neptune township school district

NEPTUNE TOWNSHIP SCHOOL DISTRICT

Algebra II Curriculum

Grades 9-12


Office of the Superintendent

60 Neptune Blvd.

Neptune, NJ 07753-4836

July 31, 2019 Document C1#1

NEPTUNE TOWNSHIP BOARD OF EDUCATION

Dorothea L. Fernandez, President

Laura G. Granelli, Vice President

Brady M. Connaughton Nicole M. Green

Jerome H. Hubbard Jason A. Jones

Mark A. Matson Michelle A. Moss

Donna Puryear Antonio Lopez, Neptune City Rep.

SCHOOL DISTRICT ADMINISTRATION

Tami R. Crader, Ed.D.

Superintendent of Schools

Matthew Gristina, Ed.D.

Assistant Superintendent of Schools

Peter J. Leonard

Business Administrator/Board Secretary

Peter I. Bartlett

Assistant Business Administrator/Assistant Board Secretary

Sally A. Millaway, Ed.D.

Director for Curriculum, Instruction & Assessment

Kathleen M. Skelton

Director of Special Services

Lakeda Demery-Alston

Supervisor of Humanities & ESL

Charles Kolinofsky

Supervisor of Data & Information

Kathleen M. Thomsen

Supervisor of Early Childhood Education

ELEMENTARY SCHOOL ADMINISTRATION

Principals

Lori B. Burns, Ed.D., Early Childhood Center

Joshua Loveland, Gables

James M. Nulle, Green Grove

Mark K. Alfone, Ed.D., Midtown Community

Janelle Williams, Shark River Hills

Jerard L. Terrell, Ed.D., Summerfield

MIDDLE SCHOOL ADMINISTRATION

Arlene M. Rogo, Ed.D., Principal

Thomas Decker, Vice Principal

Michael V. Smurro, Vice Principal

HIGH SCHOOL ADMINISTRATION

Jennifer C. Joseph, Principal

Titania M. Hawkins, Ed.D., Vice Principal

Kevin McCarthy, Vice Principal

James H. Whitson, Vice Principal

Richard Arnao, Administrator for Athletic & Co-Curricular Activities

DEPARTMENT CHAIRPERSONS

Kelly Baldino

Juan Beltran

Dawn Reinhardt

Nicole Sanyigo

Tara L. Stephenson

Karen Watt

Hillary L. Wilkins


ALGEBRA II

GRADES 9-12

CURRICULUM

Table of Contents

Acknowledgements ............................................................................................................i

District Mission Statement ............................................................................................... ii

District Educational Outcome Goals .............................................................................. iii

Course Description........................................................................................................... iv

Curriculum

Unit Title Page

Unit 1 – Systems of Equations and Matrices .................................................................... 1

Unit 2 – Quadratic Functions and Factoring ..................................................................... 9

Unit 3 – Polynomials ...................................................................................................... 17

Unit 4 – Radical and Rational Functions ........................................................................ 25

Unit 5 – Logarithms ........................................................................................................ 34

Unit 6 – Trigonometry .................................................................................................... 42

Unit 7 – Data Analysis and Statistics .............................................................................. 50

Accommodations and Modifications .............................................................................. 57

Pacing Guide ................................................................................................................... 61


Algebra II

Acknowledgements

The Neptune Township School District Algebra II Math Curriculum guide for grades 9-

12 was developed through the efforts of Kristine Beaton, teacher of Mathematics, under

the guidance of Dawn Reinhardt, Department Chairperson, Heba Abdo, Ed.D.,

Supervisor of STEM, and Sally A. Millaway, Ed.D., Director for Curriculum, Instruction

and Assessment.

The teacher is to be commended for her dedication in creating this curriculum in the UbD

format and her expertise in the area of mathematics. This curriculum guide expands upon

the instruction of algebra and infuses activities that incorporate other content areas and

promote problem-solving and active learning. It is our hope that this curriculum will

serve as a valuable resource for the staff members who teach this course and that they

will continue to make recommendations for improvement to the document.

This curriculum was written in alignment with the 2014 New Jersey Student Learning

Standards for Mathematics and the increased rigor that those standards bring to the

teaching and learning of mathematics.

i


DISTRICT MISSION STATEMENT

The primary mission of the Neptune Township School District is to prepare students for a

life-long learning process in a complex and diverse world. It is with high expectations

that our schools foster:

• A strong foundation in academic and modern technologies.

• A positive and varied approach to teaching and learning.

• An emphasis on critical thinking skills and problem-solving techniques.

• A respect for and an appreciation of our world, its resources, and its people.

• A sense of responsibility, good citizenship, and accountability.

• An involvement by the parents and the community in the learning process.

ii

Neptune Township School District

Educational Outcome Goals

The students in the Neptune Township schools will become life-long learners and

will:

Become fluent readers, writers, speakers, listeners, and viewers with

comprehension and critical thinking skills.

Acquire the mathematical skills, understandings, and attitudes that are needed to

be successful in their careers and everyday life.

Understand fundamental scientific principles, develop critical thinking skills, and

demonstrate safe practices, skepticism, and open-mindedness when collecting,

analyzing, and interpreting information.

Become technologically literate.

Demonstrate proficiency in all New Jersey Student Learning Standards (NJSLS).

Develop the ability to understand their world and to have an appreciation for the

heritage of America with a high degree of literacy in civics, history, economics

and geography.

Develop a respect for different cultures and demonstrate trustworthiness,

responsibility, fairness, caring, and citizenship.

Become culturally literate by being aware of the historical, societal, and

multicultural aspects and implications of the arts.

Demonstrate skills in decision-making, goal setting, and effective communication,

with a focus on character development.

Understand and practice the skills of family living, health, wellness and safety for

their physical, mental, emotional, and social development.

Develop consumer, family, and life skills necessary to be a functioning member

of society.

Develop the ability to be creative, inventive decision-makers with skills in

communicating ideas, thoughts and feelings.

Develop career awareness and essential technical and workplace readiness skills,

which are significant to many aspects of life and work.

iii

ALGEBRA II

CURRICULUM

COURSE DESCRIPTION

(5 credits)

This course explores the process of solving equations as well as the solutions of the

equations with problem solving applications. Students review fundamental ideas of

algebra as they gradually deepen their understanding of concepts and skills necessary for

success in more advanced mathematics courses. Students will study exponential

expressions and equations, quadratic functions, systems of equations and inequalities,

polynomial functions as well as roots and radicals and rational equations and functions.

Many topics will be explored via the graphing calculator.

iv

1

Unit Title Systems of Equations and Matrices

Unit Duration 10 Days

STAGE 1: Desired Results

Overview/Rationale: Students will extend their knowledge of solving systems of equations.

Students will learn matrix operations and use inverse matrices to solve systems of three or more

variables. Students will learn how to apply constraints based on real-life situations.

2016 New Jersey Student Learning Standards for Mathematics

Math Standards Standard Statement

N.VM Vector and Matrix Quantities

A.CED Creating Equations

A.REI Reasoning with Equations and Inequalities

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 transformations of the plane, and interpret the absolute value

of the determinant in terms of area.

A.CED.2- Create equations in two or more variables to represent relationships between quantities;

graph equations on coordinate axis with labels and scales.

A.CED.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.

A.REI.8- (+) Represent a system of linear equations as a single matrix equation in a vector variable.

A.REI.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 x 3 or greater)

2

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

MODELING/EMBEDDED

N.Q.1-Use units as a way to understand problems and to guide the solution of multi-step problems;

choose and interpret units consistently in formulas; choose and interpret the scale and the origin in

graphs and data displays.

N.Q.2-Define appropriate quantities for the purpose of descriptive modeling.

N.Q.3-Choose a level of accuracy appropriate to limitations on measurement when reporting

quantities.

A.SSE.1A- Interpret expressions that represent a quantity in terms of its context. Interpret parts of

an expression such as terms, factors, and coefficients.

A.SSE.1B- - Interpret expressions that represent a quantity in terms of its context. Interpret

complicated expressions by viewing one or more of their parts as a single entity.

A.SSE.2- Use the structure of an expression to identify ways to rewrite it.

A.CED.1- Create equations and inequalities in one variable and use them to solve problems.





A.CED.4- Rearrange formulas to highlight a quantity of interest, using the same reasoning as in

solving.

3

Essential Questions:

How are the solutions to a linear equation

and the solution to a linear system related?

What can the solution to a system of

equations in three variables be used to

represent?

How can inverse matrices be used to solve

systems of equations?

How do you apply constraints to systems

of equations?

Enduring Understandings:

Students will understand that…

Systems of equations can be solved in

multiple ways and be used to represent real

life situations.

Operations can be performed on matrices

provided the matrices are of appropriate

dimension.

Inverse matrices can be used to solve systems

of equations.

Domains can be restricted to obtain

appropriate responses in a given context.

Knowledge: Students will know…

The various procedures for solving

systems of equations (graphing,

substitution, linear

combination/elimination).

Procedures for performing addition,

subtraction and scalar multiplication on

matrices.

Transform an object using matrices.

Skills: Students will be able to…

Explain the steps to solve a linear system with

three variables.

Explain how to find the product of two

matrices.

Solve systems of equations in two and three

variables.

Use matrices to solve systems of equations.

4

Integrated Social and Emotional Learning Competencies

The following social and emotional competencies are integrated in this curriculum document:

Self-Awareness

☐ Recognize one’s own feelings and thoughts

☐ Recognize the impact of one’s feelings and thoughts on one’s own behavior

☒ Recognize one’s personal traits, strengths and limitations

☒ Recognize the importance of self-confidence in handling daily tasks and challenges

Self-Management

☐ Understand and practice strategies for managing one’s own emotions, thoughts and

behaviors

☒ Recognize the skills needed to establish and achieve personal and educational goals

☐ Identify and apply ways to persevere or overcome barriers through alternative

methods to achieve one’s goals

Social Awareness

☐ Recognize and identify the thoughts, feelings, and perspectives of others

☐ Demonstrate an awareness of the differences among individuals, groups, and

others’ cultural backgrounds

☒ Demonstrate an understanding of the need for mutual respect when viewpoints

differ

☒ Demonstrate an awareness of the expectations for social interactions in a variety of

setting

Responsible Decision Making

☒ Develop, implement and model effective problem solving and critical thinking

skill

☒ Identify the consequences associated with one’s action in order to make

constructive choices

☐ Evaluate personal, ethical, safety and civic impact of decisions

Relationship Skills

☒ Establish and maintain healthy relationships

☒ Utilize positive communication and social skills to interact effectively with others

☒ Identify ways to resist inappropriate social pressure

☒ Demonstrate the ability to present and resolve interpersonal conflicts in

constructive ways

☒ Identify who, when, where, or how to seek help for oneself or others when needed

5

In this unit plan, the following 21st Century Life and Careers skills are addressed:

Check ALL that apply –

21st Century Themes

Indicate whether these skills are:

E – encouraged

T – taught

A – assessed

Career Ready Practices

9.1 Personal Financial Literacy CRP1. Act as a responsible and

contributing citizen and employee.

Income and Careers ETA CRP2. Apply appropriate academic and

technical skills.

Money Management CRP3. Attend to personal health and

financial well-being.

Credit and Debt Management ETA CRP4. Communicate clearly and

effectively and with reason.

Planning, Saving, and Investing CRP5. Consider the environmental, social

and economic impacts of decisions.

Becoming a Critical Consumer CRP6. Demonstrate creativity and

innovation.

Civic Financial Responsibility CRP7. Employ valid and reliable research

strategies.

Insuring and Protecting ETA CRP8. Utilize critical thinking to make

sense of problems and persevere in

solving them.

9.2 Career Awareness, Exploration,

and Preparation

CRP9. Model integrity, ethical leadership

and effective management.

X Career Awareness CRP10. Plan education and career paths

aligned to personal goals.

Career Exploration CRP11. Use technology to enhance

productivity.

X Career Preparation ETA CRP12. Work productively in teams while

using cultural global competence.

Career Awareness, Exploration, and Preparation

Financial Analyst

Computer Programmer

Research Scientist

Engineer

Architect / Builder

6

Interdisciplinary Connections

New Jersey Student Learning Standards - ELA

R.1- Read closely to determine what the text say as explicitly and to make logical inferences

from it; cite specific textual evidence when writing or speaking to support conclusions drawn

from the text.

W.1- Write arguments to support claims in an analysis of substantive topics or texts using

valid reasoning and relevant and sufficient evidence.

W.2- Write informative/explanatory texts to examine and convey complex ideas and

information clearly and accurately through the effective selections organization, and analysis

of content.

Technology Integration

New Jersey Student Learning Standards for Technology

NJSLS 8.1 Educational Technology: All students will use digital tools to access, manage,

evaluate, and synthesize information in order to solve problems individually and collaborate

and to create and communicate knowledge.

Google Suite - Docs, Sheets, Slides, Forms

Microsoft Platform – Word, EXCEL, PowerPoint

NJSLS 8.2 Technology Education, Engineering, Design and Computational Thinking

All students will develop an understanding of the nature and impact of technology,

engineering, technological design, computational thinking and the designed world as they

relate to the individual, global society, and the environment.

Texas Instrument TI-84 Plus and TI-89 Calculators

7

Differentiation Options:

*Note: Follow all IEP modifications or 504 Plan

In teaching mathematics, remember one size does not fit all. Your classroom serves children from a

variety of families and backgrounds, with a variety of learning strengths and needs. Differentiated

instruction is a flexible and individual approach to instruction. Teachers need to reach out to their

students as an individual or in small groups and differentiate teaching to create the best learning

experience possible. Differentiation is not always easy, but it is critical for success.

Bear in mind you need to incorporate different instructional strategies based on the assessed needs

of your students. Throughout your unit of study, you should assess students on a regular basis. This

assessment can be formal, but is often informal and can include taking conferring notes on student

progress, examining students' work, and asking the student questions about his or her understanding

of the topic. The results of the assessment are then used to drive further instruction.

Suggestions on how to differentiate in this unit:

Provide hands-on manipulatives with format skeletons to groups of students.

Facilitate group discussions to assess understanding among varying ability levels of students.

Provide additional opportunities for advanced students.

Draw and label diagrams to represent the data for visual learners.

Provide choice to students for group selections and roles in groups.

Provide multiple forms of modeling.

Provide real-life or cross-curricular connections to the material.

Provide time for revision of work when students show need.

Teacher Resources

Supplemental Workbooks: Algebra 2 Practice Workbook. McDougal Littell. 2001

Websites:

http://www.edmentum.com Practice questions for standardized tests

http://www.kutasoftware.com Test and worksheet generator for teachers

http://khanacademy.com Tutorials on individual lessons

http://www.edmentum.com/

http://www.kutasoftware.com/

http://khanacademy.com/

8

STAGE 2: Assessment Evidence

Formative Assessments &

Other Evidence of Learning

Solve Systems by Graphing: Students will complete a

worksheet where they will discover the graphical meaning of

a solution to a system of equations.

Solving a System of Equations with Matrices: Students will

use row reduction on the calculator to show the steps of

solving a system of equations by elimination/combination.

Class work, homework, and quizzes

Summative Assessments &

Performance Tasks

Unit Assessment

STAGE 3: Learning Experiences

Teaching and Learning Actions

Instructional

Strategies

Break Even Analysis: This activity will use the graphing calculator to

solve systems of equations generated to find the break-even points for

various given financial situations.

Solving Systems of Equations: Students will use the calculator to find the

solution to a system of equations both numerically and graphically.

Coded Messages: Students will use inverse matrices to obtain a basic

understanding of encrypted and coded messages.

Animated Algebra activities from http://www.classzone.com (#151, 161,

168, 196, 211)

Teacher Directed Lessons:

Perform operations on matrices

Zero and identity matrices

Using determinant to find area and find the inverse of a matrix

Solve a system using matrices

Perform transformations given a matrix

9

Unit Title Quadratic Functions and Factoring



Overview/Rationale: Students will graph and solve quadratic functions in various ways. They will

be introduced to the complex number system and the Fundamental Theorem of Algebra.




A.SSE Seeing Structures in Expressions

F.IF Interpreting Functions

N.CN The Complex Number System

A.REI.4- Solve quadratic equations in one variable

A.SSE.3- Factor a quadratic expression to reveal the zeros of the function it defines

F.IF.7C- Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases.

N.CN.1- Know there is a complex number i such that i2 = -1, and every complex number has the

form a+bi with a and b real

N.CN.2- Use the relation i2 = -1 and the commutative, associative, and distributive properties to add,

subtract, and multiply complex numbers

N.CN.7- Solve quadratic equations with real coefficients that have complex solutions










10

MODELING/EMBEDDED






quantities.












solving

11


How are the values of a, b and c in

y=ax2+bx+c related to the graph of a

quadratic function?

How can factoring be used to solve a

quadratic function when a=1? When a≠1?

What is i?

How can you solve a quadratic equation?



Operations can be performed on all types of

numbers.

There are numbers beyond the real number

system.

Quadratic equations can be given in multiple

ways and there are diverse ways to solve the

equations, determined by the individual

equation.


How to graph a quadratic function and

identify the zeros.

How to solve a quadratic function in

various ways.

How to apply the fundamental theorem of

algebra.

How to apply operations on complex

numbers.


Graph quadratic functions.

Factor and solve quadratic equations.

Find all solutions to a quadratic equation (real

and complex).

Use the rational zero theorem to solve

quadratic equations.

Apply the quadratic formula and determine

the discriminant.

12



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


13



21st Century Themes


E – encouraged

T – taught

A – assessed


9.1 Personal Financial Literacy CRP1. Act as a responsible and contributing

citizen and employee.


technical skills.



Credit and Debt Management ETA CRP4. Communicate clearly and effectively

and with reason.




innovation.


strategies.

Insuring and Protecting ETA CRP8. Utilize critical thinking to make sense

of problems and persevere in solving

them.


and Preparation






productivity.




United States Military and Law Enforcement

Engineer

Agriculture

14





from the text

W.1- Write arguments to support claims in an analysis of substantive topics or texts using valid

reasoning and relevant and sufficient evidence.

W.2- Write informative/explanatory texts to examine and convey complex ideas and information

clearly and accurately through the effective selections organization, and analysis of content









All students will develop an understanding of the nature and impact of technology, engineering,

technological design, computational thinking and the designed world as they relate to the

individual, global society, and the environment.


Teacher Resources


Websites:







15




Perplexing Quadratic Puzzle Activity: Students have to

complete a puzzle where equations and their solutions are used

as the key to put the puzzle back together.

Mind Your P’s and Q’s -Rational Zeros Activity: This activity

uses the calculator to explore the rational zero theorem.

Students will also be required to use the Remainder and Factor

Theorem to solve polynomial equations.

Chapter Review Games and Activities: Human Tic-Tac-Toe

(page 115 Algebra 2 Chapter Resource Book)



Performance Tasks

Unit Assessment

Project: Investigating Water Flow Project (page 116-117

Algebra 2, Chapter Resource Book)






















16



Instructional

Strategies


340, 371, 388, 396)

Investigating Algebra Activity- Graph Quadratic Functions (page 1-19

Algebra 2 Chapter Resource Book): Students will discover the effects of

a, h and k in the formula y=a(x-h)2 +k.

Investigating Algebra Activity- Using Algebra Tiles to Complete the

Square (page 49 Algebra 2 Textbook- page 1-77 Algebra 2 Chapter

Resource Book): Students will use algebra tiles to determine how

completing the square method will help to solve a quadratic equation.

Teacher directed lessons:

Factoring

Solve—by factoring, finding square root (real and complex

solutions), completing the square and quadratic formula.

Complex Numbers

17

Unit Title Polynomials



Overview/Rationale: Students will extend their knowledge of polynomial identities and factoring

to polynomials of higher degree. Students will explore strategies to find all solutions to a

polynomial function. Students will explore compositions of functions and understand how changing

the order of the composition will affect the solution to the composition.



A.APR Arithmetic with Polynomials and Rational Expressions

F.BF Building Functions


N.RN The Real Number System

N.CN The Complex Number System

N.CN.9- (+) Know the Fundamental Theorem of Algebra

N.RN.3- Explain why the sum or product of two rational numbers is rational; that the sum of a

rational number and an irrational number is irrational; and that the product of a nonzero rational

number and an irrational number is irrational.

A.APR.1-understand that polynomials form a system analogous to the integers, namely, that are

closed under the operation of addition, subtraction, and multiplication; add, subtract, and multiply

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.APR.5-(+) 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. (The Binomial Theorem can be proved by mathematical induction or by a

combinatorial argument)

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

F.BF.1C- Write a function that describes a relationship between two quantities (+) Compose

functions

18

F.BF.3- Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for

specific values of k (both positive and negative); find the value of k given the graphs. Experiment

with cases and illustrate an explanation of the effects on the graph using technology. Include

recognizing even and odd functions from their graphs and algebraic expressions for them.










MODELING/EMBEDDED






quantities.












solving

19


How do you simplify algebraic

expressions with exponents?

How can you graph a higher-order

function?

What ways can you solve a higher-order

function?

How can you determine how many zeroes

a function will have?



Operations can be performed on all types of

numbers.

Functions can have higher order degrees and

can be explored similarly to quadratic

functions.

Exploring the graph of functions can be used

to help determine the number of zeroes for a

function.


How to apply the special factoring patterns

of polynomials.

How to apply the fundamental theorem of

algebra.


Evaluate polynomials.

Perform arithmetic operations with

polynomials.

Factor and solve polynomial equations.

Find all solutions to a polynomial equation

(real and complex).

Use the rational zero theorem to solve

polynomial equations.

20



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


21



21st Century Themes


E – encouraged

T – taught

A – assessed





technical skills.








innovation.


strategies.



solving them.

9.2 Career Awareness,

Exploration, and Preparation






productivity.




Aerospace Engineer

Chemical Engineer

Civil Engineer

Electrical Engineer

Mechanical Engineer

Industrial Engineer

22





from the text

















Teacher Resources


Websites:







23




Perplexing Polynomial Puzzle Activity: Students have to

complete a puzzle where equations and their solutions are used

as the key to put the puzzle back together.

Interdisciplinary Application: Students will determine the

dimensions of an aquarium based on the given volume and

relationship of the dimensions (page 2-45 Algebra 2 Chapter

Resource Book).

Mind Your P’s and Q’s /Rational Zeros Activity: This activity

uses the calculator to explore the rational zero theorem.

Students will also be required to use the Remainder and Factor

Theorem to solve polynomial equations.



Performance Tasks

Unit Assessment

Build Curve (activity): Students approach performing the basic

operations on polynomials—addition, subtraction,

multiplication and division. Given the graphs of two functions,

they plot points that lie on the graph of the sum of the functions

and draw conclusions about its behavior. Students will calculate

regressions for the given functions based on their knowledge of

polynomial functions.

Differentiation Options: *Note: Follow all IEP modifications or 504 Plan











24












Instructional

Strategies

Investigating Algebra Activity: End Behavior of Polynomial Functions:

Calculator exercise to explore the concept of end behavior for polynomial

equations. (page 94 Algebra 2 Textbook).

Polynomial Transformation (activity): This activity allows the student to see

the effect changing the coefficients has on the graph of a polynomial.


340, 371, 388, 396)

Teacher directed lessons

Perform operations

Identify special patterns (Pascal’s Triangle)

Factor and solve polynomials

Use Rational Zero Theorem on polynomial functions

25

Unit Title Radical and Rational Functions



Overview/Rationale: Students will be introduced radical and rational functions and take their prior

learning of functions to transfer what they have previously done to these new types of functions.

Students will utilize strategies to solve and graph functions and explore the various properties of the

graphs of the functions.



A.APR Arithmetic with Polynomials and Rational Expressions



A.SSE Seeing Structures in Expressions

N.Q Quantities



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.APR.6- Rewrite simple rational expressions in different forms; Write a(x)/b(x) in the form q(x) +

r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree

of b(x) using inspection, long division, or, for the more complicated examples; a computer algebra

system.

F.IF.7D- Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases. (+) Graph rational functions,

identifying zeros and asymptotes when suitable factorizations are available, and showing end

behavior.

A.REI.2- Solve simple rational and radical equations in one variable, and give examples showing

extraneous solutions may arise.

F.IF.7B- Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases. Graph square root, cube root, and

piecewise-defined functions, including step functions and absolute value functions.

26





F.BF.1C- Write a function that describes a relationship between two quantities. (+) Compose

functions.

F.BF.4A- 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.

F.BF.4B- Find Inverse functions. Verify by composition that one function is the inverse of another.

F.BF.4C- Find inverse functions. (+) Read values of an inverse function from a graph or a table,

given that the function has an inverse.

F.BF.4D- Find inverse functions. (+) Produce an invertible function from a non-invertible function

by restricting the domain.










MODELING/EMBEDDED






quantities.









27




solving equations.

A.REI.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).

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.IF.2- Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F.IF.4- For a function that models a relationship between two quantities, interpret key features of

graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal

description of the relationship. Key features include: intercepts; intervals where the function is

increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end

behavior; and periodicity.

F.IF.5- Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F.IF.6- Calculate and interpret the average rate of change of a function (presented symbolically or

as a table) over a specified interval. Estimate the rate of change from a graph.

F.IF.9- Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically in tables, or by verbal descriptions).

F.BF.1B- Write a function that describes a relationship between two quantities. Combine standard

function types using arithmetic operations.

28


How do we perform operations with

radicals and rational expressions?

How are graphs of inverse functions

related?

How do we solve and graph rational and

radical equations?

How are compositions of functions used to

create other functions?

How can we restrict the domain to produce

an invertible function?

Why is it important to classify functions as

odd or even and what does this tell us about

the behavior of the function?



There is more than one way to simplify or

solve a problem with radicals and rational

expressions.

Graphs of inverse functions show how the

domain of each function relates to the range of

the other.

Rational and radical equations can be solved

for given values and can be graphed for values

within the domain.

The composition of two or more functions

produces a new function.

Domain restrictions (asymptotes or undefined

values) have effects on the graph of a function.

There may be extraneous solutions when

solving radical equations.


The properties of rational exponents.

That domain represents all the x-values that

satisfy a function and range represents all

the y- values that satisfy a function.


Solve equations numerically, algebraically

and graphically, with and without a calculator.

Compose and double compose functions.

Find nth roots of functions.

29



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


30



21st Century Themes


E – encouraged

T – taught

A – assessed





technical skills.








innovation.


strategies.



solving them.


and Preparation






productivity.




Computer Occupations

Mathematical Occupations

Grounds Maintenance

Insurance

Brick Layer

Architect

31





from the text




clearly and accurately through the effective selections organization, and analysis of content.




evaluate, and synthesize information in order to solve problems individually and collaborate and

to create and communicate knowledge.








Teacher Resources


Websites:







32


Formative

Assessments &

Other Evidence of

Learning

Composition of Functions: Given two functions, students will compose

in both directions, find inverse of each, and then find the inverses of the

composed function. Students will then compare their answers for

individual inverses vs. composed inverses.

Graphing Calculator Activity- Use Operations with Functions: Students

will use their graphing calculators to perform operations on functions

(page 187 Algebra 2 Textbook).

Graphing Calculator Activity- Verify Operations with Rational

Expressions: Students will use the graphing calculator to graph both the

original rational function and then its simplest form and compare the

graphs. (page 335 Algebra 2 Textbook).


Summative

Assessments &

Performance Tasks

Maximum Walking Speed Activity: Students will examine the

relationship between leg length and walking speed. Students will try

walking in a flat open space at an increasing speed. When the person

walking gets the urge to run, that’s his/her maximum walking speed.

Quarter 2 Assessment

Unit Assessment













33












Instructional

Strategies

Cancer Test (worksheet): How reliable are medical tests? This exercise

shows how reliable medical tests can actually be.

Numb3rs episode “Burn Rate”: Use with TI exercise for solving radical

equations to determine energy and damage of bombs of various types

and compositions.


444, 448, 458)

Investigating Algebra- Exploring Inverse Functions: Students will

discover house functions and their inverses are related graphically

before finding the inverse of a function algebraically (page 189 Algebra

2 Textbook).


Perform operations

Graph

Solve simple equations

Composition of functions

Find inverse and verify

34

Unit Title Logarithms



Overview/Rationale: Students will be introduced to logarithms and their relationship to

exponential equations. Students will use the properties and laws of logarithms to simplify and

expand expressions to make them easier to evaluate. Students will understand the connection

between logarithmic and exponential functions and learn how to solve exponential equations using

logarithms.



A.SSE Seeing Structure in Expression


F.LE Linear, Quadratic, and Exponential Models


N.Q Quantities



F.BF.5- (+) Understand the inverse relationship between exponents and logarithms and use this

relationship to solve problems involving logarithms and exponents.

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.


solving equations.

F.BF.4A- 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.

F.BF.4B- Find inverse functions. (+) Verify by composition that one function is the inverse of

another.

F.BF.4C- Find inverse functions. (+) Read values of an inverse function from a graph or a table,

given that the function has an inverse.

F.BF.4D- Find inverse functions. (+) Produce an invertible function from a non-invertible function

by restricting the domain.

F.IF.7E- Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases. Graph exponential and logarithmic

functions, showing intercepts and end behavior, and trigonometric functions, showing period,

midline, and amplitude.

35

F.IF.4- For a function that models a relationship between two quantities, interpret key features of


















MODELING/EMBEDDED






quantities.











A.REI.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).

36

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.








What is a logarithm?

How are natural logarithm and the number

e related?

How can logarithms be used to solve

exponential functions?

How can you use technology to evaluate a

logarithm?



Logarithms are functions that help determine

what exponent was used to raise a base

number to the number given.

Logarithm and exponential functions

(including the natural logarithm and the

number e) are inverses of one another.

Logarithms are used to solve exponential

equations.

Technology can evaluate logarithms quickly

and give approximations as needed.


Natural base e is irrational (similar to

pi[π]).

The properties of logarithms.

How to solve logarithmic and exponential

equations.


Solve growth and decay functions without

graphing.

Simplify and solve logarithmic and

exponential expressions and functions.

Find domain and range of growth and decay

functions.

37



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


38



21st Century Themes


E – encouraged

T – taught

A – assessed





technical skills.

Money Management CRP3. Attend to personal health and financial

well-being.


and with reason.




innovation.


strategies.



them.



CRP9. Model integrity, ethical leadership and

effective management.




productivity.




Television Crime Shows

Actuarial Science

Nuclear Medicine

Internal Medicine

39





from the text




clearly and accurately through the effective selections organization, and analysis of content.













Teacher Resources


Websites:







40




Exponential Functions Activity: This activity uses exponential

functions to find monthly payments for a new car. There is also

an activity to model exponential growth and decay functions.

(page 4-16 Algebra 2 Chapter Resource Book).

Multi-step problem: Given data, students will write exponential

models and then compare and contrast them.



Performance Tasks

Investigating Zipf’s Law: Students will investigate the

relationship between population and rank for cities in any

country they chose which is different from countries chosen by

other members of the class. Students will use the internet to find

the country’s largest cities by population and their ranking. (At

least 10 cities are needed for the graph). Students will use their

data to make a scatter plot. (page 4-85 Algebra 2 Chapter

Resource Book).

Unit Assessment













41












Instructional

Strategies

Real-life Application: Students will explore cell phone use in the United

States. Students will be given an exponential function to model the

number of cell phone subscribers, and then will identify, describe,

graph, and draw conclusions from their findings.

Graphing Calculator Activity- Graph Logarithmic Functions: Students

will use the change of base formula to graph logarithmic functions on a

calculator. (page 266 Algebra 2 Textbook).

Research project to find various rates of interest at a bank to see the

effects of compounding interest. Students will change the compounding

from daily, weekly, monthly, quarterly, semi-annually, annually and

continuously.

Various Numbe3rs activities dealing with growth, decay, and compound

interest. (Exponential Function worksheet, Compound Interest, and

Decay Function).

Animated Algebra activities from www.classzone.com (#477, 480, 487,

502, 519)


Properties

Verify logs and exponentials are inverses

Graph

Solve

Identify transformations

42

Unit Title Trigonometry



Overview/Rationale: Students will build upon their prior understanding of trigonometric functions.

Students will be introduced to the unit circle and learn how it is used to explain the graphs and

values of trigonometric functions. Students will understand how trigonometry is related to circles

and relationship between radians, degrees and arc length.



F.TF Trigonometric Functions



N.Q Quantities

F.TF.2- Explain how the unit circle in the coordinate plane enables the extension of trigonometric

functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise

around the unit circle

F.TF.1- Understand radian measure of an angle as the length of the arc on the unit circle subtended

by the angle.

F.TF.8- Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or

tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

F.TF.5- Choose trigonometric functions to model periodic phenomena with specified amplitude,

frequency, and midline.



F.IF.7E- Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases. Graph exponential and logarithmic

functions, showing intercepts and end behavior, and trigonometric functions, showing period,

midline, and amplitude.

F. IF.4- For a function that models a relationship between two quantities, interpret key features of





43














MODELING/EMBEDDED

N.Q.1- Use units as a way to understand problems and to guide the solution of multi-step problems;



N.Q.2- Define appropriate quantities for the purpose of descriptive modeling.

N.Q.3- Choose a level of accuracy appropriate to limitations on measurement when reporting

quantities





F.IF.9- Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically in tables, or by verbal descriptions).

44


How can coordinates on the unit circle and

the Pythagorean Identity be translated to

trigonometric ratios?

What is the difference between radian and

degrees and when do we use each?

How do we graph and interpret since,

cosine and tangent functions?

How do the graphs of since, cosine and

tangent relate to the values of the unit

circle?



Trigonometric relationships can be studied

and trigonometric functions evaluated using

the unit circle.

Angle measures can be written in radian or

degree form and either can be converted to the

other. Radian measurements can often be

related to arc length and area of a sector.

Sine, cosine, and tangent functions can be

graphed and interpreted by studying their

periodicity and amplitude.

The graphs of trigonometric functions are

periodic and they model real-world

phenomena.


How to read and use the unit circle to

evaluate trigonometric functions.

The properties of two special right

triangles (30-60-90 and 45-45-90).

SOHCAHTOA (sine: opposite over

hypotenuse; cosine: adjacent over

hypotenuse; tangent: opposite over

adjacent).

How to graph a trigonometric function.


Use trigonometric ratios to label all six parts

of a right triangle.

Convert radians to degrees and degrees to

radians.

Graph trigonometric functions.

45



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


46



21st Century Themes


E – encouraged

T – taught

A – assessed





technical skills.


well-being.


and with reason.

Planning, Saving, and Investing CRP5. Consider the environmental, social and

economic impacts of decisions.

Becoming a Critical Consumer CRP6. Demonstrate creativity and innovation.


strategies.



them.








productivity.




Engineers

Mathematicians

Data Entry Specialists

Statisticians

Actuaries

Chemists

Physicists

Registered Nurses

47





from the text

















Teacher Resources


Websites:







48





Writing Across the Curriculum; How does understanding 30-

60-90 and 45-45-90 triangles help in solving all types of

triangles?


Performance Tasks

Assign students various objects/buildings/trees, etc., outside of

school. Students will find the height of each object using

trigonometric functions. Students will use their height, the

length of their shadows, degrees of elevation to model a similar

right triangle to find the height of their object. Students will

work with a partner or in groups of three to find the heights of

at least two outside objects.

Unit Assessment






















49



Instructional

Strategies

Cooperative Learning: Working with a partner, students will use right

triangle trigonometry to measure heights and distances with the school

building (height of classroom door, height of the ceiling, etc.). Students will

then measure these distances with a meter/yard stick and compare the actual

measurement to the calculated distance.

Challenge: Solve the given problems listed on a worksheet using

trigonometric and inverse ratios. Students will need to use similar right

triangles and set up proportions to solve for any missing part.

Drawbridges: How can you find the width of the opening between two

halves of a 130 ft bridge that opens at a maximum angle of 65 degrees?

Investigating Algebra Activity- Explore the Graphs of the Sine and Cosine

Functions: Students will identify the characteristics of the graphs of sine and

cosine functions on the graphing calculator before graphing them by hand.

(pages 10-15, Algebra 2 Resource Book)


867, 884)


Convert between radians and degrees

Domain and range of each

Given 1 trig value, find the other 5

Graph

Identify transformations

50

Unit Title Data Analysis and Statistics



Overview/Rationale: Students will develop an understanding of statistics through a study of

sampling strategies and applying those strategies to make inferences about populations. Students

will understand the importance of randomization and how it applies to experiments. Students will be

introduced to statistical analysis and probability distributions.



S.IC Making Inferences and Justifying Conclusions

S.ID Interpreting Categorical and Quantitative Data

S.IC.1- Understand statistics as a process for making inferences about population parameters based

on a random sample from that population

S.IC.2- Decide if a specified model is consistent with results from a given data-generating process,

e.g., using simulation.

S.IC.3- Recognize the purposes of and differences among sample surveys, experiments, and

observational studies; explain how randomization relates to each.

S.IC.4- Use data from a sample survey to estimate a population mean or proportion; develop a

margin of error through the use of simulation models for random sampling.

S.IC.5- Use data from a randomized experiment to compare two treatments; use simulations to

decide if differences between parameters are significant.

S.IC.6- Evaluate reports based on data.

S.ID.4- 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.










51


Why is it important to use a random

sample when conducting an experiment?

How do you determine the best type of

sampling to represent a population?

How is standard deviation calculated and

how is it applied to normal distribution?

Why is it important to calculate the margin

of error?



Random Sampling is important to make sure

conclusions are valid and reliable.

There are various types of sampling that can

be used based on the nature of the experiment

and population.

Standard deviation can be calculated based on

survey results and applied to a normal

distribution.

It is important to calculate margin of error for

an experiment to understand the accuracy of

its results.


The difference between the various types

of sampling.

The relationship of standard deviation to

normal distribution is important.

How to calculate the margin of error for an

experiment.


Determine what sampling is best for the

experiment.

Find the standard deviation and apply it to the

normal distribution.

Calculate the margin of error.

52



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


53



21st Century Themes


E – encouraged

T – taught

A – assessed





technical skills.


well-being.


and with reason.




innovation.


strategies.



them.








productivity.




Market Research Analysis

Meteorologist

Statistician

Financial Analyst

54





from the text

















Teacher Resources


Websites:







55



Other Evidence of

Learning

Applet exercises from FAPP, Ch. 8 found at

www.whfreeman.com/fapp8e

Writing projects from FAPP, Ch. 8, p.281.

Discrete Probability Activities from the Discrete Mathematics

Project at www.colorado.edu/education/DMP



Performance Tasks

“LOTTO Winners” activity from the Discrete Mathematics

Project at www.colorado.edu/education/DMP

Unit Assessment






















56



Instructional

Strategies

Games and probability exercises from the resource binder (section 14)

“Fascinating But Funky Functions” from the resource binder.

Investigating Algebra Activity- Using a Simulation to Test an Assumption:

Students will determine whether tossing a coin is a fair test—is the probability

of a coin landing on heads really the same as tails? (page 386-387 Algebra 2

Textbook)

Teacher directed lessons

Sample data to represent a population

Distinguish different types of sampling

Evaluate a sample

Calculate margin of error

Compare random experiments

Normal distribution

57

Accommodations and Modifications

Below please find a list of suggestions for accommodations and modifications to meet the

diverse needs of our students. Teachers should consider this a resource and understand that

they are not limited to the recommendations included below.

An accommodation changes HOW a student learns; the change needed does not alter the

grade-level standard. A modification changes WHAT a student learns; the change alters the

grade-level expectation.

Special Education and 504 Plans All modifications and accommodations must be specific to each individual child’s IEP

(Individualized Educational Plan) or 504 Plan.

Pre-teach or preview vocabulary

Repeat or reword directions

Have students repeat directions

Use of small group instruction

Pair visual prompts with verbal presentations

Ask students to restate information, directions, and assignments

Repetition and time for additional practice

Model skills/techniques to be mastered

Extended time to complete task/assignment/work

Provide a copy of class notes

Strategic seating (with a purpose - eg. less distraction)

Flexible seating

Repetition and additional practice

Use of manipulatives

Use of assistive technology (as appropriate)

Assign a peer buddy

Emphasize key words or critical information by highlighting

Use of graphic organizers

Scaffold with prompts for sentence starters

Check for understanding with more frequency

Provide oral reminders and check student work during independent practice

Chunk the assignment - broken up into smaller units, work submitted in phases

Encourage student to proofread assignments and tests

Provide regular home/school communication

Teacher checks student planner

Provide student with clear expectations in writing and grading criteria for assignments

(rubrics)

Testing Accommodations:

Students should receive all testing accommodations for Benchmark assessments that they

receive for State testing.

58

Setting: Alternate setting for assessments, small groups, screens to block distractions

Presentation: large print, test readers, use of audio, fewer questions on each page

Response: answer verbally, use large block answer sheet, speech-to-text dictation,

accept short answers

Allow for retakes

Provide study guides

Use of reference aids such as glossary, multiplication tables, calculator

Choice of test format (multiple-choice, essay, true-false)

Alternate ways to evaluate (projects or oral presentations instead of written tests)

Open-book or open-note tests

English Language Learners: All modifications and accommodations should be specific to each individual child’s LEP level

as determined by the WIDA screening or ACCESS, utilizing the WIDA Can Do Descriptors.

Pre-teach or preview vocabulary

Repeat or reword directions

Have students repeat directions

Use of small group instruction

Scaffold language based on their Can Do Descriptors

Alter materials and requirements according to Can Do Descriptors

Adjust number of paragraphs or length of writing according to their Can Do Descriptor

TPR (Total Physical Response-Sheltered Instruction strategy) Demonstrate concepts

through multi-sensory forms such as with body language, intonation


Repetition and additional practice

Model skills and techniques to be mastered

Native Language translation (peer, assistive technology, bilingual dictionary)

Emphasize key words or critical information by highlighting

Use of graphic organizers

Scaffold with prompts for sentence starters

Check for understanding with more frequency

Use of self-assessment rubrics

Increase one-on-one conferencing; frequent check ins

Use study guide to organize materials

Make vocabulary words available in a student created vocabulary notebook, vocabulary

bank, Word Wall, or vocabulary ring

Extended time

Select text complexity and tiered vocabulary according to Can Do Descriptors

Projects completed individually or with partners

Use online dictionary that includes images for words:

http://visual.merriamwebster.com/.

Use online translator to assist students with pronunciation:

http://www.reverso.net/text_translation.aspx?lang=EN.

http://visual.merriamwebster.com/

http://www.reverso.net/text_translation.aspx?lang=EN

59

Students at Risk of Failure:

Use of self-assessment rubrics for check-in


Ask students to restate information and/or directions

Opportunity for repetition and additional practice

Model skills/techniques to be mastered

Extended time

Provide copy of class notes

Strategic seating with a purpose

Provide students opportunity to make corrections and/or explain their answers

Support organizational skills

Check daily planner

Encourage student to proofread work

Assign a peer buddy

Build on students’ strengths based on Multiple Intelligences: Linguistic (verbal); Logical

(reasoning); Musical/Rhythmic; Intrapersonal Intelligence (understanding of self); Visual

Spatial Intelligence; Interpersonal Intelligence (the ability to interact with others

effectively); Kinesthetic (bodily); Naturalist Intelligence; and Learning Styles: Visual;

Auditory; Tactile; Kinesthetic; Verbal

High Achieving:

Extension Activities

Allow for student choice from a menu of differentiated outcomes; choices grouped by

complexity of thinking skills; variety of options enable students to work in the mode that

most interests them

Allow students to pursue independent projects based on their individual interests

Provide enrichment activities that include more complex material

Allow opportunities for peer collaboration and team-teaching

Set individual goals

Conduct research and provide presentation of appropriate topics

Provide students opportunity to design surveys to generate and analyze data to be used in

discussion

Allow students to move through the assignment at their own pace (as appropriate)

Strategies to Differentiate to Meet the Needs of a Diverse Learning Population

Vocabulary Sorts-students engage with the vocabulary word by sorting into groups of

similar/different rather than memorizing definitions

Provide “Realia” (real life objects to relate to the five senses) and ask questions relating

to the senses

Role Play-students create or participate in role playing situations or Reader’s Theater

Moving Circle-an inside and outside circle partner and discuss, circles moves to new

partner (Refer to Kagan Differentiated Strategies)

Brainstorm Carousel-Large Post Its around the room, group moves in a carousel to

60

music. Group discusses topic and responses on paper. Groups rotate twice to see

comments of others. (Refer to Kagan Differentiated Strategies)

Gallery Walk-Objects, books, or student work is displayed. Students examine artifacts

and rotate.

Chunking-chunk reading, tests, questions, homework, etc to focus on particular elements.

Think Pair Share Write

Think Talk Write

Think Pair Share

Note-taking -can be done through words, pictures, phrases, and sentences depending on

level

KWL (Know, Want to Know, Learned)/KWHL(Know, What to Know, How Will I

Learn, learned)/KWLS (Know, Want to Know, Learned, Still Want to Know) /KWLQ

(Know, What to Know, Learned, Questions I Still Have) Charts

Corners Cooperative Learning Strategy:

http://cooperativelearningstrategies.pbworks.com/w/page/28234420/Corners.

Circle Map strategy- place the main topic in a small circle and add student ideas in a

bigger circle around the topic. Students may use their native language with peers to

brainstorm.

Flexible grouping -as a whole class, a small group, or with a partner, temporary groups

are created: http://www.teachhub.com/flexible-grouping-differentiated-instruction-

strategy.

Jigsaw Activities -cooperative learning in a group, each group member is responsible for

becoming an "expert" on one section of the assigned material and then "teaching" it to

the other members of the team: http://www.adlit.org/strategies/22371/.

http://cooperativelearningstrategies.pbworks.com/w/page/28234420/Corners

http://www.teachhub.com/flexible-grouping-differentiated-instruction-strategy

http://www.teachhub.com/flexible-grouping-differentiated-instruction-strategy

http://www.adlit.org/strategies/22371/

61

PACING GUIDE

Day Topic/Activity NJSLS-Math Pages

1

Class Procedures

1st Day Activities

2 Solve Systems of Equations Graphically A.CED.2-3 (153-159)

3 Solve Systems of Equations Algebraically A.CED.2-3 (161-167)

4

Quiz

Solve Systems of Linear Inequalities A.CED.2-3 (168-173)

5 Solve Systems with Three Variables A.CED.2-3 (178-185)

6

Quiz

Perform Basic Matrix Operations N.VM.6-8,10 (187-193)

7 Multiply Matrices N.VM.6,9-10 (195-202)

8 Evaluate Determinants and Apply Cramer's Rule N.VM.6, 11-12 (203-209)

9 Use Inverse Matrices to Solve Linear Systems A.REI.8-9 (210-217)

10 Unit 1 Review

11 Unit 1 Assessment

12 Graph Quadratic Functions in Standard Form F.IF.7C

2-9

(236-251)

13 Graph Quadratic Functions in Vertex or Intercept Form F.IF.7C

11-17

(236-251)

14 Solve Quadratic Functions by Factoring (x2+bx+c=0) A.SSE.3a

18-24

(252-265)

15 Solve Quadratic Functions by Factoring (ax2+bx+c=0) A.SSE.3a

25-31

(252-265)

16

Quiz

Solve Quadratic Functions by Finding Square Root A.REI.4 32-37

17 Perform Operations with Complex Numbers N.CN.1, 2

41-48

(275-282)

18 Perform Operations with Complex Numbers N.CN.7, A.REI.4

41-48

(275-282)

19 Complete the Square A.SSE.3, A.REI.4 50-57

20 Use the Quadratic Formula and the Discriminant N.CN.7 58-65

21 Graph and Solve Quadratic Inequalities A.REI.4b 66-73

22 Unit 2 Review

23 Unit 2 Exam

24 PARCC prep

25 Use Properties of Exponents N.RN.3

88-93

(330-336)

26 Evaluate and Graph Polynomial Functions F.IF.7 95-102

27 Add, Subtract and Multiply Polynomials

A.APR.1,5;

F.BF.1C

104-110

(346-352)

62

28

Quiz

Factor and Solve Polynomial Equations F.IF.7C

111-117

(353-361)

29 Factor and Solve Polynomial Equations F.IF.7C

111-117

(353-361)

30 Apply the Remainder and Factor Theorems A.APR.2

120-125

(362-368)

31 Find Rational Zeros A.APR.3

128-135

(370-379)

32 Apply Fundamental Theorem of Algebra N.CN.9

137-144

(379-386)

33 Analyze Graphs of Polynomial Functions

F.IF.7C;

F.BF.3

145-150

(387-392)

34 Unit 3 Review


36

Evaluate nth Roots and Use and Apply Rational

Exponents N.RN.3

166-171

(414-427)

37 Apply Properties of Rational Exponents N.RN.2 172-179

38

Quiz

Perform Function Operations and Composition A.APR.6-7; F.BF.1C

180-186

(428-435)

39 Perform Function Operations and Composition A.APR.6-7; F.BF.1C

180-186

(428-435)

40 Use Inverse Functions F.BF.4A-D

190-197

(438-445)

41

Quiz

Graph Square Root and Cube Root Functions

F.IF.7B,D;

F.BF.3

198-203

(446-451)

42 Graph Square Root and Cube Root Functions

F.IF.7B,D;

F.BF.3

198-203

(446-451)

43 Solve Radical Equations A.REI.2

204-211

(452-459)

44

Quiz

Quarter 2 Review

45 Quarter 2 Review

46 Quarter 2 Exam

47 Writing Initiative W.1, W.2

48

Graph Simple Rational Functions F.IF.7D

310-318

(558-563)

49 Graph General Rational Functions F.IF.7D

319-325

(565-569)

50

Quiz

Multiply and Divide Rational Expressions A.APR.7

327-334

(573-581)

51 Add and Subtract Rational Expressions A.APR.7

336-344

(582-588)

52 Solve Rational Equations A.REI.2

345-351

(589-595)

63

53 Unit 4 Review


55 PARCC prep

56 Graph Exponential Growth Functions

A.CED.4;

F.IF.4, 7E;

F.BF.3

228-235

(478-491)

57 Graph Exponential Decay Functions

A.CED.4;

F.IF.4, 7E;

F.BF.3

236-241

(478-491)

58 Use Functions Involving e F.LE.4; A.CED.4

244-250

(492-498)

59

Quiz

Evaluate Logarithms F.BF.5

251-257

(499-505)

60 Evaluate Logarithms and Graph Logarithmic Functions

F.BF.3,5;

F.IF.4,7E

251-257

(499-505)

61 Apply Properties of Logarithms F.BF.5

259-265

(507-513)

62 Solve Exponential and Logarithmic Equations F.BF.4A-D,5

267-274

(515-522)

63 Write and Apply Exponential and Power Functions F.LE.4

281-288

(529-536)

64 Unit 5 Review


66 PARCC

67 PARCC

68 Use Trigonometry with Right Angles G.SRT.6, 8

556-562

(852-858)

69 Define General Angles and Use Radian Measure F.TF.1

563-569

(859-865)

70 Evaluate Trigonometric Functions of Any Angle F.TF.2

570-576

(866-872)

71

Quiz

Graph Sine, Cosine and Tangent F.TF.5; F.IF.5, 7e

612-618

(908-914)

72 Graph Sine, Cosine and Tangent F.TF.5; F.IF.5, 7e

612-618

(908-914)

73 Translate and Reflect Trigonometric Graphs F.BF.3

619-626

(915-922)

74 Unit 6 Review


76 PARCC prep

77 PARCC

78 PARCC

64

79 Use Combinations and the Binomial Theorem A.APR.5(+) 378-385

80 Construct and Interpret Binomial Distributions S.MD.3(+) 388-394

81

Quiz

Use Normal Distribution S.ID.4 399-405

82 Use Normal Distribution S.ID.4 399-405

83 Select and Draw Conclusions from Samples S.IC.1 406-411

84

Compare Surveys, Experiments and Observational

Studies S.IC.3 414-419

85 Unit 7 Review


87 Final Exam Review

88 Final Exam Review

89 Final Exam

90 Final Exam


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