph of the
parabola?
Unit Enduring Understandings
Students will understand that…
• Quadratic models occur in a variety of real world
situations
• There are several options (0,1,2) for the number of real
solutions of a quadratic.
• There are numbers other than the Real Numbers.
Unit Objectives
Students will know…
• Solve quadratic functions.
• Graph parabolas.
• Display and analyze projectile
motion.
• Find the x-intercepts of parabolas,
roots and solutions.
• Determine the vertex and general
form of a quadratic.
• Utilize the zero-product property to
solve equations.
• Factor and solve quadratic equations.
• Solve quadratic equations using the
quadratic formula.
Unit Objectives
Students will be able to…
• Solve quadratic equations by factoring or completing the
square. Use the quadratic formula to find the roots of a
second degree polynomial and to solve quadratic
equations. Graph quadratic functions and know that their
roots are the x-intercepts. Use the quadratic formula or
factoring or both to determine whether the graph of a
quadratic function will intersect the x-axis in zero, one or
two points.
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
Observation
Homework
Class participation
•
•
DO-NOW
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.corestandards.org/the-standards/mathematics
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
Textbook (McDougal Littell Algebra II)
TI-84 Graphing Calculator
Microsoft Excel
Teacher-made tests, worksheets, warm-ups, and quizzes
Computer software to support unit
Teacher Notes:
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Polynomial Functions
Target Course/Grade Level: Algebra II / 11, 12
Unit Summary
This unit is about polynomials, polynomial equations, and polynomial functions.
Primary interdisciplinary connections:
Infused within the unit are connection to the 2009 NJCCCS for Mathematics, Language Arts Literacy and
Technology.
21st century themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include:
Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership,
and cross cultural understanding and interpersonal communication.
Learning Targets
Content Standards
A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed
under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Understand the relationship between zeros and factors of polynomials.
A-APR.2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder
on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
A-APR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to
construct a rough graph of the function defined by the polynomial.
A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the
function it defines.
N-CN.8. (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x +
2i)(x – 2i).
N-CN.9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
Unit Essential Questions
• How do we perform operations on
polynomials and solve polynomial
functions?
• How do we evaluate, graph, and find
zeros of polynomial functions?
Unit Enduring Understandings
Students will understand that…
• Elements of a polynomial graph such as maximums,
minimums and zeros have real world applications.
• Polynomials can be used to maximize volumes, profits.
Unit Objectives
Students will know…
• How to simplify exponential
expressions.
• How to evaluate and graph a
polynomial function.
• Perform arithmetic operations on
polynomials. Including long and
synthetic division
• Factoring of polynomial expressions.
• Remainder and Factor Theorems.
• Finding Rational Zeros.
• Using the fundamental theorem of
algebra to determine the number of
zeros.
• Analyzing graphs of polynomial
functions.
Unit Objectives
Students will be able to…
• Perform operations on polynomials and solve polynomial
equations. They will also be able to evaluate, graph and
find the zeros of polynomial functions, and apply those
skills to solving real life problems.
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
Observation
Homework
Class participation
•
•
DO-NOW
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.corestandards.org/the-standards/mathematics
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
Textbook (McDougal Littell Algebra II)
TI-84 Graphing Calculator
Microsoft Excel
Teacher-made tests, worksheets, warm-ups, and quizzes
Computer software to support unit
Teacher Notes:
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Powers, Roots and Radicals
Target Course/Grade Level: Algebra II / 11, 12
Unit Summary
This unit is about evaluating expressions and solving equations involving radical and rational exponents.
Primary interdisciplinary connections:
Infused within the unit are connection to the 2009 NJCCCS for Mathematics, Language Arts Literacy and
Technology.
21st century themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include:
Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership,
and cross cultural understanding and interpersonal communication.
Learning Targets
Content Standards
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
exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to
hold, so (51/3)3 must equal 5.
N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
• c. Use the properties of exponents to transform expressions for exponential functions. For example
the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate
equivalent monthly interest rate if the annual rate is 15%.
A-REI.2. Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise.
A-REI.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.
F-BF.1. Write a function that describes a relationship between two quantities.
• Combine standard function types using arithmetic operations. For example, build a function that
models the temperature of a cooling body by adding a constant function to a decaying exponential,
and relate these functions to the model.
• (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of
height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the
temperature at the location of the weather balloon as a function of time.
F-BF.4. Find inverse functions.
• Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an
expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.
• (+) Verify by composition that one function is the inverse of another.
• (+) Read values of an inverse function from a graph or a table, given that the function has an
inverse.
• (+) Produce an invertible function from a non-invertible function by restricting the domain.
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.
Unit Essential Questions
• How do we evaluate expressions with
rational exponents?
• How do you graph and solve radical
equations?
Unit Enduring Understandings
Students will understand that…
• Radicals can be expressed as rational exponents.
• Composition of functions can be used to create more
efficient algorithms.
Unit Objectives
Students will know…
• How to evaluate nth roots of real
numbers (using both radical and
rational exponent notation).
• Use the properties of rational
exponents to evaluate and simplify
expressions.
• Perform operations on power
functions, including composition.
• Find and graph the inverse of a linear
and power function.
• Graphing of square and cube root
functions.
• Solve equation containing radical and
rational exponents.
Unit Objectives
Students will be able to…
• Use rational exponents and nth roots of numbers.
• Perform operations with and find inverses of functions.
• Graph and solve radical functions.
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
Observation
Homework
Class participation
•
•
DO-NOW
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.corestandards.org/the-standards/mathematics
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
Modifications (ELLs, Special Education, Gifted and Talented)
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•
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•
•
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Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
Textbook (McDougal Littell Algebra II)
TI-84 Graphing Calculator
Microsoft Excel
Teacher-made tests, worksheets, warm-ups, and quizzes
Computer software to support unit
Teacher Notes:
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Exponential Functions
Target Course/Grade Level: Algebra II / 11, 12
Unit Summary
This unit is about exponential functions.
Primary interdisciplinary connections:
Infused within the unit are connection to the 2009 NJCCCS for Mathematics, Language Arts Literacy and
Technology.
21st century themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include:
Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership,
and cross cultural understanding and interpersonal communication.
Learning Targets
Content Standards
A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
• c. Use the properties of exponents to transform expressions for exponential functions. For example
the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate
equivalent monthly interest rate if the annual rate is 15%.
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.
• e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and amplitude.
F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain
different properties of the function.
• b. Use the properties of exponents to interpret expressions for exponential functions. For example,
identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y =
(1.2)t/10, and classify them as representing exponential growth or decay.
F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential
functions.
• Prove that linear functions grow by equal differences over equal intervals, and that exponential
functions grow by equal factors over equal intervals.
• Recognize situations in which a quantity grows or decays by a constant percent rate per unit
interval relative to another.
F-LE.3. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
F-LE.4. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are
numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context.
Unit Essential Questions
• How do we model real lift data using
exponential functions?
• What is a limit?
Unit Enduring Understandings
Students will understand that…
• Exponential functions can be used to predict the future
value of cars, populations.
Unit Objectives
Students will know…
• How to graph and solve exponential
growth and decay functions.
• Use properties of exponents
Unit Objectives
Students will be able to…
• Use exponential functions to model real live situations.
• Graph and solve exponential functions.
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
Observation
Homework
Class participation
•
•
DO-NOW
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.corestandards.org/the-standards/mathematics
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
Textbook (McDougal Littell Algebra II)
TI-84 Graphing Calculator
Microsoft Excel
Teacher-made tests, worksheets, warm-ups, and quizzes
Computer software to support unit
Teacher Notes:
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Rational Functions
Target Course/Grade Level: Algebra II / 11, 12
Unit Summary
This chapter is about evaluating, solving and graphing rational functions.
Primary interdisciplinary connections:
Infused within the unit are connection to the 2009 NJCCCS for Mathematics, Language Arts Literacy and
Technology.
21st century themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include:
Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership,
and cross cultural understanding and interpersonal communication.
Learning Targets
Content Standards
A-REI.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.
A-APR.7. (+) 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.
A-REI.2. Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise.
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.
• d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are
available, and showing end behavior.
Unit Essential Questions
• How do the graphs of rational
functions differ from the graphs of
other functions that we’ve studied so
far?
• How do you simplify a complex
rational expression?
Unit Enduring Understandings
Students will understand that…
• Rational functions are the ratio of two polynomial
functions.
• Rational functions have limited domains and ranges.
Unit Objectives
Students will know…
• Perform arithmetic operations on
rational expressions and simplify the
results.
• Solve rational equations.
• Graph rational functions.
• Recognize asymptotes as limits to
rational functions.
Unit Objectives
Students will be able to…
• Simplify and perform operations with rational
expressions.
• Solve and Graph rational functions.
OCEAN COUNTY MATHEMATICS CURRICULUM
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.corestandards.org/the-standards/mathematics
•
•
•
Observation
Homework
Class participation
•
•
DO-NOW
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.corestandards.org/the-standards/mathematics
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
Textbook (McDougal Littell Algebra II)
TI-84 Graphing Calculator
Microsoft Excel
Teacher-made tests, worksheets, warm-ups, and quizzes
Computer software to support unit
Teacher Notes: