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COURSE OF STUDY UNIT PLANNING GUIDE FOR:

ALGEBRA 2

GRADE LEVEL: 10-12 PREPARED BY: LIZA FRANGIOSA 5 CREDITS RALPH LUGO 1 FULL YEAR RACHEL MASLOW TODD MINIMI SHANNON WARNOCK, SUPERVISOR OF MATHEMATICS AND SCIENCE

JULY 2017

DUMONT HIGH SCHOOL DUMONT, NEW JERSEY

ALIGNED TO THE NJSLS AND B.O.E. ADOPTED AUGUST 24, 2017

Algebra 2 – Grades 10-11 – Full Year – 5 Credits Algebra 2 is a 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, complex numbers, and basic trigonometry. Additional emphasis is placed on reinforcing foundational skills. Both scientific and graphing calculators are used as tools to assist in the development of concepts. 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 - 45% 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 - 10% 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: Full-Year 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

KEY CONCEPTS REOCCURRING EACH UNIT

Performance Indicators (NJSLS and Objectives)

Essential Questions

Activities (Approximate Time

Frame)

Vocabulary

Examples

A-CED.1 A-CED.2 A-CED.3 A-REI.6 A-REI.7 A-REI.11 A-SSE. 3 F-BF.1 F-BF.3 F-BF.4 F-IF. 1 F-IF. 2 F-IF. 4 F-IF. 5 F-IF. 6 F-IF. 7 F-IF.8 F-IF. 9 F-LE.1 F-LE.2 F-LE.3 N-Q.2 Students will be able to… 1. Find the domain and range of a function. Write in interval notation. 2. Determine if a function is even, odd, or neither. 3. Find the rate of change between two points. 4. Graph the parent function

• 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 y-

intercepts of the function?


relative max and min of a function?

• When is the function

increasing or

• Compress • Decreasing • Domain • End Behavior • Even Function • Increasing • Interval Notation • Inverse • Odd Function • Parent Function • Range • Rate of Change • Reflect • Regression • Stretch • Symmetry • System of Equations • Translate • x-Intercept • y-Intercept

and transformations by manipulating the a, h, and k values. 5. Describe the end behavior of a function. 6. Find the intercepts of a function. 7. Find the relative maxima and minima. 8. Determine when the function is increasing and decreasing. 9. Find the inverse. 10. Use the function to model real-world problems. 11. Solve systems of equations. 12. Create a scatter plot and determine the best model (linear, quadratic, exponential, …). Use the regression feature on the calculator to write a function.

decreasing? • How do you find the

inverse of each function?

• How can you use

functions to model real world situations?

• How do you solve

various systems of equations?

• How do I enter lists into a calculator and create a scatter plot?

• What is the equation

that best models the data?

UNIT #1 UNIT TITLE: STATISTICS & PROBABILITY UNIT LENGTH: 18 CLASS DAYS

Performance Indicators (NJSLS and

Objectives)

Essential Questions


Frame)

Vocabulary

Examples

S-ID.4 S-IC.1 S-IC.2 S-IC.3 S-IC.4 S-IC.5 S-IC.6 S-CP.1 S-CP.2 S-CP.3 S-CP.4 S-CP.5 S-CP.6 S-CP.7 S-MD.6 S-MD.7

Students will be able to…

1. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. 2. Represent data on two quantitative variables on a scatter plot. 3. Define populations, population parameter, random sample, and

• 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

Standard Deviation Normal Distribution Fundamental Counting Principle, Permutations & Combinations Sampling Probability Regression

• And • Association • Bell Curve • Bias • 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

Objective 1 Suppose that SAT mathematics scores for a particular year are approximately normally distributed with a mean of 510 and a standard deviation of 100. 1. What is the probability that a randomly selected score is greater than 610? 2. What is the probability between 410 and 710? Objective 2 The following data shows the age and average daily energy requirements for children and teens. Age Daily Energy 1 1110 2 1300 5 1800 11 2500 14 2800 17 3000

1. Create a graph and find a linear function to fit the data.

inference. 4. Compare theoretical and empirical results to evaluate the effectiveness of a treatment. 5. Identify situations as sample survey, experiment, or observational study. Explain how randomization relates to each. 6. 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. 7. Use data from a randomized experiment to compare two treatments. 8. Evaluate reports based on data. 9. Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events. 10. Define and identify

the sample mean and proportion and estimate population values?


and interpret the margin of error?


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?

• 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 • Permutation • Population • Population Parameter • Population Proportion • Probability • Quantitative Data • Random Sample • Regression • Residual • Sample • Sample Proportion • Sample Space • Self-Selected Sample • Scatter Plot • Shape • Skewed Distribution • Spread

2. Using your function identify what the daily energy requirements for a male of 15 years old? 3. Would your model apply to an adult male? Explain your reasoning. Objective 3 and 5 Students in a high school mathematics class decided that their term project would be a study of strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as “strict.” They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students. 1. Describe the parameter of interest and statistics students could use to estimate the parameter. 2. Is the best design for this study a sample survey, and experiment, or observational study? Explain your reasoning. 3. Describe an appropriate method for obtaining a

independent dependent events. 11. Explain properties of Independence and Conditional Probabilities. 12. Determine when a two-way frequency table is an appropriate display for a set of data. Calculate probabilities. 13. Recognize and explain the concepts of conditional probability and independence. 14. Calculate conditional probabilities. 15. Apply the Addition Rule, identify events as disjoint and interpret the probability of unions and intersections.

• How do you calculate the probability of independent events?


dependent? • How do you calculate

conditional probability and determine if events are independent?


probabilities from a two-way table?

• How do find

conditional probability and define independence in everyday situations?


classified as disjoint? How do you calculate the probabilities using the Addition Rule?

• Standard Deviation • Success • Survey • Systematic Sample • Tree Diagram • Two-way Frequency Table • Union • Variance • Venn Diagram

sample of 100 students, based on your answers in part 1 above. Objective 4 A random sample of 100 students from a specific high school resulted in 45% of them favoring a plan to implement block scheduling. Is it plausible that a majority of the students in the school actually favor the block schedule? Simulation can help answer the question. Objective 6 Twenty students counted the number of times they blinked their eyes and the number of breaths they took in one minute. The data is shown in the table. Number of Breaths

Number of Blinks

10 27 9 28 12 20 16 30 11 23 14 22 20 31 12 29 13 30 14 20

1. Compute the mean and standard deviation for the both the number of breaths and number of blinks. 2. What are the similarities and differences in the results? Objective 7 Given the data in the table below, what is the joint frequency of students who have chores and a curfew? Which marginal frequency is the largest?

Curfew: Yes

Curfew: No

Total

Chores: Yes

13 5 18

Chores: No

12 3 15

Total 25 8 33

Objective 8 From a class containing 12 girls and 10 boys, three students are to be selected to serve on a school advisory panel. Here are four different methods of making the selection. a. Select the first three

names on the class roll. b. Select the first three

students who volunteer. c. Place the names of the

22 students in a hat, mix them thoroughly, and select three names from the mix.

d. Select the first three students who show up for class tomorrow.

1. Which is the best sampling method, among these four, if you want the school panel to represent a fair and representative view of the opinions of your class? 2. Explain the weakness of the three you did not select as the best. Objective 9 Create a Venn diagram to display the information in the table. Describe the set of students who have a curfew but don’t do chores as a subset of the group.

Curfew:Yes

Curfew: No

Total

Chores: Yes

13 5 18

Chores: No

12 3 15

Total 25 8

Objective 10 What is the probability of drawing a heart from a standard deck of cards on a second draw, given that a heart was drawn on the first draw and not replaced? Are these events independent or dependent?

Objective 11,13, and 14 When rolling two number cubes: 1. What is the probability of rolling a sum that is greater then 7? 2. What is the probability of rolling a sum that is odd? 3. Are the events, rolling a sum greater than 7, and rolling a sum that is odd, independent? Justify your response. Objective 12 A two-way frequency table is shown below displaying the relationships between age and baldness. We took a sample of 100 male subjects and determined who is not or is not bald. We also recorded the age of the male subjects by categories.

Two-Way Frequency Table Bald Age Total Younger

than 45 45 or older

No 35 11 46 Yes 24 30 54 Total 59 41 100

1. What is the probability that a man from the sample is bald, given that he is under 45?

2. Are the events independent? Justify your answer. Objective 15 1. A die is thrown twice. Determine the probability that the sum of the rolls is less than 4 given that: a. At least one of the rolls

is a 1. b. The first roll is a 1. 2. Is participation in sports independent of participation in arts?

UNIT # 2 UNIT TITLE: Radical Expressions and Equations UNIT LENGTH: 18 class days


Objectives)

Essential Questions

Activities (Approximate Time Frame)

Vocabulary

Examples

A-CED.1 A-REI.2 A-REI.4 F-BF.3 F-BF.4a F-BF.4b F-IF.4 F-IF.6 F-IF.7b N-RN.1 N-RN.2 N-CN.1 N-CN.2 Students will be able to… 1. Simplify radical expressions of various indices. 2. Perform operations with radicals of various indices. 3. Rationalize denominators of various indices. 4. Write nth roots as rational exponents and vice versa. 5. Use properties of exponents to simplify expressions with rational

• 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?

Simplifying Radical Expressions Rational Exponents Imaginary Numbers Solving Equations Graphing Square and Cube Root Functions

• Coefficient • Complex Numbers • Conjugates • Domain & Range • Equal Complex Numbers • Extraneous Solutions • Imaginary Unit • Index • Like Terms • Nth Root • Power • Principal Root • Pure Imaginary Number • Radical Equations • Radicand • Rational Exponent • Rationalizing the

Denominator • Simplify • Square Root

Objective 1 Simplify

€

32x 2y 3z53 Objective 2 Simplify

€

5 12 − 3 75 Objective 3

Rationalize

€

33 5

Objective 4

Express

€

x68 in simplified

radical form. Objective 5

Simplify Objective 6 Identify the real and imaginary parts of the complex number Objective 7 Simplify Objective 8 Solve and

exponents. 6. Identify the imaginary unit i as part of the Complex Number System 7. Simplify and perform operations with complex numbers. 8. Solve equations with real and imaginary solutions. 9. Graph square and cube root functions and identify transformations on the function

• How do I transform the square and cube root function graphs?

Objective 9 Graph and

. Identify the

domain, range, x- and y-intercepts and the transformations from the parent function.

UNIT # 3 UNIT TITLE: Exploring Polynomial Functions UNIT LENGTH: 28 class days Performance Indicators (NJSLS and Objectives)

Essential Questions


Vocabulary

Examples

A-APR.1 A-APR.2 A-APR.3 A-APR.4 A-APR.5 A-APR.6 A-CED.1 A-SSE.2 A-SSE.3 A-REI.4 A-REI.7 A-REI.11 F-BF.3 F-IF.4 F-IF.6 F-IF.7c F-IF.8 F-IF.9 F-LE.1 G-GPE.2 N-CN.7 Students will be able to… 1. Graph quadratic functions of the form y = x2 and identify transformations to the parent function. 2. Derive the equation of a parabola given a focus and directrix.

• 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? • What is the end

behavior of a

Graphing Quadratic Functions and Their Properties Deriving Quadratic Equations from the Focus and Directrix Solving Quadratic Equations Using Multiple Approaches Writing Quadratic Models Solving System of Equations Graphing Polynomial Functions The Remainder and Factor Theorems Roots and Zeros Using Quadratic Techniques to Solve Polynomial Equations Binomial Theorem

• Axis of Symmetry • Binomial Theorem • Completing the Square • Complex Conjugate

Theorem • Discriminant • Even, Odd, or

Neither Function • Factor Theorem • Fundamental

Theorem of Algebra • Intercept Form • Parabola • Pascal’s Triangle • Polynomial Function • Quadratic Equation • Quadratic Formula • Quadratic Function • Rational Zero

Theorem • Remainder Theorem • Root • Standard Form • Synthetic Division • Vertex • Vertex Form • Zero • Zero Product

Property

Objective 1 Graph

€

y = −4(x − 3)2 +1 and. Identify the domain, range, x- and y-intercepts and the transformations from the parent function. Objective 2 The vertex of a parabola is located at (3, 2) and the equation of the directrix is y = -2. Find the coordinates of the focus. Objective 3 Solve the quadratic equation by graphing, factoring, completing the square and using the quadratic formula. −2x2 − 4x − 2 = 0 Objective 4 Margaret is planning a rectangular garden. Its length is 4 ft less than twice its width. Its area is 170 ft2. What are the dimensions of the garden? Objective 5 1. Solve the system by graphing and substitution.

3. Solve quadratic equations by factoring, the quadratic formula and completing the square with real and imaginary solutions. 4. Use quadratic functions to model real world situations. 5. Solve and graph systems of quadratic and linear equations. 6. Graph polynomial functions, performing transformations and indentifying key characteristics, such as end behavior, intercepts, max and min. 7. Classify functions as even, odd or neither. 8. Know and apply the Remainder Theorem to find the zeros of a polynomial function. 9. Understand the relationship between zeros and factors of polynomials. 10. Solve non-quadratic equations by using quadratic techniques. 11. Extend polynomial identities to complex

polynomial function given an even/odd degree and a positive/negative leading coefficient?


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 non-quadratic functions?

• How can you factor the

sum of two squares? • How does (x + y)n

2. The function

gives the cost, in dollars, for a small company to manufacture x items. The function

gives the revenue, also in dollars, for selling x items. How many items should the company produce so that the cost and revenue are equal? Objective 6 Describe the end behavior, number of turns for the following polynomial function. Find the zeros and relative maximum and minimum as well.

Objective 7 Is even, odd, or neither? Objective 8 Use the Remainder Theorem to determine if 3 and -2 are zeros of the function

. How do you know?

numbers. 12. Know and apply the Binomial Theorem for the expansion of (x + y)n

expand using the Binomial Theorem?

Objective 9 Given the polynomial and 1 of its factors, find the remaining factors and zeros of the polynomial

Objective 10 Solve each equation 1. 2.

€

11n4 = −44n2 3.

€

x 4 − 3x 3 + 6x 2 = 0 Objective 11 Factor

€

x2 + 4 = (x + 2i)(x − 2i) Objective 12 Expand

€

(x + y)4

UNIT # 4 UNIT TITLE: Rational Functions UNIT LENGTH: 15 class days Performance Indicators (NJSLS and Objectives)

Essential Questions


Frame)

Vocabulary

Examples

A-APR. 6 A-APR. 7 A-REI.1 A-REI.2 A-REI.11 F-IF.4 F-IF. 7

Students will be able to…

1. Graph rational expressions. Identify the vertical and horizontal asymptotes. 2. Solve problems involving inverse variation. 3. Multiply and divide rational expressions. 4. Simplify complex fractions. 5. Add and subtract rational expressions. 6. Solve rational expressions and identify extraneous solutions.

• 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?

Graphing Rational Equations Inverse Variation Multiply Divide Rational Expressions Adding and Subtracting Rational Expressions Solving Rational Equations and Inequalities

• Asymptote • Complex Fractions • Constant of Variation • Domain • Extraneous Solution • Horizontal

Asymptote • Joint Variation • Range • Rational Function • Vertical Asymptote

Objective 1 Graph the rational expression. Give the domain, range, vertical and horizontal asymptotes, and intercepts.

€

f x( ) =2

x − 5+ 3

Objective 2 If r varies inversely as t and r=18 when t=-3, find r when t=-11. Objective 3

Simplify:

Objective 4

Objective 5 Simplify:

Objective 6 Solve the equation:

UNIT #5 UNIT TITLE: Exponential and Logarithmic Functions UNIT LENGTH: 15 class days


Objectives)

Essential Questions


Frame)

Vocabulary

Examples

A-CED.1 A-CED.2 A-CED.3 A-REI.11 F-IF.8 F-BF.1 F-LE.1 F-LE.2 F-LE.3 F-LE.4 F-LE.5

Students will be able to… 1. Recognize and evaluate exponential functions. 2. Graph the exponential parent function and transformations. 3. Evaluate logarithmic expressions and convert them to exponential expressions. 4. Graph logarithms as the inverse of exponential functions. 5. Use properties of logarithms to evaluate, rewrite, expand, and

• 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 real-

life situations using exponential and logarithmic models?

• How can you graph

exponential and

Real Exponents and Exponential Functions Logarithm and Logarithmic Functions Properties of Logarithms Natural Logarithms Solving Exponential Equations Modeling

• 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

Objective 1 Todd says that y = x2 is an exponential function. Juan disagrees. Who is correct? Explain. Objective 2 Graph the function

€

y = − 2( )x−2 + 3. Identify the domain, range, x- and y-intercepts, the horizontal asymptote and the transformations from the parent function. Objective 3 1. Write the expression in logarithmic form 33= 27. 2. Write the expression in exponential form log5125 = 3. 3. Evaluate log16 4. Objective 4 Graph the function

€

y = log2 x . Identify the domain, range, x- and y-intercepts, the vertical asymptote and the transformations from the parent function. Find the inverse. Objective 5

condense logarithmic expressions. 6. Rewrite logarithmic expressions with a different base. 7. Solve exponential and logarithmic equations, including natural log with base e. 8. Use exponential growth and decay models to solve real-life problems. 9. Find compound interest with different times, including continuously compounding.

logarithmic functions?

1) Expand: a. log32x b. log6(5x/6)

2) Condense: a. log48 – log4x + 2log4y b. log5x – 2(log5 x + log59) Objective 6 Find the value log422. Objective 7 Solve:

a. 52x+7 − 1 = 8 b. log (2x) + 2 = 6 c. ln (x − 3) = 2 d. e4x = 25

Objective 8 The city of Knoxville Tennessee grew from a population of 546,488 in 1980 to a population of 585,960 in 1990.

a. Use this information to write a growth of Knoxville, where t is the number of years after 1980

b. Use your equation to predict the population of Knoxville in 2010

Objective 9 If you invest $1000 in an account paying 5%, compounded quarterly, how much money will you have after 4 year?

UNIT # 6 UNIT TITLE: Trigonometry UNIT LENGTH: 16 class days


Objectives)

Essential Questions


Vocabulary

Examples

F-TF. 1 F-TF. 2 F-TF. 5 F-TF. 8 A-SSE. 3 Students will be able to… 1. Define and find the three basic trig functions. 2. Solve for missing angle measures and/or side lengths of right triangles. 3. Draw an angle in standard position, identifying the initial and terminal sides, and rotating both clockwise and counter clockwise. 4. 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. 5. Find coterminal angles in degrees and radians.

• 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?


sign of a trigonometric function based on the quadrant?

Right Triangle Trigonometry Angles and Angle Measure Trigonometric Functions of General Angles on the Unit Circle Periodic Functions Trigonometric Identities

• 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

€

θ • Trigonometric Identity • Unit Circle • 45-45-90 Triangle • 30-60-90 Triangle

Objective 1 In the right triangle ABC, find the sin A, cos A, tan A.

Objective 2 Given triangle ABC, solve for all missing angle measures and/or side lengths.

Objective 3 Draw an angle in standard position of:

a) 60o b) -150o

Objective 4 1. Convert

€

45° to radian measure.

2. Convert

€

−π2

radians to

degrees.

6. Derive the unit circle from special right triangles and identify the signs of each function based on the quadrant. 7. Solve for exact values of each function using the unit circle. 8. Determine if a graph is periodic, even, odd, or neither, and find its amplitude, frequency and midline. 9. Identify the number of cycles and period of a given periodic function. 10. Graph one or more cycles of sine and cosine curves. Identify domain, range, amplitude, midline, and the period. 11. Use sine and cosine models to solve real-life problems. 12. Derive the Pythagorean Identity and use it to solve for other trig functions.

• How do you

determine if a function is periodic?


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?

Objective 5 Find one positive and one negative coterminal angle for each angle.

a. 45o

b.

Objective 6 Suppose theta is an angle in standard position at 30o on the unit circle with radius 1. Find the exact value of sine, cosine, and tangent of 30o. Objective 7 What is the exact value of

a. ?

b. cos 150o? Objective 8 Is the graph of y = 3sin(2x) periodic? Is it even, odd, or neither? Find its amplitude, frequency, and midline. Objective 9 Find the number of cycles and the period of y = 0.5cos2x. Objective 10 Graph y = 2sin4x. Identify the domain, range, amplitude, midline, and period.

Objective 11 1. The sound wave of a pitchfork is modeled by

. Sketch a graph of the sine curve. Identify the domain, range, amplitude, midline, and period. Find the rate of change between 0 and 1, 1 and 2, and 2 and 3. 2. Write an equation of a cosine function with a > 0, amplitude 4, and period Objective 12

Given in Quadrant

IV, find and .

UNIT #7 UNIT TITLE: Series and Sequences UNIT LENGTH: 10 class days

Performance Indicators (NJSLS

and Objectives)

Essential Questions


Vocabulary

Examples

A-SSE.4 F-IF.3 F-BF.1 F-BF.2 F-LE.2

Students will be able to… 1. Write the terms of a sequence explicitly and recursively. 2. Define and identify arithmetic sequences. 3. Define and identify geometric sequences. 4. Find the nth term of an arithmetic and geometric sequence 5. Find the position of a given term in an arithmetic and geometric sequence. 6. Find arithmetic and geometric means. 7. Find the sum of a finite arithmetic series. 8. Find the sum of a finite

• 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 nth

term of an arithmetic sequence?


arithmetic mean in a sequence?


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 nth

term of a geometric sequence?

Identifying a Sequence Explicitly & Recursively Arithmetic Sequences & Series Geometric Sequences & Series

• Arithmetic Mean • Arithmetic Sequence • Arithmetic Series • Common Difference • Common Ratio • Explicit Formula • Finite Series • Geometric Mean • Geometric Sequence • Geometric Series • Infinite Series • Recursive Formula • Sequence • Series • Term

Objective 1 1. Write a recursive definition for the sequence 5, 22, 39, 56, … 2. Write an explicit formula for each sequence 1, 4, 7, 10, … Objective 2 Determine whether the sequence is arithmetic: 2, 4, 7, 10, … Objective 3 Determine whether the sequence is geometric. If so, identify the common ratio and find the next 2 terms: 1, 3, 5, 7, … Objective 4 1. Find the 32nd term of the sequence: 2, 4, 7, 10, … 2. Find the missing term(s) of the geometric sequence 3, ___, 12, … Objective 5 What is the 100th term of the arithmetic sequence that begins 6, 11, …? Objective 6 What are the possible values of the missing geometric sequence 48, ____, 3, …?

geometric series.


position of a given term in a geometric sequence?


geometric mean in a sequence?


sum of a finite arithmetic series?


sum of a finite geometric series?

Objective 7 What is the sum of the arithmetic series 2 + 5 + 8 + 11 + 14 + 17 + 20? Objective 8 Evaluate the finite series for the specified number of terms 80 – 40 + 20 – …; n = 5.

High School Mathematics Modifications/Strategies for Student Populations

*Interdisciplinary **21st Century Themes and Skills

21st Century Themes & Skills**

Special Education/Gifted

ELL

At Risk of School Failure

Benchmarking

Career Skills 1. Multimedia/Videos 2. Public Speaking 3. Career Exploration

Communication

1. Presentations w/Visuals 2. Think-Pair-Share 3. Student presentations

Collaboration 1. Cooperative Projects 2. Project-based Learning 3. Jig Saw 4. Set and Meet goals

Creativity

1. Visual Interpretations 2. Brainstorming 3. Problem Solving and

Design

Critical Thinking 1. Problem-Based

Learning 2. Develop effective

strategies 3. Problem Solving

Special Education 1. Providing Notes/Modified

Notes a. PowerPoints b. SMART Board Notes

2. Guided Notes a. Highlighting b. Underlining c. Providing Definitions

3. Modeling 4. Chunking 5. Scaffolding 6. Repeat/Rephrase 7. Manipulatives/Visuals 8. Realia 9. Graphic Organizers 10. Study Guides 11. Portfolios 12. Modified Texts 13. Conferencing

a. Student b. Parent c. Guidance d. Administration e. CST

14. Tutoring/Extra Help Gifted

1. Bilingual Math Dictionaries

2. Total Physical Response

3. Native/Non-Native Speaker Groupings

4. Providing Notes/Modified Notes

a. PowerPoints b. SMART Board

Notes c. Include native

language in guided notes

5. Guided Notes a. Highlighting b. Underlining c. Providing

Definitions in English and native language

6. Modeling 7. Chunking 8. Scaffolding 9. Repeat/Rephrase 10. Manipulatives/

Visuals

1. Providing Notes/ Modified Notes

a. PowerPoints b. SMART Board

Notes 2. Guided Reading

a. Highlighting b. Underlining c. Providing

Definitions 3. Modeling 4. Chunking 5. Scaffolding 6. Repeat/Rephrase 7. Manipulatives/Visuals 8. Realia 9. Study Guides 10. Portfolios 11. Modified Texts 12. Priority Seating 13. Checking

Assignments Pads 14. Conferencing


1. Pre and Post SGO Assessments

2. Study Island 3. Post-lesson exit

slips 4. Self-assessment

a. Evaluate b. Compare c. Contrast d. Analyze e. Synthesize f. Create

Technology

1. PARCC Practice 2. SMART Board 3. Graphing Calculator 4. Other Graphing

technologies 5. iPads 6. SMART Response

Technology 7. Quizlet 8. Socrative 9. Kahoot 10. Flubaroo 11. Wikis 12. Google Drive 13. Study Island 14. Virtual High School

1. Self-Directed Learning Independent Research*

2. Individualized Pacing 3. Supplemental Challenge

Problems 4. Virtual High School

11. Realia 12. Graphic Organizers 13. Study Guides 14. Portfolios 15. Modified Texts 16. Conferencing


17. Tutoring/Extra Help

15. Tutoring/Extra Help

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