bundle 5 algebra ii - east allen county schools...-prentice hall algebra ii lessons 7.7, 7.8, 9.2,...

EAST ALLEN COUNTY SCHOOLS

Bundle 5

Algebra II

Big Idea: Domain and Range Radical/Rational

Functions

Enduring Understandings Essential Questions

A composite function is a combination of two functions such that the output from the first function becomes the input for the second function.

The domain and range of a rational function can be found by hand, inspection, and via technology.

Graph rational functions by using asymptotes and intercepts and graph radical

functions by translations.

The inverse of a given function can be found graphically or algebraically.

Solve a radical equation by raising both sides of the equation to the same power.

Sove a rational equation by multiplying the equation by the least common

denominator.

Why do you rationalize a denominator?

How does a rational exponent correlate to its corresponding radical?

What is the domain of f(x)/g(x)?

How do you find the domain of a radical function without graphing?

How do you find the vertical and horizontal asymptotes?

What are the differences and similarities between direct and inverse variation?

CC/Learning Targets Core Vocabulary Links to Technology A.SSE.1b A.SSE.2 A.APR.6 A.REI.11 F.IF.4

F.IF.7 e F.LE.4 A2.6.1 A2.6.6 A2.10.1

inverse like radicals complex fraction point of discontinuity

EACS Rational Function Project

- iFactor (app) - MathRefFree (app) - AlgebraGenie (app) - KhanAcademy (app) - FreeGraphingCalculator (app)

Rational_Functions_Project.pdf

http://itunes.apple.com/us/app/ifactor-quadratics/id369606383?mt=8

http://itunes.apple.com/us/app/math-ref-free/id312756358?mt=8

http://itunes.apple.com/us/app/algebra-genie/id481026577?mt=8

http://itunes.apple.com/us/app/khan-academy/id469863705?mt=8

http://itunes.apple.com/us/app/free-graphing-calculator/id378009553?mt=8

Big Idea: Domain and Range Radical/Rational

Functions

Bundle Performance Task(s)

A utility company burns coal to generate electricity. The cost C (in dollars) of removing p amount (percent) of the smokestack pollutants is given by:80,000

(100 )

pC

p

Is it possible for the company to remove 100 percent of the pollutants? Discuss why or why not, and support your response by using algebraic analysis on the given model. What happens if the company does try to remove 100 percent of the pollutants? Will the company be successful at doing so, or will the attempt end in failure, that is, will it be to much expense for the company? Draw a diagram to show what the consequences of the last question would be. Lable the vertical asymptote(s) and analyze their impact on the company’s expense. You can use draw in MS Word to draw your diagram and submit. (There are also numerous interactive graphing resources on the Internet that can be used. Google it!) **If/when opening the pdf file, it may say that the file could conatin a virus etc. Ignore the warning and click “ok” to open the file** (See the attached PDF document to hand out to students.)

Algebra 2 Math Bundle 5

Quarter 3 Jan - Feb

Trigonometry

Algebra II Algebra II – Bundle 5

CC/Learning Targets Resource of Ideas Evidence of Learning A.SSE.1

(A2.2.4a,b) Interpret expressions that represent a

quantity in terms of its context.

-Prentice Hall Algebra II Lessons 7.1, 7.2, 7.3, 7.5, 7.6, 9.1, 9.6

-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments

A.SSE.2 Use the structure of an expression to

identify ways to rewrite it. For example,

see x4 – y

4 as (x

2)2 – (y

2)2, thus

recognizing it as a difference of squares

that can be factored as (x2 – y

2)(x

2 + y

2).

-Prentice Hall Algebra II Lessons 9.3, 9.4, 9.5 - Pearson Algebra II iBook Lesson 8.4


A.APR.6 (A2.5.2a)

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.

-Prentice Hall Algebra II Lesson 6.3 - Pearson Algebra II iBook Lesson 8.6


A.APR.7

(A2.1.2a-c) 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.

-Prentice Hall Algebra II Lessons 8.1, 8.4, 8.5

-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes

Trigonometry


-Bundle Task Assessments

A.REI.2 (A2.3.6a,b) (A2.6.4a) (A2.6.5a,b)

Solve simple rational and radical

equations in one variable, and give

examples showing how extraneous

solutions may arise.

-Prentice Hall Algebra II Lessons 8.5, 8.6 - Pearson Algebra II iBook Lesson 6.5


A.REI.11 (A2.2.4c,d) (A2.3.7a,b) (A2.5.4a) (A2.5.5b) (A2.6.4a)

(A2.7.4a,b)

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.

-Prentice Hall Algebra II Lessons 7.7, 7.8, 9.2, 9.3, 9.6 - Pearson Algebra II iBook Lesson 8.6 First Concept Byte after Lesson 8.6 Second Concept Byte after Lesson 8.6 Concept Byte (after lesson 7.6)


F.IF.4

For a function that models a relationship

between two quantities, interpret key

features of graphs and tables in terms

of the quantities, and sketch graphs

showing key features given a verbal

description of the relationship. Key

features include: intercepts; intervals

where the function is increasing,

decreasing, positive, or negative;

relative maximums and minimums;

symmetries; end behavior; and

-Prentice Hall Algebra II Lessons 7.7, 7.8, 9.1, 9.2, 9.3 - MathGraph (app)


/%3ca%20href=%22http/::itunes.apple.com:us:app:mathgraph:id494113780?mt=8&uo=4%22%20target=%22itunes_store%22%3eMathGraph%20-%20Katherine%20Philip%3c:a%3e

Trigonometry


periodicity.★

F.IF.7b (A2.1.1d-f) (A2.1.4a,b) (A2.1.6c) (A2.1.7a-d) (A2.2.1b,c)

Graph functions expressed symbolically

and show key features of the graph, by

hand in simple cases and using

technology for more complicated cases.

b. Graph square root, cube root, and

piecewise-defined functions, including

step functions and absolute value

functions.

-Prentice Hall Algebra II Lessons 7.4, 7.7, 7.8, 9.2, 9.3 - Pearson Algebra II iBook Lesson 6.8 Concept Byte after Lesson 8-1 Concept Byte after Lesson 8-3 - MathGraph (app)


F.BF.1 (A2.1.3a,b)

Write a function that describes a

relationship between two quantities.

b. Combine standard function types

using arithmetic operations. For

example, build a function that models

the temperature of a cooling body by

adding a constant function to a

decaying exponential, and relate these

functions to the model.

-Prentice Hall Algebra II Lessons 7.4 - Pearson Algebra II iBook Lesson 6.6, 7.2


F.BF.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. For example, f(x) = 2x3 or f(x) =

(x + 1)/(x – 1) for x ≠ 1.

-Prentice Hall Algebra II Lessons 8.3, 8.5, 8.6 - Pearson Algebra II iBook Lesson 6.7, 7.3 Concept Byte (after lesson 6.7)


A2.6.1 a. Simplify an expression with negative

exponents.

b. Simplify an expression with fractional

exponents.

-Prentice Hall Algebra II Lessons 7.4, 7.5

-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources)

/%3ca%20href=%22http/::itunes.apple.com:us:app:mathgraph:id494113780?mt=8&uo=4%22%20target=%22itunes_store%22%3eMathGraph%20-%20Katherine%20Philip%3c:a%3e

Trigonometry


-Test -Quizzes -Bundle Task Assessments

A2.6.2 a. Find a common denominator

between algebraic fractions.

b. Perform basic operation on algebraic

fractions.

c. Simplify algebraic fractions.



A2.6.6 a. Compare direct, inverse, and joint

variation.

b. Solve a problem involving direct

variation.

c. Solve a problem involving inverse

variation.

d. Solve a problem involving joint

variation.

e. Identify the type of variation present

in a problem.

-Prentice Hall Algebra II Lesson 9.1


A2.10.1 a. Use a variety of problem-solving

strategies, such as drawing a

diagram and writing an equation.

b. Use a variety of problem-solving

strategies, such as drawing a

diagram, guess-and-check, solving a

simpler problem, writing an equation,

and working backwards.



Trigonometry


Correlating CC/Learning Targets Teacher Notes

A.SSE.1b A.APR.1 A.CED.1

A.CED.2

A.CED.3 A.CED.4 F.FIF.5 F.IF.8 F.BF.3

- Pearson Algebra II iBook Complete Lesson 6.4 Lesson 8.2 (for CC standard A.APR.1) Lesson 8.6 (for CC standard A.CED.1 Lessons 8.1, 8.2 (For CC standard A.CED.2) Lessons 6.5, 8.1 (for CC standard A.CED.4)

Rational Functions Project Project for Rational Functions:

Goal: Analyze a Rational Functions and its graph. Objectives: • Recognize a rational function.

• Explain why the denominator of a rational function cannot be zero thus recognizing these values as the places where vertical

asymptotes occur and what they graphically look like.

• Student will explain why the values where vertical asymptotes appear are excluded from domain of the function and thus the graph does not touch or cross them.

• Student will demonstrate what the graph of the function does as it approaches the vertical asymptote from the left and right.

• Student will be able to graphically recognize what a horizontal asymptote is. Learning Objective: You will explain why the denominator of a rational function cannot be zero thus recognizing these values as the places where vertical asymptotes occur (which are disastrous things to have) and graphically what vertical asymptotes look like and mean.

Learning Activity: You will use a word problem (follows) with a grading rubric to explain the possible effects of dividing by zero. (This will be a real world application of a rational function.) Learning Activity: The following is an actual mathematical model used for Cost-Benefit analysis. The model is a rational function. Read the situation and analyze what the solution should be using the algebraic techniques we have studied.

1

Rational Functions Project Project for Rational Functions: Application of Rational Functions: If you want to know why it is important to understand Rational Functions, consider the following. This application is a Cost-Benefit Model. A utility company burns coal to generate electricity. The cost C (in dollars) of removing p amount (percent) of the smokestack pollutants is given by:

( ) 80,000(100 )

pC pp

=−

Is it possible for the company to remove 100 percent of the pollutants? Discuss why or why not, and support your response by using algebraic analysis on the given model. Remember to write in complete sentences. What happens if the company does try to remove 100 percent of the pollutants? Will the company be successful at doing so, or will the attempt end in failure, that is, will it be to much expense for the company? Remember to write in complete sentences. Make a graph to show what the consequences of the last question would be. Pick your scale carefully so that all the information you want to

discuss is visible on the graph. Remember to label the axes and show units and tick marks. Show the vertical asymptotes as dashed lines and lable them. Then discuss their impact on the company’s expense. You can use Geometer’s Sketchpad which is on most of the computers in the Go Center or draw in MS Word to draw your diagram and submit. (There are also numerous interactive graphing resources on the Internet that can be used. Google it!)

This project is slightly adapted from one written by a Professor Rust. I do not know who he or she is so I cannot give more complete credit than that.

Grading Rubric for Word Problem: Here is how I will assess your work:

2

Rational Functions Project Project for Rational Functions:

3

Name: ________________________ Teacher: Mr. Polley Date Submitted: ____________ Title of Work: ___________________

Criteria Points 4 3 2 1

Explanation A complete response with a

detailed explanation showing individual insight.

Response is a clear explanation, but no personal

in depth details. Explanation is unclear. Misses key points. ____

Use Of Visuals Clear diagram or sketch with details and labeling.

Diagram or sketch with no details or labeling.

Inappropriate or unclear diagram. No diagram or sketch. ____

Mechanics No math errors.

Complete sentences and properly constructed paragraphs

No major math errors, serious flaws in reasoning,

or major grammar and sentence structure problems

May be some serious math errors, flaws in reasoning, or grammar and sentence

structure mistakes

Major math errors, serious flaws in reasoning, major

grammar and sentence structure mistakes

____

Demonstrated Knowledge

Shows complete understanding of the questions, mathematical

ideas, and processes, gives individual insight to problem.

Shows understanding of the problem, ideas, and

processes, but no individual insight added only definitions given.

Response shows some understanding of the

problem.

Response shows a complete lack of

understanding for the problem.

____

Requirements Goes beyond the requirements of the problem, explains concepts

in detail enhancing answers with own insights and reasoning.

Meets the requirements of the problem, may explain

concepts by stating definitions, instead of

contributing own insights.

Hardly meets the requirements of the

problem.

Does not meet the requirements of the

problem. ____

Total----> ____ Teacher Comments:

Due 3/28 for 1st period and 3/29 for 7th period

bundle 5 algebra ii - east allen county schools...-prentice hall algebra ii lessons 7.7, 7.8, 9.2,...

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