COURSE OF STUDY UNIT PLANNING GUIDE FOR · Algebra 2 H is designed to challenge high achieving students, who are recommended based on their performance in Algebra 1 and Geometry

COURSE OF STUDY UNIT PLANNING GUIDE FOR:

ALGEBRA 2 H

5 CREDITS GRADE LEVEL: 10121 FULL YEAR

PREPARED BY: LIZA FRANGIOSA

JACLYN HRNCIAR

SHANNON WARNOCK SUPERVISOR OF MATHEMATICS AND SCIENCE

JULY 2018

DUMONT HIGH SCHOOL DUMONT, NEW JERSEY

BORN DATE: AUGUST 24, 2017 ALIGNED TO THE NJSLS AND B.O.E. ADOPTED AUGUST 23, 2018

Algebra 2 H – Grades 1011 – Full Year – 5 Credits (Weighted Course, Prerequisite: Meets admissions criteria) Algebra 2 H is designed to challenge high achieving students, who are recommended based on their performance in Algebra 1 and Geometry. This is a more rigorous second year course in algebra, which consists of a curriculum rich in application and problem solving. Topics covered include graphing, systems of equations, quadratic functions, polynomial functions, rational functions, logarithmic functions, exponential functions, statistics, probability, series, sequences, complex numbers, and basic trigonometry. Both scientific and graphing calculators are used as tools to assist in the development of concepts. This course is geared for students planning to pursue advanced studies in mathematics and science. COURSE REQUIREMENTS AND EXPECTATIONS A student will receive 5 credits for successfully completing course work. A grade of "D" or higher must be achieved in order to pass the course. The following criteria are used to determine the grade for the course: A. Tests 50% of the grade

Tests will be given periodically. These may include alternative assessments that will count as tests. B. Quizzes 35% of the grade

Quizzes (announced and unannounced) based on class lessons or homework assignments will be given frequently to assess understanding of individual concepts. These may include alternative assessments that will count as quizzes.

C. Homework 10% of the grade Homework will be evaluated for completeness, neatness, and/or accuracy.

D. Class Participation/Class Work 5% of the grade Class Participation/Class Work will be evaluated a minimum of twice per marking period according to the departmental rubric (see page 3). The grade is based on the student's participation/work during class. Thus, consistent attendance is imperative.

E. Final Examination Final examinations will count as follows: FullYear Courses Weighting Semester Courses Weighting Quarter 1 22.5% of final grade Quarter 1 45% of final grade Quarter 2 22.5% of final grade Quarter 2 45% of final grade Quarter 3 22.5% of final grade Final Exam 10% of final grade Quarter 4 22.5% of final grade Final 10% of final grade

Any work missed when the student has been absent is expected to be made up in a reasonable time. Usually one or two days are allowed for each day absent unless there are unusual circumstances, in which case the student is to request special arrangements with the teacher. Extra help is available. Ask your teacher where he/she will be when you are planning to come in for extra help.

High School Mathematics Participation Rubric

1(60) Inadequate

2(70) Limited

3(80) Partial

4(90) Adequate

5(100) Superior

Attendance

Almost never with attendance policies and/or punctuality Almost never makes up work in timely fashion

Rarely abides by attendance policies and/or punctuality Rarely makes up work in timely fashion

Sometimes struggles with attendance policies and/or punctuality Sometimes makes up work in timely fashion

Almost always punctual Almost always makes up work in timely fashion Not disruptive when tardy

Always punctual Always makes up work in a timely fashion

Preparedness

Almost never has pencil, books, calculators, and/or notebooks Almost never has assignments on time

Rarely has pencil, books, calculators, and/or notebooks Rarely has assignments on time

Sometimes has pencil, books, calculators, and/or notebooks Sometimes has assignments on time

Almost always has pencil, books, calculators, and/or notebooks Almost always has assignments on time

Always has pencil, books, calculators, and/or notebooks Always has assignments on time

Oral

Participation

Almost never asks & answers questions without prompting

Rarely asks & answers questions without prompting

Sometimes asks & answers questions without prompting

Almost always asks & answers questions without prompting

Always asks & answers questions without prompting (daily)

Written

Participation

Almost never takes notes Almost never makes corrections on homework/ class work and/or applies teacher recommendations to writing

Rarely takes notes Rarely makes corrections on homework/ class work and/or applies teacher recommendations to writing

Sometimes takes notes Sometimes makes corrections on homework/ class work and/or applies teacher recommendations to writing

Almost always takes notes Almost always makes corrections on homework/ class work and applies teacher recommendations to writing

Always takes notes Always makes corrections on homework/ classwork and applies teacher recommendations to writing

Cooperative Learning

Almost never provides meaningful input Almost never focused on the assignment Almost never assumes a leadership role

Rarely provides meaningful input Rarely focused on the assignment Rarely assumes a leadership role

Sometimes provides meaningful input Sometimes focused on the assignment Sometimes assumes a leadership role

Almost always provides meaningful input Almost always focused on the assignment Almost always assumes a leadership role

Always provides meaningful input Always focused on the assignment Usually assumes a leadership role

General Behavior

Almost never shows respect for peers and teacher Almost never remains focused on assignments Almost never abides by all class & school rules ALMOST NEVER HAS CELL PHONE/IPOD

Rarely shows respect for peers and teacher Rarely remains focused on assignments Rarely abides by all class & school rules ALMOST NEVER HAS CELL PHONE/IPOD

Sometimes shows respect for peers and teacher Sometimes remains focused on assignments Sometimes abides by all class & school rules NEVER HAS CELL PHONE/IPOD

Almost always shows respect for peers and teacher Almost always remains focused on assignments Almost always abides by all class & school rules NEVER HAS CELL PHONE/IPOD

Always shows respect for peers and teacher Always remains focused on assignments Always abides by all class & school rules NEVER HAS CELL PHONE/IPOD

*Score of Zero Results from Limited or No Response to Class Participation/Class Work

Unit 1: Functions Number of Days 13

NJSLSM NQ.A. Reason quantitatively and use units to solve problems. 1. Use units as a way to understand problems and to guide the solution of multistep problems; choose and

interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

2. Define appropriate quantities for the purpose of descriptive modeling. ACED.A. Create equations that describe numbers or relationships

4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. AREI.D. 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).

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.

FIF.A. Understand the concept of a function and use function notation 1. Understand that a function from one set (called the domain) to another set (called the range) assigns to

each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f ( x ) denotes the output of f corresponding to the input x . The graph of f is the graph of the equation y = f ( x ).

2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

FIF.B. Interpret functions that arise in applications in terms of the context 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.

5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

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.

FIF.C. 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. 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different

properties of the function. 9. Compare properties of two functions each represented in a different way (algebraically, graphically,

numerically in tables, or by verbal descriptions). FBF.B. Build new functions from existing functions

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.

4. Find inverse functions. a. 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. c. Read values of an inverse function from a graph or a table, given that the function has an inverse.

Standards for Mathematical Practices

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.6 Attend to precision. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Science and Engineering Practices (SEP)

SEP.2 Developing and Using Models SEP.5 Using Mathematics and Computational Thinking

NJSLS for ELA Companion Standards for Science: RST

RST.1112.4. Determine the meaning of symbols, key terms, and other domainspecific words and phrases as they are used in a specific scientific or technical context relevant to grades 1112 texts and topics.

RST.1112.9. Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible.

NJSLS for ELA Companion Standards for Science: WHST

WHST.1112.4. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

WHST.1112.9. Draw evidence from informational texts to support analysis, reflection, and research.

Career Ready Practices (CRPs)

CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP6. Demonstrate creativity and innovation. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity.

21st Century: Personal Financial Literacy (9.1)

NA

21st Century: Career Awareness, Exploration, and Preparation (9.2)

NA

Educational Technology (8.1)

8.1.12.A.3 Collaborate in online courses, learning communities, social networks or virtual worlds to discuss a resolution to a problem or issue.

Technology Education, Engineering, Design, and Computational Thinking Programming (8.2)

NA

Students will be able to...

Find the domain and range of a function. Write in interval notation. Determine if a function is even, odd, or neither. Find the rate of change between two points. Graph the parent function and transformations by manipulating the a, h, and k values. Describe the end behavior of a function. Find the intercepts of a function. Find the relative maxima and minima. Determine when the function is increasing and decreasing. Find the inverse. Use the function to model realworld problems.

Essential Questions How do you identify and write in interval notation the domain and range of a function? How do you determine if a function is even, odd, or neither graphically and algebraically? How do you find the rate of change between two points on a graph? Can you graph parent functions and graph multiple transformations? What is the end behavior of the function? What are the x and yintercepts of the function? How do you find the relative max and min of a function? When is the function increasing or decreasing?

How do you find the inverse of each function? How can you use functions to model real world situations?

Activities Transformation Stations Inverse Discovery Domain & Range Exit Slip Functions Review Study Island

Resources Study Island Khan Academy Big Ideas Kuta Software New Jersey Center for Teaching & Learning Pearson

Vocabulary Compress Decreasing Dependent Domain End Behavior Even Function Increasing Independent Variable Interval Notation Inverse Odd Function Parent Function Range Rate of Change Reflect Relative Minimum Relative Maximum Stretch Symmetry System of Equations Translate

XIntercept YIntercept

Technology/GAFE Videos on functions posted to Classroom Link to Khan Academy

Special Education/504

Formula Sheet on Average Rate of Change Providing Notes/Modified Notes

SMART Board Notes Guided Notes on Functions

Highlighting Underlining Providing Definitions

Chunking of function vocabulary Scaffolding on functions Repeat/Rephrase vocabulary and notation of functions Graphic Organizers on functions Study Guides on Functions Modified Assessments Conferencing

Student Parent Guidance Administration CST

Tutoring/Extra Help

ELL (SEI) Bilingual Math Dictionaries Total Physical Response Native/NonNative Speaker Groupings Formula Sheet on Average Rate of Change Providing Notes/Modified Notes

Include native language in guided notes Highlighting Underlining Providing Definitions in English and native language

Chunking of function vocabulary

Scaffolding on functions Repeat/Rephrase vocabulary and notation of functions Graphic Organizers on functions Study Guides on Functions Modified Assessments Conferencing


Tutoring/Extra Help

At Risk of School Failure

Formula Sheet on Average Rate of Change Providing Notes/Modified Notes

SMART Board Notes Guided Notes on Functions


Chunking of function vocabulary Scaffolding on functions Repeat/Rephrase vocabulary and notation of functions Graphic Organizers on functions Study Guides on Functions Modified Assessments Priority Seating Checking Assignments Pads Conferencing


Tutoring/Extra Help

Gifted & Talented SelfDirected Learning on Domain & Range

Supplemental Challenge Problems Transforming the Graph of a Function, Real World Average Rate of Change

Formative, Summative, Benchmark, and Alternative Assessments

Formative: Exit Slips Homework Khan Academy assignments Study Island assignments Functions, Transformation, Inverse Quizzes

Summative: Function Test Benchmark: Summer Assignment & Assessment

Unit 2: Quadratic and Radical Functions Number of Days 20

NJSLSM AAPR.A. Perform arithmetic operations on polynomials 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. 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. ASSE.A. Interpret the structure of expressions

1. Interpret expressions that represent a quantity in terms of its context. 1 a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity.

2. Use the structure of an expression to identify ways to rewrite it. ACED.A. Create equations that describe numbers or relationships

1. Create equations and inequalities in one variable and use them to solve problems. 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. 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

AREI.A. 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.

2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

AREI.B. Solve equations and inequalities in one variable 4. Solve quadratic equations in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form ( x – p ) 2 = q that has the same solutions. Derive the quadratic formula from this form.

b. Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b .

AREI.C. Solve systems of equations

7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

AREI.D. 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). 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.

ASSE.B. Write expressions in equivalent forms to solve problems 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. c. Use the properties of exponents to transform expressions for exponential functions.

FIF.B. Interpret functions that arise in applications in terms of the context 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.

5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

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.


using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewisedefined functions, including step functions and

absolute value functions. 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different

properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros,

extreme values, and symmetry of the graph, and interpret these in terms of a context.

9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

FBF.B. Build new functions from existing functions 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.

4. Find inverse functions. a. 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. c. Read values of an inverse function from a graph or a table, given that the function has an inverse.

NRN.A. Extend the properties of exponents to rational exponents. 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. 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

NRN.B. Use properties of rational and irrational numbers. 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.

NCN.A. Perform arithmetic operations with complex numbers. 1. Know there is a complex number i such that i 2 = –1, and every complex number has the form a + bi with

a and b real. 2. Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and

multiply complex numbers. 3. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex

numbers. NCN.C. Use complex numbers in polynomial identities and equations.

7. Solve quadratic equations with real coefficients that have complex solutions. 8. Extend polynomial identities to the complex numbers.


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.6 Attend to precision. MP.5 Use appropriate tools strategically.

Science and SEP.1 Asking Questions and Defining Problems

Engineering Practices (SEP)

SEP.2 Developing and Using Models SEP.5 Using Mathematics and Computational Thinking





WHST.1112.1. Write arguments focused on disciplinespecific content. C. Use transitions (e.g. words, phrases, clauses) to link the major sections of the text, create cohesion, and

clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.


CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity.


NA


NA




NA

Students will be able Simplify radical expressions of various indices.

to... Perform operations with radicals of various indices. Rationalize denominators of various indices. Write nth roots as rational exponents and vice versa. Use properties of exponents to simplify expressions with rational exponents. Identify the imaginary unit i as part of the Complex Number System Simplify and perform operations with complex numbers. Solve equations with real and imaginary solutions. Graph square and cube root functions and identify transformations on the function Rationalize denominators with complex conjugates. Graph quadratic functions of the form y = x 2 and identify transformations to the parent function. Derive the equation of a parabola given a focus and directrix. Solve quadratic equations by factoring, the quadratic formula and completing the square with real and imaginary

solutions. Use quadratic functions to model real world situations. Solve and graph systems of quadratic and linear equations.

Essential Questions How do you simplify radicals with various indices? When can radical expressions be simplified? When and how do you rationalize a denominator? How do you rewrite radical expressions with rational exponents? How do you simplify expressions with rational exponents? What is a complex number and how is it written in standard form? What operations hold true for complex numbers? What are extraneous solutions? How do I know if a solution is viable? How do I transform the square and cube root function graphs? What are the characteristics of a quadratic function? What is the resulting graph after transforming the parent function? What are the focus and directrix of a parabola? When is it appropriate to solve by factoring, the quadratic formula, and completing the square? How are the real solutions of a quadratic equation related to the graph of the function? How do I use a system of three equations to write a quadratic function? What does the solution of a system represent?

Activities Complex Number Patterns Quadratic Transformation Stations Nth Root & Rational Exponent Discovery

Graphing Radical & Quadratics Exit Slip Quadratics & Radical Review Study Island


Vocabulary Axis of Symmetry Coefficient Completing the Square Complex Numbers Complex Conjugate Theorem Conjugates Discriminant Equal Complex Numbers Extraneous Solutions Imaginary Unit Index Intercept Form Like Terms n th Root Parabola Power Polynomial Function Pure Imaginary Number Quadratic Equation Quadratic Formula Quadratic Function Radical Equations Radicand Rational Exponent Rationalizing the Denominator Root

Simplify Square Root Standard Form Vertex Vertex Form Zero Zero Product Property

Technology/GAFE Videos on focus and directrix posted to Classroom Link to Khan Academy


Formula Sheet for Quadratic Formula Providing Notes/Modified Notes

SMART Board Notes on Radicals & Quadratics Guided Notes on Radicals & Quadratics


Modeling on Radicals & Quadratics Chunking on Radicals & Quadratics Scaffolding on Radicals & Quadratics Manipulatives/Visuals on Radicals & Quadratics Graphic Organizers on Simplifying Nth Roots, How to Solve Quadratic Equations, Complex Number System Study Guides on Radicals & Quadratics Conferencing


Tutoring/Extra Help

ELL (SEI) Bilingual Math Dictionaries Total Physical Response Native/NonNative Speaker Groupings Formula Sheet for Quadratic Formula Providing Notes/Modified Notes

SMART Board Notes on Radicals & Quadratics Guided Notes on Radicals & Quadratics

Highlighting Underlining Include native language in guided notes Providing Definitions in English and native language

Modeling on Radicals & Quadratics Chunking on Radicals & Quadratics Scaffolding on Radicals & Quadratics Manipulatives/Visuals on Radicals & Quadratics Graphic Organizers on Simplifying Nth Roots, How to Solve Quadratic Equations, Complex Number System Study Guides on Radicals & Quadratics Conferencing


Tutoring/Extra Help


Providing Notes/Modified Notes SMART Board Notes on Radicals & Quadratics

Guided Notes on Radicals & Quadratics Highlighting Underlining Providing Definitions

Modeling on Radicals & Quadratics Chunking on Radicals & Quadratics Scaffolding on Radicals & Quadratics Manipulatives/Visuals on Radicals & Quadratics Graphic Organizers on Simplifying Nth Roots, How to Solve Quadratic Equations, Complex Number System Study Guides on Radicals & Quadratics Priority Seating Checking Assignments Pads Conferencing

Student Parent

Guidance Administration CST

Tutoring/Extra Help

Gifted & Talented SelfDirected Learning on Focus & Directrix Supplemental Challenge Problems on Powers of a Complex Number, Completing the Square, Linear & Quadratic

Systems


Formative: Exit Slips Homework Khan Academy assignments Study Island assignments Simplifying Radicals, Nth Root, Solving & Graphing Radicals, Solving Quadratics, Modeling with

Quadratics Quizzes Summative: Radical & Quadratics Test

Unit 3: Polynomial Functions Number of Days 20

NJSLSM NCN.C. Use complex numbers in polynomial identities and equations. 8. Extend polynomial identities to the complex numbers. 9. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

AAPR.A. Perform arithmetic operations on polynomials 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. AAPR.B. Understand the relationship between zeros and factors of polynomials

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 ).

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.

AAPR.C. Use polynomial identities to solve problems 4. Prove polynomial identities and use them to describe numerical relationships.

AAPR.D. Rewrite rational expressions 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.


using technology for more complicated cases. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and

showing end behavior.


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Science and SEP.2 Developing and Using Models

Engineering Practices (SEP)

SEP.5 Using Mathematics and Computational Thinking








CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity.


NA


NA




NA


Graph polynomial functions, performing transformations and identifying key characteristics, such as end behavior, intercepts, max and min.

Classify functions as even, odd or neither. Know and apply the Remainder Theorem to find the zeros of a polynomial function. Understand the relationship between zeros and factors of polynomials. Solve nonquadratic equations by using quadratic techniques. Extend polynomial identities to complex numbers.

Essential Questions What is the end behavior of a polynomial function given an even/odd degree and a positive/negative leading coefficient?

How do you find the relative minimum/maximum of a function? How do I tell graphically and algebraically if a function is even, odd, or neither? When is the function increasing, decreasing, or constant? How can the factors of a polynomial be found using long and synthetic division? What are the zeros of a function given the factors? What are the factors given the zeros? How can factoring techniques solve for the solutions of nonquadratic functions? How can you factor the sum of two squares?

Activities End Behavior Discovery Factoring Polynomial Exit Slip Division of Polynomials Stations Polynomial Review Study Island

Resources Study Island Khan Academy Big Ideas Kuta Software Pearson

Vocabulary Factor Theorem Factored Form Fundamental Theorem of Algebra Polynomial Function Rational Root Theorem Remainder Theorem Root Synthetic Division

Zero

Technology/GAFE Videos on Polynomials posted to Classroom Link to Khan Academy


Providing Notes/Modified Notes on Polynomials SMART Board Notes Factoring Reference Sheet

Guided Notes on Polynomials Highlighting Underlining Providing Definitions

Graphic Organizers on Factoring Polynomials Study Guides on Polynomials Modified Assessments Conferencing


Tutoring/Extra Help

ELL (SEI) Bilingual Math Dictionaries Total Physical Response Native/NonNative Speaker Groupings Providing Notes/Modified Notes on Polynomials

SMART Board Notes Include native language in guided notes Factoring Reference Sheet

Guided Notes on Polynomials Highlighting Underlining Providing Definitions in English and native language

Graphic Organizers on Polynomials Study Guides on Polynomials Modified Assessments

Conferencing Student Parent Guidance Administration CST

Tutoring/Extra Help


Providing Notes/Modified Notes on Polynomials SMART Board Notes Factoring Reference Sheet

Guided Notes on Polynomials Highlighting Underlining Providing Definitions

Graphic Organizers on Factoring Polynomials Study Guides on Polynomials Modified Assessments Priority Seating Checking Assignments Pads Conferencing


Tutoring/Extra Help

Gifted & Talented Supplemental Challenge Problems on Modeling Real World Situations with Polynomials


Formative: Exit Slips Homework Khan Academy assignments Study Island assignments Factoring, Modeling with Polynomials, Dividing Quizzes

Summative: Polynomial Test

Alternative Assessment: Polynomial Birthday Poster

Unit 4: Exponential and Logarithmic Functions Number of Days 18

NJSLSM ASSE.A. Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context. 1

a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity.

2. Use the structure of an expression to identify ways to rewrite it. ASSE.B. Write expressions in equivalent forms to solve problems

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. AREI.D. Represent and solve equations and inequalities graphically



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. 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.

FBF.B. Build new functions from existing functions 5. Use the inverse relationship between exponents and logarithms to solve problems involving logarithms

and exponents. FLE.A. Construct and compare linear and exponential models and solve problems

1. Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential

functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to

another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit

interval relative to another.

2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table).

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.

4. Understand the inverse relationship between exponents and logarithms. For exponential models, express as a logarithm the solution to ab ct = d where a , c , and d are numbers and the base b is 2, 10, or e ; evaluate the logarithm using technology.

FLE.B. Interpret expressions for functions in terms of the situation they model 5. Interpret the parameters in a linear or exponential function in terms of a context.


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.


SEP.1 Asking Questions and Defining Problems SEP.2 Developing and Using Model SEP.5 Using Mathematics and Computational Thinking



RST.1112.7 . Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem.





CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity.


9.1.12.B.8 Describe and calculate interest and fees that are applied to various forms of spending, debt, and saving. 9.1.12.B.9 Research the types and characteristics of various financial organizations in the community (e.g., banks,

credit unions, checkcashing stores, et. al.). 9.1.12.C.1 Compare and contrast the financial benefits of different products and services offered by a variety of

financial institutions. 9.1.12.C.2 Compare and compute interest and compound interest and develop an amortization table using business

tools. 9.1.12.C.3 Compute and assess the accumulating effect of interest paid over time when using a variety of sources

of credit.


NA




NA


Recognize and evaluate exponential functions. Graph the exponential parent function and transformations. Evaluate logarithmic expressions and convert them to exponential expressions. Graph logarithms as the inverse of exponential functions. Use properties of logarithms to evaluate, rewrite, expand, and condense logarithmic expressions. Rewrite logarithmic expressions with a different base. Solve exponential and logarithmic equations, including natural log with base e. Use exponential growth and decay models to solve reallife problems. Find compound interest with different times, including continuously compounding.

Essential Questions What is an exponential function? What is a logarithmic function? What are the properties of logarithms and how can they be used to evaluate and solve logarithmic equations? What is the common logarithm? What is the natural logarithm? What is the change of base formula? How do you solve exponential and logarithmic equations?

How can you solve reallife situations using exponential and logarithmic models? How can you graph exponential and logarithmic functions?

Activities Exponential Growth Video Logarithms Graphic Organizer Investigation on Logarithm Properties Investigating e Compare and Contrast Compound Interest Formulas Study Island


Vocabulary Change of Base Common Logarithm Compound Continuously Compound Interest Decay Factor Euler’s Number Exponential Decay Exponential Function Exponential Growth Growth Factor Logarithmic Function Natural Logarithm Product Property for Logarithms Quotient Property for Logarithms Power Property of Logarithms Rate

Technology/GAFE Videos on logarithms posted to Classroom Link to Khan Academy


Providing Notes/Modified Notes on Exponential and Logarithms SMART Board Notes

Guided Notes on Exponential and Logarithms Highlighting Underlining Providing Definitions

Modeling with Exponential Functions Graphic Organizers Exponential vs Logarithm Study Guides on Exponential and Logarithmic Functions Modified Assessments Conferencing


Tutoring/Extra Help

ELL (SEI) Bilingual Math Dictionaries Total Physical Response Native/NonNative Speaker Groupings Providing Notes/Modified Notes on Exponential and Logarithms

SMART Board Notes Include native language in guided notes

Guided Notes on Exponential and Logarithms Highlighting Underlining Providing Definitions in English and native language

Modeling with Exponential Functions Graphic Organizers Exponential vs Logarithm Study Guides on Exponential and Logarithmic Functions Modified Assessments Conferencing

Student

Parent Guidance Administration CST

Tutoring/Extra Help


Providing Notes/Modified Notes on Exponential and Logarithms SMART Board Notes

Guided Notes on Exponential and Logarithms Highlighting Underlining Providing Definitions

Modeling with Exponential Functions Graphic Organizers Exponential vs Logarithm Study Guides on Exponential and Logarithmic Functions Modified Assessments Priority Seating Checking Assignments Pads Conferencing


Tutoring/Extra Help

Gifted & Talented SelfDirected Learning on Applications of Exponential Functions Supplemental Challenge Problems Exponential Parameters, Solving Logarithm Equations


Formative: Graphing Exponential and Logarithmic Functions Exit Slips Homework Khan Academy assignments Study Island assignments Exponential and Logarithm Quizzes

Summative: Exponential and Logarithm Test Alternative Assessment: Newspaper Interest Project

Unit 5: Rational Functions Number of Days 15

NJSLSM ASSE.A. Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context.


2. Use the structure of an expression to identify ways to rewrite it. AAPR.A. Perform arithmetic operations on polynomials

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.

AAPR.D. Rewrite rational expressions 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.

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.

AREI.A. Understand solving equations as a process of reasoning and explain the reasoning 2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous

solutions may arise. AREI.D. Represent and solve equations and inequalities graphically



using technology for more complicated cases. d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are

available, and showing end behavior.


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

MP.7 Look for and make use of structure.


SEP.1 Asking Questions and Defining Problems SEP.2 Developing and Using Models SEP.5 Using Mathematics and Computational Thinking







CRP4. Communicate clearly and effectively and with reason. CRP7. Employ valid and reliable research strategies. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity.


NA


NA




NA


Graph rational expressions. Identify the vertical and horizontal asymptotes. Solve problems involving inverse variation. Multiply and divide rational expressions. Simplify complex fractions. Add and subtract rational expressions. Solve rational expressions and identify extraneous solutions.

Essential Questions How do we graph a rational function and find the domain and range? How do you determine if two variables vary inversely and write the function? How do you add, subtract, multiply, and divide rational expressions? How do you solve rational equations? When does a rational equation have an extraneous solution?

Activities Operations with Rational Expressions Stations Investigation on Graphing Rational Functions Modeling with Variation


Vocabulary Asymptote Complex Fractions Constant of Variation Domain Extraneous Solution Horizontal Asymptote Joint Variation Range Rational Function Vertical Asymptote

Technology/GAFE Link to Khan Academy

Special Providing Notes/Modified Notes on Rational Functions

Education/504 SMART Board Notes Guided Notes on Rational Functions


Operations with Rational Expressions Graphic Organizer Study Guides on Graphing, Operations with Rational Expressions Modified Assessments Conferencing


Tutoring/Extra Help

ELL (SEI) Bilingual Math Dictionaries Total Physical Response Native/NonNative Speaker Groupings Providing Notes/Modified Notes on Rational Functions


Guided Notes Highlighting Underlining Providing Definitions in English and native language

Operations with Rational Expressions Graphic Organizer Study Guides on Graphing, Operations with Rational Expressions Modified Assessments Conferencing


Tutoring/Extra Help


Providing Notes/Modified Notes on Rational Functions SMART Board Notes

Guided Notes on Rational Functions Highlighting Underlining Providing Definitions

Operations with Rational Expressions Graphic Organizer Study Guides on Graphing, Operations with Rational Expressions Modified Assessments Priority Seating Checking Assignments Pads Conferencing


Tutoring/Extra Help

Gifted & Talented Supplemental Challenge Problems on Joint Variation, Slant Asymptotes


Formative: Operations on Rational Expressions Exit Slips Homework Khan Academy assignments Study Island assignments Operations, Graphing, Solving Rational Equations Quizzes

Summative: Rational Test

Unit 6: Trigonometry Number of Days 20

NJSLSM FIF.C. 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. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and

trigonometric functions, showing period, midline, and amplitude. FTF.A. Extend the domain of trigonometric functions using the unit circle

1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 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. 3. Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6,

and use the unit circle to express the values of sine, cosines, and tangent for p x , p+ x , and 2p– x in terms of their values for x , where x is any real number.

4. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. FTF.B. Model periodic phenomena with trigonometric functions

5. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

FTF.C. Prove and apply trigonometric identities 8. Prove the Pythagorean identity sin 2 (θ) + cos 2 (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.


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.









CRP4. Communicate clearly and effectively and with reason. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity.


NA


NA




NA


Define and find the three basic trig functions. Solve for missing angle measures and/or side lengths of right triangles. Draw an angle in standard position, identifying the initial and terminal sides, and rotating both clockwise and

counterclockwise. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Convert

from degrees to radians and from radians to degrees. Find coterminal angles in degrees and radians. Derive the unit circle from special right triangles and identify the signs of each function based on the quadrant. Solve for exact values of each function using the unit circle. Determine if a graph is periodic, even, odd, or neither, and find its amplitude, frequency and midline. Identify the number of cycles and period of a given periodic function.

Graph one or more cycles of sine and cosine curves. Identify domain, range, amplitude, midline, and the period. Use sine and cosine models to solve reallife problems. Derive the Pythagorean Identity and use it to solve for other trig functions.

Essential Questions What are the 3 basic trig functions? How do you solve a right triangle? What is standard position? How are radian and degree measure related? How do you convert radians to degrees and vice versa? Why is it necessary to find coterminal angles? How do you use special right triangles to derive the exact values on the unit circle? How do you find the sign of a trigonometric function based on the quadrant? How do you determine if a function is periodic? How do you find the period, amplitude, frequency, and midline of a trigonometric function? How do you model periodic phenomena using the sine and cosine functions? How do you derive the Pythagorean Identity using the unit circle?

Activities Graphing Sine and Cosine with Transformations Stations Creating the Unit Circle


Vocabulary Amplitude Clockwise Rotation Cosine Function Coterminal Angles Counterclockwise Rotation Cycle Frequency Initial Side Midline Period

Periodic Function Pythagorean Identity Quadrant Radian Sine Function Standard Position Tangent Function Terminal side Theta Trigonometric Identity Unit Circle 454590 Triangle 306090 Triangle

Technology/GAFE Trig Tour 1.0.10 posted to Classroom Link to Khan Academy


Providing Notes/Modified Notes on Trigonometry SMART Board Notes

Guided Notes on Trigonometry Highlighting Underlining Providing Definitions

Graphic Organizers on Special Right Triangles Study Guide on Trigonometry Modified Assessments Conferencing


Tutoring/Extra Help

ELL (SEI) Bilingual Math Dictionaries Total Physical Response Native/NonNative Speaker Groupings

Providing Notes/Modified Notes SMART Board Notes Guided Notes Highlighting Underlining Include native language

Guided Notes on Trigonometry Highlighting Underlining Providing Definitions in English and native language

Graphic Organizers on Special Right Triangles Study Guide on Trigonometry Modified Assessments Conferencing


Tutoring/Extra Help


Providing Notes/Modified Notes on Trigonometry SMART Board Notes

Guided Notes on Trigonometry Highlighting Underlining Providing Definitions

Graphic Organizers on Special Right Triangles Study Guide on Trigonometry Modified Assessments Priority Seating Checking Assignments Pads Conferencing

Student Parent Guidance Administration

CST Tutoring/Extra Help

Gifted & Talented SelfDirected Learning on basic trigonometric functions Supplemental Challenge Problems with Angle of Elevation and Depression, Graphing Extension


Summative: Exit Slips Homework Khan Academy assignments Study Island assignments Basic Trig, Identities, Unit Circle Quizzes

Formative: Trigonometry Test

Unit 7: Sequences & Series Number of Days 6

NJSLSM ASSE.A. Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context.


2. Use the structure of an expression to identify ways to rewrite it. ASSE.B. Write expressions in equivalent forms to solve problems

3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

4. Derive and/or explain the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

FIF.A. Understand the concept of a function and use function notation 3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the

integers. FIF.C. Analyze functions using different representations

8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

FBF.A. Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities.

a. Determine an explicit expression, a recursive process, or steps for calculation from a context. 2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to

model situations, and translate between the two forms.


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.



NJSLS for ELA RST.1112.4. Determine the meaning of symbols, key terms, and other domainspecific words and phrases as they

Companion Standards for Science: RST

are used in a specific scientific or technical context relevant to grades 1112 texts and topics.





CRP4. Communicate clearly and effectively and with reason. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity.


NA


NA




NA


Write the terms of a sequence explicitly and recursively. Define and identify arithmetic sequences. Define and identify geometric sequences. Find the nth term of an arithmetic and geometric sequence Find the position of a given term in an arithmetic and geometric sequence. Find arithmetic and geometric means. Find the sum of a finite arithmetic series. Find the sum of a finite geometric series.

Find the sum of an infinite geometric series.

Essential Questions How can you represent the terms of a sequence explicitly? How can you represent the terms of a sequence recursively? What is an arithmetic sequence and how do you identify it? How do you find the n th term of an arithmetic sequence? How do you find the arithmetic mean in a sequence? How do you find the position of a given term in an arithmetic sequence? What is a geometric sequence and how do you identify it? How do you find the n th term of a geometric sequence? How do you find the position of a given term in a geometric sequence? How do you find the geometric mean in a sequence? How do you find the sum of a finite arithmetic series? How do you find the sum of a finite geometric series? When does an infinite series converge or diverge? How do you find the sum of an infinite geometric series?

Activities Identify Arithmetic and Geometric Sequences and Series


Vocabulary Arithmetic Mean Arithmetic Sequence Arithmetic Series Common Difference Common Ratio Converge Diverge Explicit Formula Finite Series Geometric Mean Geometric Sequence Geometric Series

Infinite Series Recursive Formula Sequence Series Term

Technology/GAFE Link to Khan Academy


Providing Notes/Modified Notes on Series and Sequences SMART Board Notes

Guided Notes on Series and Sequences Highlighting Underlining Providing Definitions

Study Guide on Series and Sequences Modified Assessments Conferencing


Tutoring/Extra Help

ELL (SEI) Bilingual Math Dictionaries Total Physical Response Native/NonNative Speaker Groupings Providing Notes/Modified Notes on Series and Sequences


Guided Notes Guided Notes on Series and Sequences Highlighting Underlining Providing Definitions in English and native language

Study Guide on Series and Sequences Modified Assessments

Conferencing Student Parent Guidance Administration CST

Tutoring/Extra Help


Providing Notes/Modified Notes on Series and Sequences SMART Board Notes

Guided Notes on Series and Sequences Highlighting Underlining Providing Definitions

Study Guide on Series and Sequences Modified Assessments Priority Seating Checking Assignments Pads Conferencing


Tutoring/Extra Help

Gifted & Talented Supplemental Challenge Problems on The King’s Grain


Formative: Exit Slips Homework Khan Academy assignments Study Island assignments Sequences, Series Quizzes

Summative: Sequence and Series Test

Unit 8: Statistics & Probability Number of Days 20

NJSLSM AAPR.C. Use polynomial identities to solve problems 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. SID.A. Summarize, represent, and interpret data on a single count or measurement variable

1. Represent data with plots on the real number line (dot plots, histograms, and box plots). 2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and

spread (interquartile range, standard deviation) of two or more different data sets. 3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible

effects of extreme data points (outliers). 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.

SID.B. Summarize, represent, and interpret data on two categorical and quantitative variables 5. Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies

in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data (including with the use of technology); use functions fitted to data to

solve problems in the context of the data. b. Informally assess the fit of a function by plotting and analyzing residuals, including with the use

of technology. c. Fit a linear function for a scatter plot that suggests a linear association.

SID.C. Interpret linear models 7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of

the data. 8. Compute (using technology) and interpret the correlation coefficient of a linear fit. 9. Distinguish between correlation and causation.

SIC.A. Understand and evaluate random processes underlying statistical experiments 1. Understand statistics as a process for making inferences about population parameters based on a random

sample from that population. 2. Decide if a specified model is consistent with results from a given datagenerating process, e.g., using

simulation. SIC.B. Make inferences and justify conclusions from sample surveys, experiments, and observational studies

3. Recognize the purposes of and differences among sample surveys, experiments, and observational

studies; explain how randomization relates to each. 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. 5. Use data from a randomized experiment to compare two treatments; use simulations to decide if

differences between parameters are significant. 6. Evaluate reports based on data.

SCP.A. Understand independence and conditional probability and use them to interpret data 1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of

the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). 2. Understand that two events A and B are independent if the probability of A and B occurring together is

the product of their probabilities, and use this characterization to determine if they are independent. 3. Understand the conditional probability of A given B as P ( A and B )/ P ( B ), and interpret independence of A

and B as saying that the conditional probability of A given B is the same as the probability of A , and the conditional probability of B given A is the same as the probability of B .

4. Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities.

5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

SCP.B. Use the rules of probability to compute probabilities of compound events in a uniform probability model 6. Find the conditional probability of A given B as the fraction of B ’s outcomes that also belong to A, and

interpret the answer in terms of the model. 7. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the

model. 8. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) =

P(B)P(A|B), and interpret the answer in terms of the model. 9. Use permutations and combinations to compute probabilities of compound events and solve problems.


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Science and Engineering Practices

SEP.1 Asking Questions and Defining Problems SEP.3 Planning and Carrying Out Investigations

(SEP) SEP.4 Analyzing and Interpreting Data SEP.5 Using Mathematics and Computational Thinking



RST.1112.6. Analyze the author's purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, identifying important issues that remain unresolved.

RST.1112.8. Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information.


WHST.1112.1. Write arguments focused on disciplinespecific content. A. Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the

claim(s) from alternate or opposing claims, and create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence.

B. Develop claim(s) and counterclaims using sound reasoning and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases.


WHST.1112.5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience.

WHST.1112.6. Use technology, including the Internet, to produce, share, and update writing products in response to ongoing feedback, including new arguments or information.


CRP4. Communicate clearly and effectively and with reason. CRP6. Demonstrate creativity and innovation. CRP7. Employ valid and reliable research strategies. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity.


9.1.12.A.3 Analyze the relationship between various careers and personal earning goals.

21st Century: Career Awareness, Exploration, and

9.2.12.C.1 Review career goals and determine steps necessary for attainment.

Preparation (9.2)




NA


Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

Represent data on two quantitative variables on a scatter plot. Define populations, population parameter, random sample, and inference. Compare theoretical and empirical results to evaluate the effectiveness of a treatment. Identify situations as sample survey, experiment, or observational study. Explain how randomization relates to

each. 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. Use data from a randomized experiment to compare two treatments. Evaluate reports based on data. Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or

complements of other events. Define and identify independent dependent events. Explain properties of Independence and Conditional Probabilities. Determine when a twoway frequency table is an appropriate display for a set of data. Calculate probabilities. Recognize and explain the concepts of conditional probability and independence. Calculate conditional probabilities. Apply the Addition Rule, identify events as disjoint and interpret the probability of unions and intersections. Know and apply the Binomial Theorem for the expansion of (x + y)n Calculate probabilities for binomial experiments.

Essential Questions How do you estimate population percentages using the mean and standard deviation? How do you recognize if the estimation procedure is not appropriate? How do you fit a function to data and determine how the variables are related?

How do you draw a sample that represents a population well? When should a simulation model be questioned? What are the purposes and differences among surveying, experimenting, and observational studies? How do you calculate the sample mean and proportion and estimate population values? How do you calculate and interpret the margin of error? How do you calculate the mean and standard deviation of two treatment groups and the difference of the means? How do you use the results of a simulation to create a confidence interval? How do you categorize variables? What inferences can be made from a data report? Given data, how do you draw a Venn diagram? How do you create and read a two way table, defining sample space? When are two events independent? How do you calculate the probability of independent events? When are two events dependent? How do you calculate conditional probability and determine if events are independent? How do you calculate probabilities from a twoway table? How do find conditional probability and define independence in everyday situations? When are two events classified as disjoint? How do you calculate the probabilities using the Addition Rule? How do you create Pascal’s Triangle? How do you use the Binomial Theorem to expand (x + y)n ? How do you find the probability of a trial in a binomial experiment?

Activities Sampling Method Graphing Calculator Activity Independent and Dependent Events Activity Selecting the Best Model for Real World Data Graphing Calculator Activity

Resources Study Island Khan Academy Big Ideas New Jersey Center for Teaching & Learning Kuta Software Pearson

Vocabulary And Association Bell Curve Bias

Binomial Theorem Box and Whisker Plot Categorical Data Causation Center Combination Complementary Events Conditional Probability Conditional Relative Frequency Confidence Interval Control Group Convenience Sample Correlation Data Dependent Events Distribution Dot Plot Empirical Rule Event Experiment Experimental Group Failure Frequency Table Fundamental Counting Principle Histogram Inclusive Events Independent Events Inference Interquartile Range Intersection Joint Relative Frequency Law of Large Numbers Marginal Relative Frequency Margin of Error Mean Median Measures of Central Tendency

Mode Mutually Exclusive Events Normal Distribution Observational Study Odds Outcome Or Outlier Pascal’s Triangle Permutation Population Population Parameter Population Proportion Probability Quantitative Data Random Sample Regression Residual Sample Sample Proportion Sample Space SelfSelected Sample Scatter Plot Shape Skewed Distribution Spread Standard Deviation Success Survey Systematic Sample Tree Diagram Trial Twoway Frequency Table Union Variance Venn Diagram

Technology/GAFE Video Pascal’s Triangle and Binomial Probability posted to Classroom


Providing Notes/Modified Notes on Statistics and Probability SMART Board Notes

Guided Notes on Statistics and Probability Highlighting Underlining Providing Definitions

Graphic Organizers on Sampling Methods Study Guide on Statistics and Probability Modified Assessments Conferencing


Tutoring/Extra Help

ELL (SEI) Bilingual Math Dictionaries Total Physical Response Native/NonNative Speaker Groupings Guided Notes on Statistics and Probability

Highlighting Underlining Providing Definitions in English and native language

Graphic Organizers on Sampling Methods Study Guide on Statistics and Probability Modified Assessments Conferencing


Tutoring/Extra Help


Providing Notes/Modified Notes on Statistics and Probability SMART Board Notes

Guided Notes on Statistics and Probability Highlighting Underlining Providing Definitions

Graphic Organizers on Sampling Methods Study Guide on Statistics and Probability Modified Assessments Priority Seating Checking Assignments Pads Conferencing


Tutoring/Extra Help

Gifted & Talented Supplemental Challenge Problem Expanding Binomials, Margin of Error


Formative: Exit Slips Homework Khan Academy assignments Study Island assignments Measures of Center and Variation, Sampling Methods and Design, Probability Quizzes

Alternative: Simple Random Sample Activity

Summative: Statistics and Probability Tests

Documents

COURSE OF STUDY UNIT PLANNING GUIDE FOR · Algebra 2 H is designed to challenge high achieving students, who are recommended based on their performance in Algebra 1 and Geometry