unit 1 - polynomialsroselle.sharpschool.net/userfiles/servers/server_3152275... · 2014. 3. 19. ·...

1

UNIT 1 - POLYNOMIALS

Total Number of Days: 15 days (A and B days meet alternate days) Grade/Course: 11/Algebra 2

ESSENTIAL QUESTIONS ENDURING UNDERSTANDINGS

How are the real solutions of a quadratic equation related to the graph of the related quadratic function?

What does the degree of a polynomial tell you about its related polynomial function?

For a polynomial function, how are factors, zeros and x-intercepts related?

For a polynomial function, how are factors and roots related?

A basis for the complex numbers is a number whose square is -1. Every quadratic equation has complex number solutions. Knowing the zeros of polynomial functions can help you understand the

behavior of its graph. The degree of a polynomial equation tells you how many roots the equation

has. You can use much of what you know about multiplying and dividing

fractions to multiply and divide rational expressions. When solving an equation involving rational expressions multiplying by the

common denominator can result in extraneous solutions.

PACING CONTENT SKILLS STANDARDS (CCCS/MP)

RESOURCES LEARNING ACTIVITIES/ASSESSME

NTS Pearson

Pearson OTHER

(e.g., tech)

1 Unit 1 Pre-Assessment

Complex number system

Quadratic Functions with Complex Solutions

Functions Polynomials

N.CN.1, 2, 7, 9 A.SSE.1, A.APR.A.1,2,3 MP 1-8

Rewrite questions similar to the Unit 1 test. 15 MC, 5 SR, 5 OE

1 day Q1

1. Complex number system

Find the value of i raised to a power. Example 1: Evaluate i17.

N.CN.1 Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real.

Algebra 2 Student

Textbook Section 4-8

Basic: Problems 1-7 EXS: 8-46, 48, 50, 56,

http://www.suitcaseofdreams.net/Powers_i.htm#A1 http://www.regentsprep.org/Regents/math/algtrig/ATO6/powerlesson.htm

Algebra Lab Algebra 2 Student Textbook Section 4-8 Solve It Page 248 or PowerAlgebra (textbook website)

Algebra 2 Interactive Digital Path Chapter 4

http://www.suitcaseofdreams.net/Powers_i.htm#A1



http://www.regentsprep.org/Regents/math/algtrig/ATO6/powerlesson.htm





https://www.pearsonsuccessnet.com/snpapp/iText/getTeacherHomepage.do?newServiceId=6000&newPageId=10100


2

MP 2, 7

57, 73-89 Average: Problems 1-7 EXS: 9-43 odd, 45-69, 73-89 Advanced: Problems 1-7 EXS: 9-43, 45-72, 73-89

Vocabulary

Support PowerAlgebra (textbook website)

Algebra 2 Other Resources Teacher Resources Chapter 4 Additional Vocabulary Support 4-8

Chapter 4-8 View Solve it

Assessments Quiz – Teacher created Students will create

the pattern of powers of i.

Questions on finding the value of i raised to a power.

Last 1/3 of the period.

BASIC SKILLS REVIEW PARCC/HSPA PREP

Using the Distributive Property for problem solving

A –CED.1 Create equations and inequalities in one variable and use them to solve problems. MP 4, 2

Review of the distributive property Algebra 1 textbook pg 96 Problem 3 or PowerAlgebra (textbook website) Algebra 1 Interactive Digital Path Chapter 2 Chapter 2-3 View Instruction Problem 3

WORKSHEET: http://tullyschools.org/hsteachers/dneuman/IntegratedAlgebra/IntegratedAlgebraNotes/01September/008ChapterWordProblems/ChapterWordProblems.pdf

Example: Half the sum of six times a number and eighteen is the same as twice the number less twenty.






http://tullyschools.org/hsteachers/dneuman/IntegratedAlgebra/IntegratedAlgebraNotes/01September/008ChapterWordProblems/ChapterWordProblems.pdf








3

2 days Q 2,3,4

2. Complex number system

Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Example 1: Evaluate (8 + 3i) + (–1 – 5i). Example 2: Evaluate (8 + 3i) – (–1 – 5i). Example 3: Evaluate (8 + 3i)(–1 – 5i).

N.CN.2 Use Properties of operations to add, subtract, and multiply complex numbers MP 2, 7

Algebra 2 Student Textbook Section 4-8 Basic: Problems 1-7 EXS: 8-46, 48, 50, 56, 57, 73-89 Average: Problems 1-7 EXS: 9-43 odd, 45-69, 73-89 Advanced: Problems 1-7 EXS: 9-43, 45-72, 73-89

http://www.regentsprep.org/Regents/math/algtrig/ATO6/lessonadd.htm http://www.regentsprep.org/Regents/math/algtrig/ATO6/multlesson.htm http://www.regentsprep.org/Regents/math/algtrig/ATO6/practicepageadd.htm http://www.regentsprep.org/Regents/math/algtrig/ATO6/multprac.htm

Algebra Lab PowerAlgebra (textbook website)

Algebra 2 Textbook Interactive Digital Path Chapter 4 Chapter 4-8 View Instruction Problems 3, 3 Alternate, 4 Section A pg 34, Student Activity 3, Powers of i http://www.projectmaths.ie/documents/teachers/tl_complex_numbers.pdf

Assessment

Quiz - Teacher created One of each to add,

subtract, and multiply complex numbers.

http://www.regentsprep.org/Regents/math/algtrig/ATO6/lessonadd.htm




http://www.regentsprep.org/Regents/math/algtrig/ATO6/multlesson.htm




http://www.regentsprep.org/Regents/math/algtrig/ATO6/practicepageadd.htm





http://www.regentsprep.org/Regents/math/algtrig/ATO6/multprac.htm






http://www.projectmaths.ie/documents/teachers/tl_complex_numbers.pdf



4

Last 1/3 of

the period.


Factoring Trinomials where a = 1 Example 1: p2 + 13p + 40 Example 2: n2 – 16n + 60 Example 3: x2 – 14x + 48 Example 4: x2 – 2x – 35

A.SSE.A.1a Interpret parts of an expression, such as terms, factors, and coefficients. MP 7

Extra practice Algebra 1 review section 8-5 PowerAlgebra (textbook website)

Algebra 2 Interactive Digital Path Chapter 8 Chapter 8-5 View Solve it Instruction Problems 1 to 5

Classwork http://www.regentsprep.org/Regents/math/ALGEBRA/AV6/Ltri1.htm http://www.youtube.com/watch?v=aYIUQ-6IJu8 http://www.regentsprep.org/Regents/math/ALGEBRA/AV6/PracFact2.htm

Algebra Lab TI-84 Activity http://mathbits.com/MathBits/TISection/Algebra1/Factoring.htm

Homework http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Factoring%201.pdf

http://www.corestandards.org/Math/Content/6/EE/A/3




http://www.regentsprep.org/Regents/math/ALGEBRA/AV6/Ltri1.htm




http://www.youtube.com/watch?v=aYIUQ-6IJu8



http://www.regentsprep.org/Regents/math/ALGEBRA/AV6/PracFact2.htm




http://mathbits.com/MathBits/TISection/Algebra1/Factoring.htm



http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Factoring%201.pdf



5

2 days

Q 5,6,7

3. Quadratic Functions with Complex Solutions

Solve quadratic equations using the quadratic formula. Example 1: x2 – 2x + 10 = 0 Example 2: x2 – 6x = –9

N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. MP 2, 7

Algebra 2 Textbook TE Lesson 4-7 pg 240-244 Basic: Problems 1-4 EXS: 11-42, 57-59, 67, 78-90 Average: Problems 1-4 EXS: 11-37 odd, 39-69, 78-90 Advanced: Problems 1-4 EXS: 11-37 odd, 39-77, 78-90

http://www.virtualnerd.com/algebra-2/quadratics/formula-discriminant/quadratic-formula/complex-solutions-quadratic-formula-Example http://www.regentsprep.org/Regents/math/ALGEBRA/AE5/indexAE5.htm http://terzicmath.weebly.com/uploads/5/7/3/3/5733011/real-and-complex-solutions.pdf

Algebra Lab Algebra 2 Solve It - Text pg 240 or PowerAlgebra (textbook website)

Algebra 2 Interactive Digital Path Chapter 4 Chapter 4-7 View Solve it

Algebra Lab Dynamic Activity at same website as above

Assessment Quiz - Teacher created quiz – three questions – all with complex solutions including one that can be solved by the square root method.

http://www.virtualnerd.com/algebra-2/quadratics/formula-discriminant/quadratic-formula/complex-solutions-quadratic-formula-example









http://www.regentsprep.org/Regents/math/ALGEBRA/AE5/indexAE5.htm




http://terzicmath.weebly.com/uploads/5/7/3/3/5733011/real-and-complex-solutions.pdf







6

Last 1/3 of

the period.


Applications of Percents A –CED.1

Create equations and inequalities in one variable and use them to solve problems. MP 4,2

Algebra 2 text Basic Review Student Text pg 972

Worksheet: http://teachers.sduhsd.net/mlewis1/syllabus_files/PA7/Chapter%209/PA7%20Worksheet-discounts_mark-ups%203.pdf

Application problems with sales discount, markup, and sales tax.

1 day

Q8,9,10

4. Functions Identify what parts of equations represent. Example 1: C = M – x/100 * M The equation above represents the final cost of an item after a discount. Which part of the formula is the discount? Example 2: The expression P(1.05)2 gives the number of dollars in an investment account over years after the initial amount is invested. The account earns a simple annual interest. a. What does 2 represent

N.CN.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. MP 2

5-6

ALL

1. C = P + x

100* P

The equation above represents the final cost of an item after sales tax. Which part of the formula is the tax? 2. The expression 7000(1.02)t gives the number of dollars in an investment account over years after the initial amount is invested. The account earns a simple annual interest. a. What does 7000 represent in the context of the problem?

Algebra Lab Take some word problems from the web that are similar to the ones on the test and write questions about the word problems.

Enrichment Have students create their own problems and solutions.

http://teachers.sduhsd.net/mlewis1/syllabus_files/PA7/Chapter%209/PA7%20Worksheet-discounts_mark-ups%203.pdf








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in the context of the problem? b. What does 1.05 represent in the context of the problem? Example 3: A 30-ounce solution that is 25 percent acid has x ounces of pure acid added to it. The following expression is used to answer some questions about the mixture. (0.25(30) + x)/(30 + x) a. What does 30 + x represent? b. What does 0.25(30) + x represent?

b. What does 1.02 represent in the context of the problem? 3. A 25-ounce solution that is 55 percent acid has x ounces of pure acid added to it. The following expression is used to answer some questions about the mixture.

0.55(25) + x

25 + x

a. What does 25 + x represent? b. What does 0.55(25) + x represent?

Last 1/3 of

the period.


Applications of adding fractions

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.

Algebra 2 Basic Review Student Text pg 973 Example 1 and Q 1, 2, 5

Teacher created material.

Example problem: Paul practices a tenth of an hour of basketball on Friday, two and a quarter hours of basketball on Saturday, and one and five-sixths hours of basketball on Sunday. How many hours of basketball did he practice altogether?

Part of a period

MID UNIT TEST

Mid unit test to determine areas of weakness that need to be addressed before the

N.CN.1, 2, 7, 9

MP 7, 5


Test to determine skills that need reteaching.

Use problems similar to

8

state unit test. the pre-assessment that have been covered.

2 days

Q11, 12

5. Polynomials

Write polynomial expressions. Example 1: Rewrite the expression 6x + [2x/(x+5)] as one rational expression that is equivalent to the expression for all x values, where x ≠ –5. Example 2: A box in the shape of a rectangular prism has a width that is 5 inches greater than the height and a length that is 2 inches greater than the width. Write a polynomial expression in standard form for the volume of the box. Explain the meaning of any variables used.

A.SSE.1 Interpret expressions that represent a quantity in terms of its context. 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. For Example, interpret P(1+r)n as the product of P and a factor not depending on P.

MP 3, 6

EXAMPLE 1 Basic/ELLS Rewrite the expression 3x + [2x/5] as one rational expression that is equivalent to the expression for all x values. Regular Rewrite the expression 7x + [5x/(x+8)] as one rational expression that is equivalent to the expression for all x values, where x ≠ –8. Enrichment

EXAMPLE 2 Basic/ELLS Give questions similar to Example 2. Regular Give questions similar to Example 2 but some have sides that are less than the height. Enrichment Give questions similar to Example 2 but some have sides that are less than the height. These questions should also include some with fractions for the change.

Assessment

Example 1 Two questions to

answer similar to the basic and regular.

A third question where students are required to explain how the process is similar to finding the common denominator of a regular fraction.



A third question where students are required to explain how the process is similar to finding the common denominator of a regular fraction.

9

Rewrite the expression 7x + [5x/(x+8)] as one rational expression that is equivalent to the expression for all x values, where x ≠ –8.

Last 1/3 of

the period.


Solving equations using the distributive property and combining like terms.

A –CED.1

Create equations and inequalities in one variable and use them to solve problems.

MP 4,2

Teacher created material. http://www.youtube.com/watch?v=hVCVW2cfcsA

Example: The perimeter of a rectangle is 104m. The length is 7m more than twice the width. What are the dimensions of the rectangle?

1 day Q 13

Polynomials Arithmetic operations with polynomials. Example 1: (-14x7 + 19x6 - 17) + (5x5 - 10x4 + 18) Example 2: (8x3 - 8x - 4) - (-16x6 + 9x3 - 6x2) Example 3:

(-3x + 8) (-4x3 + 8x2 -

A.APR.A.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

Basic (2r + 9r4) – (8r - 7r2 + 4r4) Regular (3b3 + 8) – (9b3 + 7 + b4) + (5b4 + 6) Enrichment (4b5 – 3b3 + 8) – (4b4 +

http://www.mathsisfun.com/algebra/polynomials-adding-subtracting.html http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Adding+Subtracting%20Polynomials.pdf

Algebra Lab http://www.regentsprep.org/Regents/math/ALGEBRA/teachres/TRcubes.htm http://www.regentsprep.org/Regents/math/ALGEBRA/AV2/indexAV2.htm

Assessment

http://www.youtube.com/watch?v=hVCVW2cfcsA




http://www.corestandards.org/Math/Content/HSA/APR/A/1

http://www.mathsisfun.com/algebra/polynomials-adding-subtracting.html





http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Adding+Subtracting%20Polynomials.pdf







http://www.regentsprep.org/Regents/math/ALGEBRA/teachres/TRcubes.htm




http://www.regentsprep.org/Regents/math/ALGEBRA/AV2/indexAV2.htm




10

2x + 12) multiply polynomials.

MP 3

9b3 + 7 + b) + (5b2 + 6) Verify results http://education.ti.com/en/us/activity/detail?id=BE17AD49E4E14CDA81B9BA66A3587E10

http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_04/study_guide/pdfs/alg1_pssg_G063.pdf



At least one should not have like terms in each expression.

Last 1/3 of

the period.


Using the TI-84 to find the roots of quadratics.

A.APR.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

MP 2


http://mathbits.com/MathBits/TISection/Algebra2/zerofunctions.htm Students will be given quadratics to find the roots using the calculator. Then students will be given a cubic and quartic to do the same.

1 day

Q14

Polynomials Determine the roots of polynomial functions.

A.APR.3


MP 7

Algebra 2 Basic, Regular, Advance Page 355 question 4

http://www.ck12.org/book/CK-12-Algebra-I---Honors/r3/section/7.9/ http://www.augustatech.edu/math/molik/PolynomialFunctions.pdf

Algebra Lab Algebra 2 Teachers Edition pg 346 Performance Task 3

Assessment Given a graph,

determine the roots. Given a polynomial

expression,

http://education.ti.com/en/us/activity/detail?id=BE17AD49E4E14CDA81B9BA66A3587E10















http://mathbits.com/MathBits/TISection/Algebra2/zerofunctions.htm



http://www.ck12.org/book/CK-12-Algebra-I---Honors/r3/section/7.9/





http://www.augustatech.edu/math/molik/PolynomialFunctions.pdf





11

determine the roots.

Last 1/3 of

the period.


Multiplying and factoring perfect square trinomials and differences of squares.

A.APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

MP 3

http://www.themathpage.com/alg/difference-two-squares.htm http://www.themathpage.com/alg/perfect-square-trinomial.htm

Example: Multiply (x + 9)(x – 9) (x + 6)2 Factor x2 – 100 9x2 – 24x + 16

2 days

Q15

Polynomials Difference of Squares Difference of Cubes Sum of Cubes

A.APR.3


MP 7

Algebra 2 Student


Basic: Problems 1-4 EXS: 11-35 odd, 37, 38 Average: Problems 1-4 EXS: 25-35 odd, 37, 38, 39-49 odd, 51-57 which by class) Advanced: Problems 1-4 From Average plus

http://www.mathsisfun.com/algebra/polynomials-difference-two-cubes.html http://www.mathsisfun.com/definitions/difference-of-squares.html

Algebra Lab Algebra 2 Teachers Edition pg 346 Performance Task 3

Assessment Given polynomials, students will determine if they are Difference of Squares, Difference of Cubes, Sum of Cubes.

http://www.themathpage.com/alg/difference-two-squares.htm




http://www.themathpage.com/alg/perfect-square-trinomial.htm





http://www.mathsisfun.com/algebra/polynomials-difference-two-cubes.html





http://www.mathsisfun.com/definitions/difference-of-squares.html





12

58-60

Last 1/3 of

the period.


Write the equations of lines.

A.CED.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MP 4, 2

Student Textbook

Section 2-3 & 2-4

Selected problems should be determined by the skills of the class.

http://www.education.com/study-help/article/pre-calculus-help-slope-equation-line/ http://www.education.com/study-help/article/pre-calculus-help-pre-calculus-chapter-1/

Example: What is the equation of the line containing the points (0, −1) and (5, 1)? Find an equation of the line containing the point (−1, −5) and parallel to the line y = 2 x − 4.

1 day

Q16,17, 18

Polynomials Linear Factors and End Behavior

A.APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

MP 7

Algebra 2 Student

Textbook Section 5-1 &

5-2 Basic: Problems 1-4 EXS: pg 285 9-39 odd Average: Problems 1-4 EXS: pg 286 40-54 Advanced:

http://www.purplemath.com/modules/polyends.htm

Algebra Lab Algebra 2

Teachers Edition pg 280

Solve it or PowerAlgebra (textbook website)


Assessment

http://www.education.com/study-help/article/pre-calculus-help-slope-equation-line/







http://www.education.com/study-help/article/pre-calculus-help-pre-calculus-chapter-1/













13

Problems 1-4 From Average plus pg 287 55-57

Given a graph, determine the roots.

Given a polynomial expression, determine the roots and describe the end behavior.

Last 1/3 of

the period.


Counting Principle S.CP.9

Use permutations and combinations to compute probabilities of compound events and solve problems. MP 2

Student Textbook

Section 11-1 All: Problem 1 EXS: pg 678 9-11

http://www.regentsprep.org/Regents/math/ALGEBRA/APR1/PracCnt.htm

Example: A movie theater sells 3 sizes of popcorn (small, medium, and large) with 3 choices of toppings (no butter, butter, extra butter). How many possible ways can a bag of popcorn be purchased?

Last 1/3 of

the period.

Basic Skills PARCC/HSPA Prep

Mixed problem solving problems based on unit basic skill review.

A –CED.1, 2 A.SSE.A.1a 7.EE.3 A.APR.3 S.CP.9


Quiz on Basic Skills

Part of a period

END UNIT TEST

End unit test to determine areas of weakness that need to be addressed before the state unit test.

A.SSE.1 A.APR.1, 3



Use problems similar to the pre-assessment that have been covered since the mid-unit test.

INSTRUCTIONAL FOCUS OF UNIT





14

1. Use Properties of operations to add, subtract, and multiply complex numbers.

2. Solve quadratic equations with real coefficients that have complex solutions.

3. Show that the fundamental Theorem of Algebra is true for quadratic polynomials

4. Interpret coefficients, terms, degree, powers (positive and negative), leading coefficients and monomials in polynomial and

rational expressions in terms of context.

5. Restructure by performing arithmetic operations on polynomial/rational expressions.

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

problems. For Example, calculate mortgage payments.

7. Use an appropriate factoring technique to factor expressions completely including expressions with complex numbers.

8. Explain the relationship between zeros and factors of polynomials and use zeros to construct a rough graph of the function defined

by the polynomial.

PARCC FRAMEWORK/ASSESSMENT

PARCC EXEMPLARS: www.parcconline.org (copy & paste the url or link into search engine)

Complex Numbers: http://www.projectmaths.ie/documents/teachers/tl_complex_numbers.pdf

Polynomials: http://www.projectmaths.ie/students/stran4lc/student-activity-polynomial.pdf

1. It is given that: . Find the value of p.

HSPA EXEMPLARS:

Number And Numerical Operations:

http://www.riverdell.org/cms/lib05/NJ01001380/Centricity/Domain/56/Number%20Sense%20Practice%20Problems.pdf

Question 81 - Candra had a gift card for $130. She spent $20.83 on Friday and $56.51 on Saturday using her gift card. Then, on Sunday she returned

an item she bought on Saturday, and $13.76 was credited back to her gift card. How much money is left on Candra's gift card on Monday?

Candra’s friend, Alex, also received a gift card. The amount on his gift card is 20% less than Candra’s. How much does Alex have on his gift

http://www.parcconline.org/


http://www.projectmaths.ie/students/stran4lc/student-activity-polynomial.pdf


15

card.

If Alex bought three items and returned one to end up spending 75% of the balance of his card, create four transactions to reflect this.

Patterns And Algebra: http://mslaplantesmathclass.weebly.com/uploads/1/7/3/7/17373129/4.10.2013.pdf

Billie Sue's BBQ had their grand opening this year. The first month they did not turn a profit. However, each month thereafter, they have had steady

profits of $1,600 per month. If x represents the number of months they have profited, which of the following equations represents the amount of

profits after x months?

A. y = 1,600x B. y = 1,600 – x C. y = 1,600x + x D. y = x + 1,600

To make low fat cottage cheese, milk containing 4% butterfat is mixed with 10 gallons of milk containing 1% butterfat to obtain a mixture

containing 2% butterfat. How many gallons of the richer milk is used? If the equation is (.02)(10 + x) = (.01)(10) + (.04)(x) explain how

each of the following relate to the original question.

a. What does (.02)(10 + x) represent?

b. What does (.01)(10) represent?

C. What does (.04)(x) represent?

21ST CENTURY SKILLS (4Cs & CTE Standards)

9.4.D Business, Management & Administration Career Cluster 9.4.E Education & Training Career Cluster 9.4.F Finance Career Cluster 9.4.N Marketing Career Cluster 9.4.O Science, Technology, Engineering & Mathematics Career Cluster 9.4.P Transportation, Distribution & Logistics Career Cluster 9.4.12.D.2, 9.4.12.E.2, 9.4.12.F.2, 9.4.12.N.2, 9.4.12.O.2, 9.4.12.P.2

Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities.

9.4.12.D.4, 9.4.12.E.4 Solve mathematical problems and use the information to make business decisions and enhance business management duties.

9.4.12.F.4

Solve mathematical problems to obtain information for decision-making in financial settings.

9.4.12.N.4 Solve mathematical problems to obtain information for marketing decision-making.

9.4.12.O.15

http://mslaplantesmathclass.weebly.com/uploads/1/7/3/7/17373129/4.10.2013.pdf

16

Prepare science, technology, engineering, and mathematics material in oral, written, or visual formats to provide information to an intended audience and to fulfill the specific communication needs of that audience.

9.4.H(5) Biotechnology Research and Development 9.4.12.H.(5).2

Apply biochemistry, cell biology, genetics, mathematics, microbiology, molecular biology, organic chemistry, and statistics concepts to conduct effective biotechnology research and development.

9.4.O(1) Engineering and Technology 9.4.12.O.(1).1

Apply the concepts, processes, guiding principles, and standards of school mathematics to solve science, technology, engineering, and mathematics problems.

9.4.12.O.(1).7 Use mathematics, science, and technology concepts and processes to solve problems in projects involving design and/or production (e.g., medical, agricultural, biotechnological, energy and power, information and communication, transportation, manufacturing, and construction).

9.4.O(2) Science and Mathematics 9.4.12.O.(2).1

Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve problems and issues in the real world.

9.4.12.O.(2).2 Apply science and mathematics when developing plans, processes, and projects to find solutions to real world problems.

9.4.12.O.(2).3 Assess the impact that science and mathematics have on society when used to develop projects or products.

9.4.12.O.(2).4 Use scientific and mathematical problem-solving skills and abilities to develop realistic solutions to assigned projects, and illustrate how science and mathematics impact problem-solving in modern society.

9.4.12.O.(2).6 Demonstrate the knowledge and technical skills needed to obtain and succeed in a chosen scientific and mathematical field.

MODIFICATIONS/ACCOMMODATIONS

17

APPENDIX (Teacher resource extensions)

1. E-Text, Interactive Digital Resources, Teacher Resources Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true

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

2. Reason abstractly and quantitatively.

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

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

SLO 6 Communicate the precise answer to a real-world problem.

7. Look for and make use of structure.

SLO 5 Identify structural similarities between integers and polynomials.

SLO 7 Identify expressions as single entities, e.g. the difference of two squares.

8. Look for and express regularity in repeated reasoning.

SLO 6 Arrive at the formula for finite geometric series by reasoning about how to get from one term in the series to the next. All of the content presented in this course has connections to the standards for mathematical practices. * This course includes exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)

https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true

18

UNIT 2 – Expressions and Equations (1)



What are the operations that apply to all function? How can Geometric and Analytic representations be

used to describe the behavior of the function? How are algebraic, numeric, and graphic

representations of functions related? How does representing functions graphically help you

solve a system of equations? How does writing equivalent equations help you solve a

system of equations? What does the degree of a polynomial tell you about its

related polynomial function? For a polynomial function, how are factors, zeros and x-

intercepts related? For a polynomial function, how are factors and roots

related?

You can add, subtract, multiply, and divide functions based on how you perform these operations for real numbers. One difference, however, is that you must consider the domain of each function.

To solve a system of equations, find a set of values that replace the variables in the equations and make each equation true.

You can solve a system of equations by writing equivalent systems until the value on one variable is clear. Then substitute to find the values of the other variables.

You can factor many quadratic trinomials into products of two binomials.

To find the zeros of a quadratic function, you must set the equation equal to zero..

A polynomial function has distinguishing “behaviors”. You can look at its algebraic form and know something about its graph. You can look at its graph and know something about its algebraic form.

Knowing the zeros of polynomial functions can help you understand the behavior of its graph.

You can divide polynomials using steps that are similar to the long division steps that you use to divide whole numbers.

The degree of a polynomial equation tells you how many roots the equation has.


RESOURCES LEARNING ACTIVITIES/ASSESSME

NTS Pearson

OTHER (e.g., tech)


Exponents and Radicals

Rational expression Equations in one

N.RN.1, 2 A.APR.6 A.REI.1,6 A.SSE.3


19

variable System of Equations Equivalent Expressions Key features of graphs

F.IF.4

2

1. Exponents and Radicals.

1. Solve exponential equations. Ex:

If , what is the

value of x? Explain your reasoning. 2. Rewrite radical expression in exponential forms: Ex:

Rewrite the

expression as a power of 5.

N.RN.1

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. N.RN.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents. MP 1, 8

Algebra 2 Student


Basic: Problems 1-4 EXS: 10-30, 33-37, 56-67 Average: Problems 1-4 EXS: 11-29 odd, 31-48, 56-67 Advanced: Problems 1-4 11-29 odd, 31-67

Student Textbook

Section 6-4

Basic: Problems

Interactive Digital Path 6-1 Roots and 8-6-1 Radical Expressions PowerAlgebra (textbook website)

Algebra 2 Interactive Digital Path Chapter 6 Chapter 6-1 View Solve it Dynamic Activity 6-4 Rational Exponents PowerAlgebra (textbook website)

Algebra 2 Interactive Digital Path Chapter 6 Chapter 6-4 View Dynamic

Algebra Lab Algebra 2 Student Textbook Section 6-1 Concept Byte Page 360

Algebra Lab Student Textbook Section 6-4 Solve It Page 381 or on web at PowerAlgebra (textbook website)


Assessment Three question quiz: Two calculation questions similar to the Examples shown. One reasoning question requiring a written response that shows a student understands how the exponent power









20

1-6 EXS: 10-67, 72-82 E, 56-67, 98-119 Average: Problems 1-6 EXS: 11-65 odd, 67-90, 98-119 Advanced: Problems 1-6 11-65 odd, 67-119

Activity

relates to the radical.



Simplify radical expressions

N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

MP 4


This will be a review of the process to simplify

radicals. This skill will be applied in the next test

prep.

3

2. Rational expression

Dividing Polynomials using long or synthetic method. Ex: Divide A) 4x2 +2x +1

x -2, where

x ¹ 2? B) Simplify

A.APR.6

Rewrite rational expressions. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) +

Student Textbook

Section 5-4

Basic: Problems 1-5 EXS: 9-41, 43, 48, 50, 67-85

Interactive Digital Path 5-4 Dividing Polynomials http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000061&is

Algebra Lab Student Textbook Section 5-4 Solve It Page 303 or on the web at http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000061&isHtml5Sco=false

Algebra Lab

http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000061&isHtml5Sco=false












21

2 2

2 2

3 10 5 6

2 11 5 2 7 3

x x x x

x x x 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. MP 1, 2, 3, 6

Average: Problems 1-5 EXS: 9-39 odd, 40-62, 67-85

Advanced: Problems 1-5 EXS: 9-39 odd, 40-66, 67-85

Student Textbook

Section 8-4

Basic: Problems 1-4 EXS: 8-27, 31-33, 37, 50-67


Advanced: Problems 1-4 EXS: 9-25

Html5Sco=false

Interactive Digital Path 8-4 Rational Expressions http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000094&isHtml5Sco=false

Student Textbook Section 8-4 Solve It Page 527 or on web at http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000094&isHtml5

Sco=false

Click on Solve It Tab

Assessment Three question quiz: Two calculation questions similar to the Examples shown. One reasoning question requiring a written response where students will discuss the processes of long and synthetic division.














22

odd, 27-67



Problem solving with radicals.

N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

MP 4


Three part open ended question where students will find the width, area, and area of a shaded region where the answers must be written in radical form.

2

3. Equations in One variable

Solving radical Equations EX: solve for x

5 2 5 12x- + =

A.REI.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.

A.REI.2

Understand solving equations as a process of

Student Textbook Section 6-

5

Basic: Problems 1-5 EXS: 9-47, 57-60, 63-65

Average: Problems 1-5 EXS: 9-43 odd 45-67, 73-96

Advanced: Problems 1-5 EXS: 9-43 odd, 45-72

Interactive Digital Path 6-5 Solving Square Root and Other Radical Expressions http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000075&isHtml5Sco=false


Assessment

Three question quiz: Two calculation

questions similar to the Example shown.

One reasoning question requiring a written response where students will discuss why the solution normally has ± in front of it and in what situations it is not needed.














23

reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give Examples showing how extraneous solutions may arise.



Solving radical word problems.

N-RN.A.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

MP 3


Example: A shop needs to make a frame where

the height is 1/2 its width. It is to be enlarged

to have an area of 60.5 square inches. What will be the dimensions of the

enlargement?

Part of a period

MID UNIT TEST

Mid unit test to determine areas of weakness that need to be addressed before the state unit test.

N.RN.1, 2 A.APR.6 A.REI.1, 2



3

4. System of Equations

1. Solve system of linear equations by graphing. EX:

13

2

1 1

6 3

y x

y x

A.REI.6

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of

Student Textbook Section 3-1

Basic: Problems 1-4 EXS: 7-28,

Interactive Digital Path 3-1 Solving Systems Using Tables and Graphs http://www.pearsonsuccessnet.c









24

2. Solve the system of equations algebraically. EX: 2 3 8

4 2 10

x y

x y

3. Solve system of equations graphically and algebraically. EX: y = 2x +5

y = x2 + 4x -10

linear equations in two variables.

A.REI.7

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For Example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3. MP 6

30-36 even, 38-43, 53-67


Advanced: Problems 1-4 EXS: 7-27 odd, 29-52 Student Textbook Section 3-2



Advanced:

om/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000036&isHtml5Sco=false

Interactive Digital Path 3-2 Solving Systems Algebraically http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000037&isHtml5Sco=false

Algebra Lab

Section 3-1 Dynamic Activity on the web at http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000075&isHtml5Sco=false

Algebra Lab

Student Textbook Section 3-2 Solve It Page 142 or on the web at http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000037&isHtml5Sco=false

Algebra Lab Section 3-2 Dynamic

Activity on the web at http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000037&isHtml5

Sco=false
























25

Problems 1-5 EXS: 11-41 odd, 43-66,

67-80



Problem Solving with Systems of Linear Equations

A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

MP 4,2


Example: At Pinho’s, Sam bought 2 donuts and 5 muffins spending $14.25. Amy bought 3 donuts and 2 muffins spending $9. How much do they charge for a donut? How much for a muffin?

2

5. Equivalent Expressions.

Use properties of exponents to simplify exponential functions. Ex: Simplify the following function

f x( ) = 3x ×23x+2

A.SSE.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. c. Use the properties of exponents to transform expressions for exponential


Basic: Problems 1-6 EXS: 10-67, 72-82 E, 56-67, 98-119

Average: Problems 1-6 EXS: 11-65 odd, 67-90,

Interactive Digital Path 6-4 Rational Exponents http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000073&isHtml5Sco=false

Interactive Digital Path 6-5 Solving Square Root and Other

Algebra Lab Student Textbook Section 6-4 Solve It Page 381 or on web at http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000073&isHtml5Sco=false

Click on Dynamic Activity Tab

Algebra Lab Student Textbook Section 6-5 Solve It Page 390 or on the web at http://www.pearsonsuccessne















26

functions. For Example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. MP 4, 3

98-119

Advanced: Problems 1-6 11-65 odd, 67-119




Advanced: Problems 1-5

EXS: 9-43 odd, 45-72

Radical Expressions http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000075&isHtml5Sco=false

t.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000075&isHtml5Sco=false

Assessment

Two question quiz: Two calculation

questions similar to the Example shown.



Multiplying with scientific notation.

N-RN.A.2

Rewrite expressions involving radicals


Example: The speed of light is approximately 3 x 10 8 m/s. How far does light travel in 6.0 x 101 seconds?









27

and rational exponents using the properties of exponents.

MP 3, 8

2

6. Key features of graphs

End behavior of a function. EX: Find the end behavior of the function f(x)=x4 – 4 x3 + 3 x + 25.

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.

MP 4, 2

Student Textbook Section 5-1 Basic: Problems 1-4 EXS: 8-39, 40-50 Even, 58-71 Average: Problems 1-4 EXS: 9-39, 40-54 Even, 58-71 Advanced: Problems 1-4 EXS: 9-39 odd, 40-71 67 Page 283

http://hotmath.com/hotmath_help/topics/end-behavior-of-a-function.html

Interactive Digital Path 5-1 Polynomial Functions http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000075&isHtml5Sco=false

Algebra Lab Student Textbook Section 5-1 Solve It Page 280 or on web at http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000073&isHtml5

Sco=false

Assessments

Three question quiz: Two questions similar

to the Example shown. One reasoning

question requiring a written response where students will discuss how they can sometimes determine the roots visually.

Last 1/3 of the

Basic Skills PARCC/HSPA

Mixed problem solving problems based on unit

N-RN.A.2 A.REI.6

Teacher created




















28

period. Prep basic skill review. material.

Part of a period

END UNIT TEST


A.REI.6, 7 A.SSE.3 F.IF.4




1. Use properties of integer exponents to explain and convert between expressions involving radicals and rational exponents, using

correct notation. For Example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3

must equal 5.

2. Rewrite simple rational expressions in different forms using inspection, long division, or, for the more complicated Examples, a

computer algebra system.

3. Solve simple equations in one variable and use them to solve problems, justify each step in the process and the solution and in the

case of rational and radical equations show how extraneous solutions may arise.

4. Solve systems of linear equations and simple systems consisting of a linear and a quadratic equation in two variables, algebraically

and graphically.

Write equivalent expressions for exponential functions using the properties of exponents.Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include:

intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.


PARCC EXEMPLARS: www.parcconline.org (copy & paste the url or link into search engine)

Complex Numbers: http://www.projectmaths.ie/documents/teachers/tl_complex_numbers.pdf

http://www.parcconline.org/


29

Polynomials: http://www.projectmaths.ie/students/stran4lc/student-activity-polynomial.pdf

It is given that: . Find the value of p.

HSPA EXEMPLARS:

Number And Numerical Operations:


Question 81 - Candra had a gift card for $130. She spent $20.83 on Friday and $56.51 on Saturday using her gift card. Then, on Sunday she returned

an item she bought on Saturday, and $13.76 was credited back to her gift card. How much money is left on Candra's gift card on Monday?

Candra’s friend, Alex, also received a gift card. The amount on his gift card is 20% less than Candra’s. How much does Alex have on his gift

card.

If Alex bought three items and returned one to end up spending 75% of the balance of his card, create four transactions to reflect this.

Patterns And Algebra: http://mslaplantesmathclass.weebly.com/uploads/1/7/3/7/17373129/4.10.2013.pdf

Billie Sue's BBQ had their grand opening this year. The first month they did not turn a profit. However, each month thereafter, they have had steady

profits of $1,600 per month. If x represents the number of months they have profited, which of the following equations represents the amount of

profits after x months?

A. y = 1,600x B. y = 1,600 – x C. y = 1,600x + x D. y = x + 1,600

To make low fat cottage cheese, milk containing 4% butterfat is mixed with 10 gallons of milk containing 1% butterfat to obtain a mixture

containing 2% butterfat. How many gallons of the richer milk is used? If the equation is (.02)(10 + x) = (.01)(10) + (.04)(x) explain how

each of the following relate to the original question.

a. What does (.02)(10 + x) represent?

b. What does (.01)(10) represent?

C. What does (.04)(x) represent?


9.4.D Business, Management & Administration Career Cluster 9.4.E Education & Training Career Cluster 9.4.F Finance Career Cluster 9.4.N Marketing Career Cluster 9.4.O Science, Technology, Engineering & Mathematics Career Cluster 9.4.P Transportation, Distribution & Logistics Career Cluster

http://www.projectmaths.ie/students/stran4lc/student-activity-polynomial.pdf


http://mslaplantesmathclass.weebly.com/uploads/1/7/3/7/17373129/4.10.2013.pdf

30

9.4.12.D.2, 9.4.12.E.2, 9.4.12.F.2, 9.4.12.N.2, 9.4.12.O.2, 9.4.12.P.2



9.4.12.F.4



9.4.12.O.15 Prepare science, technology, engineering, and mathematics material in oral, written, or visual formats to provide information to an intended audience and to fulfill the specific communication needs of that audience.









31






E-Text, Interactive Digital Resources, Teacher Resources Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true

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

SLO 3 Use problems that involve may givens of the need to be composed or decomposed before they can be solved

2. Reason abstractly and quantitatively.

SLO 5 Using properties of exponents to determine if two expressions are equal.

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

4. Model with mathematics. *

5. Use appropriate tools strategically.

SLO 6 Use graphing technically when available.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.


32

All of the content presented in this course has connections to the standards for mathematical practices.

* This course includes exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)

UNIT 3 – Expressions and Equations (2)



How does representing functions graphically help you solve a system of equations?

For a polynomial function, how are factors, zeros and x-intercepts related?

How do you model a quantity that changes regularly over time by the same percentage?

How can you model periodic behavior?

To solve a system of equations, find a set of values that replace the variables in the equations and make each equation true.

A polynomial function has distinguishing “behaviors”. You can look at its algebraic form and know something about its graph. You can look at its graph and know something about its algebraic form.

Periodic behavior is behavior that repeats over intervals of equal length. An angle with a full circle of rotation measure 2π radians.


RESOURCES LEARNING

ACTIVITIES/ASSESSMENTS Pearson OTHER

(e.g., tech)

33


Systems of equations Arithmetic Sequences Geometric Sequences Inverse of functions. Functions and their graphs. Exponential functions. Radian Measures Trig

A.REI.11 F.BF.2 F.BF.4 F.IF.4 F.IF.7 F.LE.5 F.TF.1 F.TF.2 F.TF.8 F.TF.5


2

1. Systems of equations

Determine the solution from the graph of the system. EXAMPLE 1: What is the solution set?

EXAMPLE 2: For the functions a and b defined below,

A.REI.11 Find approximate solutions for the intersections of functions and 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) involving linear, polynomial, rational, absolute value, and exponential

SECTION 4-9 Basic: Problem 1 Pg 262 Q 8 – 13 Average: Problem 1 Pg 262 - 263 Q 8 – 13, 41 - 46 Advanced: Problem 1 Pg 262 - 263 Q 8 – 13, 41 – 46, 53-55

Understand that where the graphs intersect is the solution.

Understand that when looking at the table of values in the graphing calculator the solutions are where all the y values are the same.

Algebra Lab Concept Byte pg 477 Questions 1 – 3

Algebra Lab Concept Byte pg 484-485 Questions 1 – 12

Algebra Lab Teacher created worksheets with systems of two different types of equations including: Rational with linear. Square root with absolute value.

34

sketch a graph without the use of a calculator and use the graph to identify the solution set to a(x) = b(x). a(x) = 4/x b(x) = 1/2x + 1 EXAMPLE 3: For the functions defined above, fill in the tables of values. Then give the solution set to g(x) = h(x). Explain your answer.

g(x) = h(x) = | x – 6 |

functions. MP 1, 4, 5

Then have students make up some of their own. They should graph them and determine the solution set. If the solution set is not easy to find, students should adjust the parameters of the problem until it is.

Last 1/3 of

the period.


Patterns in mathematics

8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats

http://en.wikibooks.org/wiki/SA_NC_Doing_Investigations/Chapter_6#Number_Patterns_Activity_1 http://www-rohan.sdsu.edu/~ituba/math303s08/mathideas/mmi10_01_02.pdf

Algebra Lab

After covering the patterns, have students create their own pattern, then write a

question and solution.

This should also include a paragraph or two in writing where students can explain they understand the process.

http://en.wikibooks.org/wiki/SA_NC_Doing_Investigations/Chapter_6#Number_Patterns_Activity_1







http://www-rohan.sdsu.edu/~ituba/math303s08/mathideas/mmi10_01_02.pdf






35

eventually into a rational number. MP

2

2. Arithmetic Sequences

Write the explicit and recursive form of an arithmetic sequence. EXAMPLE: Julia makes $2.00 an hour for first hour of work, $4.00 her second hour, $6.00 her third hour and so on. How much money will she earn on her 12th hour of work? Write a recursive and explicit rule for this problem.

F.BF.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 3

Section 9-2 Basic: Problems 1-4 EXS: 7-25, 31-35, 49-53, 61, 75-88 Average: Problems 1-4 EXS: 7-25 odd, 26-62, 75-88 Advanced Problems 1-4 EXS: 7-25 odd, 26-88

http://www.algebralab.org/lessons/lesson.aspx?file=algebra_arithseq.xml

Algebra Lab Solve it pg 572 also on http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000100&isHtml5Sco=false Dynamic Activity also on same web site.

Last 1/3 of

the period.


Combinations and Permutations

S.CP.9 Use permutations and combinations to compute probabilities of compound events and solve problems.

http://www.mathsisfun.com/combinatorics/combinations-permutations.html http://www.regentsprep.org/Regents/math/algtrig/ATS5/Lcomb.htm

Example: Permutation: In how many ways can 4 of 7 different kinds of bushes be planted along a walkway? Combination: How many ways are there to select 3 bracelets from a box

of 20?










http://www.mathsisfun.com/combinatorics/combinations-permutations.html






http://www.regentsprep.org/Regents/math/algtrig/ATS5/Lcomb.htm





36

2

3. Geometric Sequences

Write the explicit and recursive form of a geometric sequence. EXAMPLE: A ball is dropped, and for each bounce after the first bounce, the ball reaches a height that is a constant percent of the preceding height. After the first bounce, it reaches a height of 30 feet, and after the third bounce it reaches a height of 10.8 feet. Write an explicit rule for the height after the nth bounce, an, where n represents the bounce number.

F.BF.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 4, 2

Section 9-3 Basic: Problems 1-4 EXS: 7-31, 36-44 even, 48-50, 59, 63-81 Average: Problems 1-4 EXS: 7-31 odd, 32-59, 63-81 Advanced: Problems 1-4 EXS: 7-31 odd, 32-62, 63-81

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_GeoSeq.xml

Algebra Lab Solve it pg 580 also on http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000102&isHtml5Sco=false Dynamic Activity also on same web site.

Last 1/3 of

the period.


Simple probability S.MD.6 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

http://www.mathsisfun.com/data/probability.html

Example: There are five balls in a bag: 2 red, 2 blue, and 1 white. What is the probability of randomly choosing a red ball?














37

2

4. Geometric Sequences

Write the recursive formula of a geometric sequence in visual form. Example:

Write a recursive formula for the pattern shown.

F.BF.2

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

http://www.skwirk.com.au/p-c_s-12_u-223_t-599_c-2236/VIC/5/Patterns-number-and-geometric/Patterns-and-algebra/Patterns-and-algebra/Maths/

Last 1/3 of

the period.


Dependent and Independent Events

S.CP.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.


Example: You throw a die twice. What is the probability of throwing a six and then a second six? Are these independent or dependent events? A bowl contains 4 peaches and 4 apricots. Maxine randomly selects one, puts it back, and then randomly selects another. What is the probability that both selections were apricots?

















38

2

5. Inverse of functions.

Find the inverse of a given function. EXAMPLES: Write an expression for the inverse of f(X)

= 4x

7 + 3.

What is the inverse function for

f(x) =

2 2x

3

, where

0 ?x

If f(x) = 4

x – 3 find

1 ,f x where x > 3.

F.BF.4

Determine the inverse function for a simple function that has an inverse and write an expression for it. MP 4

Section 6-7

Basic: Problems 1-6 EXS: 8-43, 48-54 even, 65, 75-95


Advanced: Problems 1-6 EXS: 9-42-74, 75-95

Section 7-3

Basic: Problems 1-5 EXS:12-47, 58-61, 72-76 even, 85-98

Average: Problems 1-5 EXS:13-43 odd, 44-79, 85-98

Advanced: Problems 1-5 EXS:13-43, odd, 44-84, 85-98

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_FunctionsRelationsInverses.xml http://www.mathworksheetsgo.com/sheets/algebra-2/functions-and-relations/inverse-functions-worksheet.php

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_FunctionsRelationsInverses.xml






http://www.mathworksheetsgo.com/sheets/algebra-2/functions-and-relations/inverse-functions-worksheet.php








39

Last 1/3 of

the period.


Mutually exclusive and non-mutually exclusive events.

S.CP.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.

http://www.nutshellmath.com/textbooks_glossary_demos/demos_content/alg2_compound_probability.html http://www.mathsisfun.com/data/probability-events-mutually-exclusive.html

Example: A pair of dice is rolled. What is the probability that the sum of the numbers rolled is either 7 or 11? A pair of dice is rolled. What is the probability that the sum of the numbers rolled is either an even number or a multiple of 3?

2

6. Functions and their graphs.

Describing key features of functions. EXAMPLE 1: Describe each of the following key features of the graph of f(x) = (x – 4)(x – 3)2(x + 1)3

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

USE THE FOLLOWING SECTIONS2-3 2-5, 4-1, 4-2, 4-3, 5-1, 5-8, 13-1, 13-4, 13-5

Section 5-1 Basic: Problems 1-4 EXS: 8-39, 40-50, even, 51, 58-71


Advanced:

http://www.youtube.com/watch?v=GALfCd-2XRQ http://learni.st/users/S33572/boards/2366-reading-and-interpreting-graphs-common-core-standard-9-12-f-if-4

Algebra Lab Concept Byte pp 459-460

Algebra Lab

Concept Byte pp 477 http://olhs.olentangy.k12.oh.us/teachers/kevin_streib/Algebra%20I

The above web site has the solution keys to some really good questions on this topic. However, the original worksheets are not available.

http://www.nutshellmath.com/textbooks_glossary_demos/demos_content/alg2_compound_probability.html







http://www.mathsisfun.com/data/probability-events-mutually-exclusive.html





http://www.youtube.com/watch?v=GALfCd-2XRQ



http://learni.st/users/S33572/boards/2366-reading-and-interpreting-graphs-common-core-standard-9-12-f-if-4








http://olhs.olentangy.k12.oh.us/teachers/kevin_streib/Algebra%20I



40

Example 2: Use the graph of the function f to answer the following questions. For what values of x is f < 0?

increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. MP 6, 4

Problems 1-4 9-39 odd, 40-71

Section 8-3 Basic: Problems 1-5 EXS: 13-42, 50-76

Average: Problems 1-5 13-35 odd, 36-47, 50-76

Advanced: Problems 1-5 EXS: 13—35 odd, 36-49, 50-76

USE THE FOLLOWING SECTIONS 7-1, 7-2, 7-3, 13-4, 13-5, 13-6, 13-7, 13-8

41

Last 1/3 of

the period.

Basic Skills PARCC/HSPA

Prep

Geometric Probability

S.MD.7 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

http://www.nutshellmath.com/textbooks_glossary_demos/demos_content/alg2_compound_probabilit

y.html

http://www.mathsisfun.com/dat

a/probability-events-mutually-

exclusive.html

Example:

Find the probability that a randomly chosen point in

the figure lies in the shaded region. Give all

answers in fraction and percent forms.

2

7. Exponential functions.

Modeling with exponential functions. EXAMPLE: The population, in thousands, of a certain city can be modeled by the function

0.25

180 0.94 ,t

P t

where t is the number of years since 2000. What was the population of the city in the year 2000? What is the rate of change of the city’s population?

F.LE.5

Interpret the parameters in a linear or exponential function in terms of a context. MP 1, 2, 6, 5

Section 7-2 Basic: Problems 1-5 EXS: 7-33, 35, 38-40 even, 44-62 Average: Problems: 1-5 EXS: 7-29 odd, 31-41, 44-62 Advanced: Problems 1-5 EXS: 7-29 odd, 31-62

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ExponentsApps.xml http://www.opentextbookstore.com/precalc/1.3/Chapter%204.pdf

Algebra Lab Solve it pg 442 also found on http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000082&isHtml5Sco=false

Dynamic activity on same site as above.













http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ExponentsApps.xml





http://www.opentextbookstore.com/precalc/1.3/Chapter%204.pdf









42

Last 1/3 of

the period.


Measures of Central Tendency

http://www.regentsprep.org/Regents/math/ALGEBRA/AD2/measure.htm

http://www.keswick.hs.yrdsb.edu.on.ca/DeptResources/Math/MBF3CWebsite/Resources/Statistics/MeasureofCentralTendencyPractice.pdf

1

8. Radian Measures

Measuring angles with radians. EXAMPLE: Convert as required.

60° = radian 3

5

= degrees

T.TF.1

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

Section 13-3 Basic: Problems 1-4 EXS: 6-34, 35-49, 54-68 Average: Problems 1-4 7-33 odd, 35-50, 54-68 Advanced: Problems 1-4 7—33 odd, 35-53, 54-68

http://www.mathwarehouse.com/trigonometry/radians/convert-degee-to-radians.php


Last 1/3 of

the period.


Bar and circle graphs http://www.mathsisfun.com/data/bar-graphs.html http://www.mathsisfun.com/data/pie-charts.html

Algebra Lab Pg 982

http://nces.ed.gov/nceskids/createagraph/default.aspx





















http://www.mathsisfun.com/data/bar-graphs.html




http://www.mathsisfun.com/data/pie-charts.html






43

1

9. Trig functions

Use trig identities to solve problems. EXAMPLE: If sinθ = 5/7 and cosθ < 0, then in which quadrant does the terminal side of θ lie when it is placed in standard position? What are the values of cosθ and tanθ ? Explain your reasoning and show your work.

T.TF.2

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

F.TF.8

Prove the Pythagorean identity sin 2 (θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

USE THE FOLLOWING SECTIONS Section 13-4 Section 13-5 Section 13-6 Section 14-1




Algebra Lab

Solve it pg 861 also found on http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000143&isHtml5Sco=false















44

Last 1/3 of

the period.


Descriptive Statistics and Histograms

http://www.mathsisfun.com/data/histograms.html

Algebra Lab Pg 983


1

10. Periodic functions

Modeling trig functions. EXAMPLE: The amount of daylight, in hours per day, can be approximated by the function

where t is the number of days since the most recent January 1 (including January 1). Using this approximation, what are the maximum and minimum amounts of daylight throughout the year? Maximum: _________ Minimum: _________

T.TF.5

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

USE THE FOLLOWING SECTIONS 13-4 13-5 13-6 13-7




Algebra Lab

Solve it pg 875 also found on http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=vlo&internalId=131112100000145&isHtml5Sco=false





















45

Part of a period

END UNIT TEST


A.REI.11 F.BF.2 F.BF.4 F.IF.4 F.IF.7 F.LE.5 F.TF.1 F.TF.2 F.TF.8 F.TF.5



Use problems similar to the pre-assessment that have been covered since the mid-unit test.


Find approximate solutions for the intersections of functions and 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) involving linear, polynomial, rational, absolute value, and exponential functions.

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Determine the inverse function for a simple function that has an inverse and write an expression for it. Graph functions expressed symbolically and show key features of the graph (including intercepts, intervals where the function is increasing, decreasing,

positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity) by hand in simple cases and using technology for more complicated cases.

Interpret the parameters in a linear or exponential function in terms of a context. Uses the radian measure of an angle to find the length of the arc in the unit circle subtended by the angle and find the measure of the angle given the length

of the arc. 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) and use the Pythagorean identity (sin θ )2 + (cos θ )2 = 1 to find sin θ , cos θ , or tan θ , given sin θ , cos θ , or tan θ , and the quadrant of the angle.

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



9.4.D Business, Management & Administration Career Cluster 9.4.E Education & Training Career Cluster 9.4.F Finance Career Cluster 9.4.N Marketing Career Cluster 9.4.O Science, Technology, Engineering & Mathematics Career Cluster 9.4.P Transportation, Distribution & Logistics Career Cluster

46

9.4.12.D.2, 9.4.12.E.2, 9.4.12.F.2, 9.4.12.N.2, 9.4.12.O.2, 9.4.12.P.2 Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities.


9.4.12.F.4












47






E-Text, Interactive Digital Resources, Teacher Resources Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively.

SLO 7 Make connections between the unit circle and trigonometric functions. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. * 5. Use appropriate tools strategically. 6. Attend to precision.

SLO 7 Use precise language to explain why trigonometric functions are radian measures of angles traversed counter-clockwise around the unit circle.

7. Look for and make use of structure. SLO 3 Use the structure of a function to determine if it has an inverse.

8. Look for and express regularity in repeated reasoning. All of the content presented in this course has connections to the standards for mathematical practices. * This course includes the exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)


48

UNIT 4 MODELING WITH FUNCTIONS

Total Number of Days: 14 days (A and B days meet every other day) Grade/Course: 11/Algebra 2


What are the different types of functions? How can Geometric and Analytic

representations be used to describe the behavior of the function?

How are exponential functions and logarithmic functions related?

There are sets of functions, called families, in which each function is a transformation of a special function called the parent.

You can use logarithms to solve exponential equations; and conversely, you can use exponents to solve logarithmic properties.

You can translate periodic functions in the same way that you translate other functions.


RESOURCES LEARNING ACTIVITIES/ASSESS

MENTS Pearson

Pearson OTHER

(e.g., tech)


Equation of parabola Graphing functions Average rate of change Writing functions Compare graphs of

different functions Combine functions Transformations of

graphs Exponential and

logarithmic models

G.PE.2 N.Q.2 F.IF.4, 6, 7, 8, 9 F.BF.1, 3 F.LE.4

Rewrite questions similar to the Unit 4 test.

1

1. Equation of Parabola Q 1

Write the equation of parabolas using the distance formula. EX: Find the equation of a

G.PE.2 Derive the equation of a parabola given a focus and directrix.

Section 10-2 Basic: Problems 1-5 EXS: 7-33, 38-42 even, 45, 55, 59-69

http://www.mathwarehouse.com/quadratic/parabola/focus-and-directrix-of-parabola.php http://swh.spr

ALGEBRA LAB Solve it! Pg 622 and on Interactive Digital Path

Here’s Why It Works Activity (paper

http://www.mathwarehouse.com/quadratic/parabola/focus-and-directrix-of-parabola.php







http://swh.springbranchisd.com/LinkClick.aspx?fileticket=WxTPGm3-oaY%3D&tabid=16646

49

parabola with focus (0,4) and directrix y = -3

Average: Problems 1-5 EXS: 7-33 odd, 34-55, 59-69 Advanced: Problems 1-5 EXS: 7-33 odd, 34-69

ingbranchisd.com/LinkClick.aspx?fileticket=WxTPGm3-oaY%3D&tabid=16646

folding) Teachers Edition pg 623

ASSESSMENT • Identify the parts

of a parabola • Explain how the

distance formula relates to this

• Find an equation using the distance formula

Last 1/3 of

the period.

Basic Skills

PARCC/HSPA Prep

Distance Formula G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

http://www.youtube.com/watch?v=PuqdjXyBavY

Example: A 50 feet ladder is placed 35 feet away from a wall. The distance from the ground straight up to the top of the wall is 60 feet. Check whether the ladder reaches the top of the wall?

1

1. Equation of Parabola Q 2

Write the equation of parabolas in vertex form. EX: Find the equation of a parabola with focus (0,4) and directrix x = -3

G.PE.2 Derive the equation of a parabola given a focus and directrix.

Section 10-2 Basic: Problems 1-5 EXS: 7-33, 38-42 even, 45, 55, 59-69 Average: Problems 1-5 EXS: 7-33

http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

ALGEBRA LAB Dynamic Activity on Interactive Digital Path

ASSESSMENT • Find the equation

of two parabolas in vertex form.

• One should open up or down and












50

odd, 34-55, 59-69 Advanced: Problems 1-5 EXS: 7-33 odd, 34-69

the other open left or right.

• At least on should open in the negative direction.

• Explain how the focus and directrix will give a clue as to what direction the parabola opens in.

Last 1/3 of

the period.

Basic Skills

PARCC/HSPA Prep

Real Number Systems N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.

http://www.mathsisfun.com/decimal-fraction-percentage.html

Example: Which of the following is NOT a correct statement? a) 63% of 63 is less than 63. b) 115% of 63 is more than 63. c) 1/3% of 63 is the same as 1/3 of 63. d) 100% of 63 is equal to 63.

2

2. Graphing Functions Q 3, 4, 5

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. EX 1: You are given the graph below; create a word problem that matches the information labeled on the graph.

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

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,

Section CB 2-4 Page 90 & 91 Examples 1-5 EXS: 1

http://www.mathsisfun.com/sets/function-floor-ceiling.html http://www.mathsisfun.com/sets/functions-piecewise.html http://www.mathsisfun.com/sets/function-exponential.html

ALGEBRA LAB Worksheets for practice available on http://www.ciclt.net/ul/okresa/MATHEMATICS%20II%20Unit%205%20Step%20and%20Piecewise%20Functions.pdf

ASSESSMENT Quiz - Graph a step, piecewise, and exponential function OR







http://www.mathsisfun.com/sets/function-floor-ceiling.html





http://www.mathsisfun.com/sets/functions-piecewise.html




http://www.mathsisfun.com/sets/function-exponential.html





http://www.ciclt.net/ul/okresa/MATHEMATICS%20II%20Unit%205%20Step%20and%20Piecewise%20Functions.pdf





51

EX 2: The amount of snow in mm during a major snow storm is given by the function h(x) below, where x is the time in hours,

Graph the function h(x)

on the coordinate plane below.

Describe the change in the height of the snow on the ground during the 50-hour period.

and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. e. Graph exponential and logarithmic functions, showing intercepts and end behavior. MP 6, 4

http://a4a.learnport.org/forum/topics/piecewise-function-cell-phone-activity?xg_source=activity http://www.regentsprep.org/Regents/math/ALGEBRA/AE7/ExpDecayL.htm

• Use a project to assess where students do the same thing but with more detailed explanation.

2 0 10

3 1010 30

10 3

8 30 50

x

h x x x

x

http://a4a.learnport.org/forum/topics/piecewise-function-cell-phone-activity?xg_source=activity








http://www.regentsprep.org/Regents/math/ALGEBRA/AE7/ExpDecayL.htm






52

Last 1/3 of

the period.

Basic Skills

PARCC/HSPA Prep

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

http://www.youtube.com/watch?v=XKCZn5MLKvk

Example: Change 75 km/hr to m/min. Show your process.

2

3. Average rate of change Q 6, 7, 8

Calculate the average rate of change for a function. EX 1: Find the average rate of change for the function f(x) = 5(3)x on intervals of length1, starting at 0. What do you observe about the rate of change? EX 2: A data set with equally spaced inputs is given.

x 2 3 5 7

y 12

16

32

42

F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. MP 1, 4, 5, 7

Textbook: Page 336 Q 20-23 Page 337 Q 35 Page 760 Q 17

Average%20Rate%20of%20Change/Average%20Rate%20of%20Change.pdf http://www.youtube.com/watch?v=iJ_0nPUUlOg http://www.youtube.com/watch?v=iJ_0nPUUlOg&feature=youtu.be

http://earthmath.kennesaw.edu/main_site/review_topics/rate_of_change.htm

ASSESSMENT Quiz – Rate of Change from a table and another from a graph.

Last 1/3 of

the period.

Basic Skills

PARCC/HSPA Prep

Direct Variation A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Lesson 2-2 Pg 71-72 Q 25, 26, 34

http://courses.dcs.its.utexas.edu/speedway-files/highschool/ASKME/shared/template.php?moviePath=../ALG-1A-04321/flash/unit02/u02tu08propDire/&movieName=u02tu08propDire.s

Example: The exchange rate from U.S. dollars to British pound sterling (£) was approximately $1.79 to £1 in 2004. Write and solve a direct variation equation to determine how many





http://cims.nyu.edu/~kiryl/Precalculus/Section_2.4-Average%20Rate%20of%20Change/Average%20Rate%20of%20Change.pdf






http://www.youtube.com/watch?v=iJ_0nPUUlOg




http://www.youtube.com/watch?v=iJ_0nPUUlOg&feature=youtu.be









http://courses.dcs.its.utexas.edu/speedway-files/highschool/ASKME/shared/template.php?moviePath=../ALG-1A-04321/flash/unit02/u02tu08propDire/&movieName=u02tu08propDire.swf













53

wf pounds sterling you would receive in exchange for US$90.

2

4. Writing functions Q 9, 10, 11

Write and explain a function to represent quantity. EX 1: Write a function for the volume of the following shape. EX 2: The density, D, of the water in the ocean is related to the pressure, p, underwater

and the height, ℎ of the water column in meters by

the function where

g is the acceleration due to gravity. (Facts: Density of sea seawater is about 1025 kg/m3, and g is about 10 m/s2)

F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. MP 7

Textbook: Page 414

http://www.sophia.org/volume-of-composite-figures--3/volume-of-composite-figures-tutorial http://www.sophia.org/volume-of-composite-figures--3/volume-of-composite-figures--5-tutorial http://map.mathshell.org/materials/download.php?fileid=684

http://www.mathwarehouse.com/geometry/parabola/standard-to-vertex-form.php

Algebra Lab (for Example 1)

For the geometric composite figures, have students find the volume of the composites to start. Then have students look at the original formulas for each and combine the formulas without the numbers from the problem. Last have students use literal equations to rewrite the combined formulas for other variables.

h

r

http://www.sophia.org/volume-of-composite-figures--3/volume-of-composite-figures-tutorial








http://www.sophia.org/volume-of-composite-figures--3/volume-of-composite-figures--5-tutorial









http://map.mathshell.org/materials/download.php?fileid=684












54

Find the gravity, g, given the density and the pressure.

Indicate the type of proportionality, direct or inverse, that relates height to pressure and density.

EX 3: Rewrite the equation of the parabola f(x) = 2x2 + x -3,

in vertex form and find the vertex.

Last 1/3 of

the period.

Basic Skills

PARCC/HSPA Prep

Proportional Division A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i7/bk8_7i3.htm

Example: If three students share $180 in the ratio 1 : 2 : 3, how much is the largest share?

Part of a period

MID UNIT TEST

Mid unit test to determine areas of weakness that need to be addressed before the state unit test.

G.PE.2 N.Q.2 F.IF.4, 6, 7, 8


Test to determine skills that need

reteaching.

2

5. Compare graphs of different functions

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by

F.IF.9 Compare properties of two functions each represented in a different

Page 860 Q 1-8

http://a4a.learnport.org/page/comparing-functions http://a4a.lear

Algebra Lab Give students different graphs to function. Have them








http://a4a.learnport.org/page/comparing-functions





55

Q 12, 13, 14

verbal descriptions) EX 1: Compare the graph of the two parabolas:

- The graph of f is a parabola with vertex (0,0) and focus (6,0).

- g :y =1

4x2

EX 2: Compare the following graph to the function

g(x) = 2cos x( ) +1. Include maximum, minimum, amplitudes, and periods.

way (algebraically, graphically, numerically in tables, or by verbal descriptions). For Example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. MP 1, 3, 5, 6, 8

nport.org/page/comparing-functions

graph them on the graphing calculator and sketch them by hand. Have students describe the characteristics of each graph then compare the characteristics across the different graphs.

Assessment Give students different graphs to function and ask them to list some key characteristics. Then have them compare pairs of functions.

3

2

2 2

2

3

2

2

y

x

56

Last 1/3 of

the period.


Angles with parallel lines G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

http://www.regentsprep.org/Regents/math/geometry/GP8/Lparallel.htm http://www.mathwarehouse.com/geometry/angle/parallel-lines-cut-transversal.php

Example: What is the value of x?

1

6. Combine functions Q 15, 16, 17, 18

Write a function that combines two relations or more. EX: Write a function that gives the area A, as a function of x for a square and 2 semicircles:

F.BF.1 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.

http://scc.scdsb.edu.on.ca/Students/onlinecourses/Sacchetto/AFIC%20web%20page/pdf%20files/7-8%20Applications%20of%20Logs%20&%20Exp.pdf

http://www.purplemath.com/modules/quadprob.htm http://www.nlreg.com/cooling.htm

Assessment

Four questions, one of each related to the unit test questions.

http://www.regentsprep.org/Regents/math/geometry/GP8/Lparallel.htm






http://www.mathwarehouse.com/geometry/angle/parallel-lines-cut-transversal.php


















http://www.purplemath.com/modules/quadprob.htm



http://www.nlreg.com/cooling.htm

http://www.nlreg.com/cooling.htm

57

Last 1/3 of

the period.

Basic Skills

PARCC/HSPA Prep

Triangle congruence. G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

http://www.regentsprep.org/Regents/math/geometry/GP4/Ltriangles.htm http://www.regentsprep.org/Regents/math/geometry/GP4/PracCon2.htm

Example problem: ΔABC ≅ ΔDEF as shown. Find x.

2

7. Transformation of graphs Q 19, 20, 21

EX: Explain the differences between the two functions: f(X) = x2 g(X) = 3x2+4

F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. MP 3, 5, 8

Section 7-2 Basic: Problems 1-5 EXS: 7-333, 35, 38-40 even, 44-62 Average: Problems 1-5 EXS: 7-29 odd, 31-41, 44-62 Advanced: Problems 1-5 EXS: 7-29 odd, 31-62

https://teacher.ocps.net/theodore.klenk/mathwebpage/media/calchorizontalandverticalstretches.pdfhow http://www.youtube.com/watch?v=kFw3XU0wisU

Algebra Lab Give students different functions to graph the horizontal and vertical stretch and shrink.

Students should come up with a set of rules so they understand what changes in the function create what changes in the graph.

Assessment Quiz – three questions similar to the unit test.

B C D B C D

http://www.regentsprep.org/Regents/math/geometry/GP4/Ltriangles.htm






http://www.regentsprep.org/Regents/math/geometry/GP4/PracCon2.htm






https://teacher.ocps.net/theodore.klenk/mathwebpage/media/calchorizontalandverticalstretches.pdfhow








http://www.youtube.com/watch?v=kFw3XU0wisU




58

Last 1/3 of

the period.

Basic Skills

PARCC/HSPA Prep

Angles in circles G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

http://www.regentsprep.org/Regents/math/geometry/GG2/CylinderPage.htm

Example problem: A cylinder and a cone each have a radius of 3 cm. and a height of 8 cm. What is the ratio of the volume of the cone to the volume of the cylinder?

2

8. Exponential and logarithmic models Q 22, 23, 24

Solve exponential equations using logarithms. EX: What is the value of x that satisfy the equation: 32x = 12

F.LE.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. MP 4

Section 7-5 Basic: Problems 1-6 EXS: 7-45, 46-54 even, 60, 61, 84-100 Average: Problems 1-6 EXS: 7-45 odd, 46-78, 84-100 Advanced: Problems 1-6 EXS: 7-45 odd, 46-83, 84-100

http://www.edu.gov.on.ca/eng/studentsuccess/lms/files/tips4rm/mhf4u_unit_5.pdf

Algebra Lab Instruction problem 1 from Interactive Digial Path Lesson 7-5. http://www.youtube.com/watch?v=5R5mKpLsfYg













http://www.youtube.com/watch?v=5R5mKpLsfYg



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Last 1/3 of

the period.


Mixed problem solving problems based on unit basic skill review.

A –CED.1, 2 A.SSE.A.1a 7.EE.3 A.APR.3 S.CP.9



Part of a period

END UNIT TEST


A.REI.6, 7 A.SSE.3 F.IF.4




Derive the equation of a parabola given a focus and directrix. Graph functions that model relationships between two quantities, expressed symbolically, and show key features of the graph (including intercepts, intervals

where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity) by hand in simple cases and using technology for more complicated cases.

Estimate, calculate and interpret the average rate of change of a function presented symbolically, in a table, or graphically over a specified interval. Rewrite a function in different but equivalent forms to identify and explain different properties of the function. Analyze and compare properties of two functions when each is represented in a different form (algebraically, graphically, numerically in tables, or by verbal

descriptions). Construct a function that combines standard function types using arithmetic operations to model a relationship between two quantities. Identify and illustrate (using technology) an explanation of the effects 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. Express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

PARCC FRAMEWORK/ASSESSMENT OVERVIEW http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsAlgII_Nov2012V3_FINAL.pdf http://www.parcconline.org/sites/parcc/files/ESTableAlgebra2EOYforPARCC_FinalV2.pdf EXAMPLES https://sites.google.com/site/jacobsmathdepartment/parcc-assessments http://www.parcconline.org/samples/mathematics/high-school-mathematics

http://www.parcconline.org/sites/parcc/files/ESTableAlgebra2EOYforPARCC_FinalV2.pdf

https://sites.google.com/site/jacobsmathdepartment/parcc-assessments

http://www.parcconline.org/samples/mathematics/high-school-mathematics

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9.4.12.F.4








9.4.12.O.(1).7 Use mathematics, science, and technology concepts and processes to solve problems in projects involving design and/or production (e.g., medical,

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agricultural, biotechnological, energy and power, information and communication, transportation, manufacturing, and construction).







MODIFICATIONS/ACCOMMODATIONS TEXTBOOK RELATED MATERIALS Guided Instruction – Virtual Nerd Videos available on the Interactive Digital Path (see Appendix for login site) Algebra 2 Companion – Vocabulary worktext to be used as the lesson is taught Reteaching Worksheet – Simplified explanations of the concepts with additional practice TOOLS Graphing Calculators where applicable Manipulatives where applicable Graphic Organizers Sketching the problem where applicable Interactive web sites You Tube STRATEGIES Highlight important ideas Pair or group activities Visual and graphic depictions of the problem Peer tutoring Formative assessments to determine need

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Frequent feedback to students Appropriate pacing of the material Allow adequate processing time Monitor student work and responses TEACHER WEB SITES FOR IDEAS http://nichcy.org/research/ee/math http://www.cehd.umn.edu/nceo/presentations/NCTMLEPIEPStrategiesMathGlossaryHandout.pdf http://floridarti.usf.edu/resources/format/pdf/Classroom%20Cognitive%20and%20Metacognitive%20Strategies%20for%20Teachers_Revised_SR_09.08.10.pdf http://www2.edc.org/accessmath/resources/strategiestoollist.pdf http://www.glencoe.com/sec/teachingtoday/subject/intervention_strategies.phtml


E-Text, Interactive Digital Resources, Teacher Resources Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true Mathematical Practices 1. Make sense of problems and persevere in solving them.

SLO 6 Use more complex real-world context than those use in Algebra I. 2. Reason abstractly and quantitatively.

SLO 3 Interpret the rate of change in context. SLO 8 Convert between exponential and logarithmic models

3. Construct viable arguments and critique the reasoning of others. SLO 4 Justify why two different forms of a function are equivalent.

4. Model with mathematics. * 5. Use appropriate tools strategically.

SLO 7 Use technology when available. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

http://nichcy.org/research/ee/math

http://www.cehd.umn.edu/nceo/presentations/NCTMLEPIEPStrategiesMathGlossaryHandout.pdf

http://floridarti.usf.edu/resources/format/pdf/Classroom%20Cognitive%20and%20Metacognitive%20Strategies%20for%20Teachers_Revised_SR_09.08.10.pdf

http://floridarti.usf.edu/resources/format/pdf/Classroom%20Cognitive%20and%20Metacognitive%20Strategies%20for%20Teachers_Revised_SR_09.08.10.pdf

http://www2.edc.org/accessmath/resources/strategiestoollist.pdf

http://www.glencoe.com/sec/teachingtoday/subject/intervention_strategies.phtml


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All of the content presented in this course has connections to the standards for mathematical practices. * This course includes the exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)

UNIT 5 Inference and Conclusions from Data

Total Number of Days: 11 days (A and B days meet every other day) Grade/Course: 11/Algebra 2


How can we gather, organize and display data to communicate and justify results in the real world?

How can we analyze data to make inferences and/or predictions, based on surveys, experiments, probability and observational studies?

You can describe and compare sets of data using various statistical measures, depending on what characteristics you want to study.

Standard deviation is a measure of how far the numbers in a data set deviate from the mean.

You can get good statistical information about population by studying a sample of the population.


RESOURCES LEARNING ACTIVITIES/ASSE

SSMENTS Pearson

Pearson OTHER

(e.g., tech)


Sample space, events outcomes, unions, intersections and complements

Independent events Conditional probability and

independence The definition of conditional

probability. Random sample, statistic,

parameter, population and sample

The meaning of theoretical and experimental statistics

Survey, an experiment, and

S.CP.1, 2, 5, 6 S.IC.1, 2, 3, 4, 5, 6

Rewrite questions similar to the Unit 4 test.

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an observational study Mean, proportion and

margin of error Conduct an experiment or

simulation and the meaning of significance

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1. Sample space, events outcomes, unions, intersections and complements Q 1,2

Describe the union and intersection of events, and the complement of an event. EX:

Use the calendar above to list the outcomes in the events “a date after April 15 and not on a Monday or Saturday”

S.CP.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”). MP 2, 4

NONE Find: List the outcomes of multiple events

http://www.youtube.com/watch?v=2RxW3UWpi2c http://www.virtualnerd.com/common-core/hss-statistics-probability/HSS-CP-conditional-probability-rules/A/1/sample-space-definition

http://www.virtualnerd.com/common-core/hss-statistics-probability/HSS-CP-conditional-probability-rules/A/2/dependent-independent-events-Example



3D Geometry G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

http://www.mathopenref.com/cubevolume.html

Example: If a cube has a volume of 64cu.cm, the length of ONE edge would = A. 6 cm. B. 4 cm. C. 8 cm. D. 16 cm.

1 2. Independe

Justify that two events are independent through the use of

S.CP.2 Understand that two

ALGEBRA 1 TEXT CB 12-

http://www.youtube.com/

http://www.illustrativemathematics.org/ill

http://www.youtube.com/watch?v=2RxW3UWpi2c




http://www.virtualnerd.com/common-core/hss-statistics-probability/HSS-CP-conditional-probability-rules/A/1/sample-space-definition












http://www.virtualnerd.com/common-core/hss-statistics-probability/HSS-CP-conditional-probability-rules/A/2/dependent-independent-events-example













http://www.youtube.com/watch?v=WDP_O3msUXk

http://www.youtube.com/watch?v=WDP_O3msUXk

http://www.illustrativemathematics.org/illustrations/950

http://www.illustrativemathematics.org/illustrations/950

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nt events Q 3,4,5

probability rules. EX:

Use the frequency table above to find the probability that a person buys: a) Instant tea b) 100g tea c) 200 g Tea bags c) 50g packet tea EX 2: The table below shows the enrollment in art and biology classes at a small school.

Enrolled in

Art classes

Did not enroll in art

classes

Enrolled in Biology classes

x 54

Did not enroll in biology classes

45 81

What is the value of x if the

Tea bag

s

Packet tea

Instant tea

Total 50 g 3 19 4

100 g

34 0 59 200

g 16

Total 24 100

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. S.CP.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. S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified.

5 Section 11-4 Problems 1-4 Basic: EXS: 8-26, 34-49 Average: EXS: 9-19 odd, 20-31, 34-49 Advanced: EXS: 9-19 odd, 20-49

watch?v=WDP_O3msUXk

ustrations/950 http://www.cpalms.org/RESOURCES/URLresourcebar.aspx?ResourceID=vRQBCoxzGfo=D

http://www.cpalms.org/RESOURCES/URLresourcebar.aspx?ResourceID=vRQBCoxzGfo=D





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events “selected student is enrolled in Art classes” and “selected student is enrolled in Biology classes” are independent? Show your work.

Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For Example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. MP 2, 4



Maximize Area G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost;

http://cims.nyu.edu/~kiryl/Calculus/Section_4.5--Optimization%20Problems/Optimization_Problems.pdf

Example: John has 100 feet of fencing and wants to fence off the largest possible space. John says a circle would be best, but his cousin Jack









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working with typographic grid systems based on ratios).

says a square would give you the largest space. Who is correct? Draw diagrams, show work, and explain your solution.

1

3. Conditional probability and independence. Q 6,7,8

Recognize conditional probability and independence in everyday situations. EX 1:

A checkerboard has 64 sectors of equal size, with 32 white sectors and 32 black sectors. When throwing a coin on the board, the coin is equally likely to land on a white sector or a black sector. A boy throws a coin four times and lands on black. He guesses that the next time the coin will land on black. Is his guessing accurate? Why or why not?

S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For Example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. MP 2, 4

Sect 11-4 Problems 1-4 Basic: EXS: 8-26, 34-49 Average: EXS: 9-19 odd, 20-31, 34-49 Advanced: EXS: 9-19 odd, 20-49

http://www.youtube.com/watch?v=tbBW2VVFgso




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EX 2: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first. Explain why the two events are not independent. Describe the change that could make them independent.



3D Geometry G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

http://www.virtualnerd.com/pre-algebra/perimeter-area-volume/volume/volume-Examples/cylinder-height-from-volume

Example: Mr. Braunsdorf has a circular above ground swimming pool. If the 20 ft diameter pool holds 1256 ft3 of water, how deep is it? (Use 7r = 3.14)

1

4. The definition of conditional probability. Q 9,10,11

Compute the probability of A or B using the Addition Rule for probability. EX 1: A bag contains 4 red, 2 blue, 6 green, and 8 white marbles. What is the probability of selecting a white marble at

S.CP.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.

Section 11-3 Problems 1-5 Basic: EXS: 9-37, 45-62 Average:

http://www.mathgoodies.com/lessons/vol6/addition_rules.html

http://www.virtualnerd.com/pre-algebra/perimeter-area-volume/volume/volume-examples/cylinder-height-from-volume













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random from this bag, not replacing the marble, and then selecting another white marble? Round your answer to the nearest tenth of a percent if necessary. EX 2: You shuffle a standard deck of playing cards and choose a card at random. What is the probability that you choose a face card (jack, queen, king, or a club)?

S.CP.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. MP 1, 2

EXS: 9-29 odd, 31-42, 45-62 Advanced: EXS: 9-29 odd, 31-62



Midpoint Formula G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

http://www.sophia.org/applying-the-midpoint-formula-with-one-endpoint/applying-the-midpoint-formula-with-one-endpoint-tutorial

Example: Given: M (-1,-2) is the midpoint of AB where A is (-4,2). Find the coordinates of the other endpoint, B.

1

5. Random sample, statistic, parameter,

Make inferences about a population from a random sample

S.IC.1 Understand statistics as a process for

Section 11-7 Problems 1-3

http://www.sophia.org/standard-deviation-tutorial
















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population and sample Q 12,13

EX: The points scored in each game played by the boys’ and girls’ basketball teams last season are given, Boys Team: 56, 81, 80, 75, 48, 65, 90, 66, 70, 70 Girls Team: 60, 72, 61, 58, 78, 65, 66, 55, 65, 73 Interpret the data as to which team is more consistent in their scoring (use the standard deviation).

making inferences about population parameters based on a random sample from that population. MP 1, 2

Basic: EXS: 6-13, 15, 17, 20, 21, 24-27 Average: EXS: 7-13 odd, 14-21, 24-37 Advanced: EXS: 7-13 odd, 14-37



Shaded Region G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

http://www.onlinemathlearning.com/area-shaded-region.html

Example: Find the area of a given shaded region.

1

6. The meaning of theoretical and

Design a simulation that models a desired event EX:

S.IC.2 Decide if a specified model is consistent

Section 11-2 Problem 1, 2, 3, 5










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experimental statistics Q 14, 15

Suppose we throw a coin 10 times, and we only see heads 3 times. What can we say about the fairness of this coin?

with results from a given data-generating process, e.g., using simulation. For Example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model? MP 2, 4

Basic: EXS: 8-28, 31-35, 37-51 Average: EXS: 9-27 odd 28-35, 37-51 Advanced: EXS: 9-27 odd, 28-36, 37-51



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

http://www.chem.tamu.edu/class/fyp/mathrev/mr-scnot.html

Example: The speed of light is approximately 299.8 million meters per second. What is that speed in scientific notation form?

1

7. Survey, an experiment, and an observational study Q 16, 17,18

Recognize a survey, an experiment and an observational study EX: Jason is interested in finding the number of students who would be willing to donate $10

S.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how

Section 11-8 Problem 1-3 Basic: EXS: 6-12, 15-19, 23, 26-38

http://www.regentsprep.org/Regents/math/algtrig/ATS1/StatSurveylesson.htm










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or an hour of time to help a local food bank? Explain how can randomization be applied?

randomization relates to each. MP 1, 2

Average: EXS: 7-11 odd, 15-19, 21-23, 26-38 Advanced: EXS: 7-11 odd, 16-19, 23, 24, 26-38



Ordering Rational Numbers N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

http://www.etap.org/demo/Algebra1/lesson2/instruction4tutor.html

Example: Arrange the following numbers in order from LEAST to GREATEST: 1/3, 2/5, 0.6, 0.125

2

8. Mean, proportion and margin of error Q 19,20

EX: The midterm scores for 20 random students (in a class of 100): 82 45 37 98 100 74 87 89 63 76 75 61 43 99 86 75 92 65 80 86 Estimate the mean score of all students and identify the range of scores within 2 standard deviations of the mean.

S.IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. MP 1, 2

Section 11-7 Problem 1-3 Basic: EXS: 6-13, 15, 17, 20, 21, 24-27 Average: EXS: 7-13 odd, 14-21, 24-37 Advanced: EXS: 7-13 odd, 14-37

http://psy2.ucsd.edu/~dhuber/ch5_hays.pdf http://www.regentsprep.org/Regents/math/algtrig/ATS1/Dispersion.htm







http://psy2.ucsd.edu/~dhuber/ch5_hays.pdf



http://www.regentsprep.org/Regents/math/algtrig/ATS1/Dispersion.htm




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Angles G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

http://www.freemathhelp.com/feliz-angles-triangle.html

Example: If A is a right angle, and m B = 43o, then m C =

2

9. Conduct an experiment or simulation and the meaning of significance Q 21, 22

Decide if the differences between parameters are significant EX:

1. The heights, in millimeters, of 10 seedlings from 2 seed types are shown. Seed A: 56, 61, 48, 51, 59, 65,

S.IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. S.IC.6 Evaluate reports based on data. MP 1, 2

(Use Algebra 1 Text Resources Section 12-4) Section 11-6 Problem 1-5 Basic: EXS: 7-23, 25, 30-43 Average: EXS: 7-15

http://www.regentsprep.org/Regents/math/algtrig/ATS1/CentralTendency.htm










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49, 71, 69, 64 Seed B: 55,63, 58, 47, 61, 46, 53, 47, 41, 59 Make box-and-whisker plots comparing the samples. Which seed type is, on average, taller?

odd, 16-27, 30-43 Advanced: EXS: 7-15 odd, 16-43

Part of a period

END UNIT TEST


S.CP. 1-7 S.IC.1-6




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”).

Use two-way frequency tables to determine if events are independent and to calculate/approximate conditional probability. Use everyday language to explain independence and conditional probability in real-world situations. Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A and apply the addition [P(A or B) = P(A) + P(B) – P(A and

B)] rule of probability in a uniform probability model; interpret the results in terms of the model. Make inferences about population parameters based on a random sample from that population. Determine if the outcomes and properties of a specified model are consistent with results from a given data-generating process using simulation. Identify different methods and purposes for conducting sample surveys, experiments, and observational studies and 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 and use simulations to decide if differences between parameters are significant;

evaluate reports based on data.

PARCC FRAMEWORK/ASSESSMENT OVERVIEW http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsAlgII_Nov2012V3_FINAL.pdf http://www.parcconline.org/sites/parcc/files/ESTableAlgebra2EOYforPARCC_FinalV2.pdf EXAMPLES https://sites.google.com/site/jacobsmathdepartment/parcc-assessments http://www.parcconline.org/samples/mathematics/high-school-mathematics


http://www.parcconline.org/sites/parcc/files/ESTableAlgebra2EOYforPARCC_FinalV2.pdf

https://sites.google.com/site/jacobsmathdepartment/parcc-assessments

http://www.parcconline.org/samples/mathematics/high-school-mathematics

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9.4.12.F.4









9.4.O(2) Science and Mathematics

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9.4.12.O.(2).1 Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve problems and issues in the real world.







E-Text, Interactive Digital Resources, Teacher Resources Login at https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true

Probability concepts: http://www.marlboro.edu/academics/study/mathematics/courses/probability

Probability and statistics problems: http://learn.tkschools.org/mwilkinson/Algebra%20II/alg2%20Chapter%2012%20Notes.pdf Mathematical Practices

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively.

SLO 6 Compare theoretical and empirical data. 3. Construct viable arguments and critique the reasoning of others.

SLO 7 Explain when and why you would use a sample survey, experiment, or an observational study; develop the meaning of statistical significance.


http://www.marlboro.edu/academics/study/mathematics/courses/probability

http://learn.tkschools.org/mwilkinson/Algebra%20II/alg2%20Chapter%2012%20Notes.pdf

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4. Model with mathematics.* 5. Use appropriate tools strategically. 6. Attend to precision.

SLO 9 Examine the scope and nature of conclusions drawn in the reports. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

All of the content presented in this course has connections to the standards for mathematical practices. *This course includes the exponential and logarithmic functions as modeling tools. (PARCC Model Content Frameworks)

unit 1 - polynomialsroselle.sharpschool.net/userfiles/servers/server_3152275... · 2014. 3. 19. ·...

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