MOUNT VERNON CITY SCHOOL DISTRICT

Algebra 2 andTrigonometry ®

Curriculum Guide

THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THEALGEBRA 2 AND TRIGONOMETRY ® CURRICULUM IN MOUNT

VERNON.

2015-16

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Mount Vernon City School District

Board of Education

Adriane SaundersPresident

Serigne GningueVice President

Board TrusteesCharmaine FearonRosemarie Jarosz

Micah J.B. McOwenOmar McDowell

Darcy MillerWanda WhiteLesly Zamor

Superintendent of SchoolsDr. Kenneth Hamilton

Deputy SuperintendentDr. Jeff Gorman

Assistant Superintendent of BusinessKen Silver

Assistant Superintendent of Human ResourcesDenise Gagne-Kurpiewski

Administrator of Mathematics and Science (K-12)Dr. Satish Jagnandan

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TABLE OF CONTENTS

I. COVER …..……………………………………....... 1

II. MVCSD BOARD OF EDUCATION …..……………………………………....... 2

III. TABLE OF CONTENTS …..……………………………………....... 3

IV. IMPORTANT DATES …..……………………………………....... 4

V. VISION STATEMENT …..……………………………………....... 5

VI. PHILOSOPHY OF MATHEMATICS CURRICULUM ……………. 6

VII. MVCSD ALGEBRA 2 TRIGONOMETRY ® PACING GUIDE …………..... 7

VIII. SUGGESTED LIST OF MATHEMATICAL LANGUAGE …………... 24

IX. SETUP OF A MATHEMATICS CLASSROOM …………... 29

X. SECONDARY GRADING POLICY …………... 30

XI. SAMPLE NOTEBOOK RUBRIC …………... 31

XII. CLASSROOM AESTHETICS …………... 32

XIII. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON …………... 33

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IMPORTANT DATES 2015-16

REPORT CARD – 10 WEEK PERIOD

MARKINGPERIOD

MARKINGPERIODBEGINS

INTERIMPROGRESSREPORTS

MARKINGPERIOD

ENDS

DURATION REPORT CARDDISTRIBUTION

MP 1 September 8,2015

October 9,2015

November13, 2015

10 weeks Week ofNov. 23, 2015

MP 2 November16, 2015

December 18,2015

January 29,2016

10 weeks Week ofFebruary 8, 2016

MP 3 February 1,2016

March 11,2016

April 15,2016

9 weeks Week ofApril 25, 2016

MP 4 April 18,2016

May 20,2016

June 23,2016

10 weeks Last Day ofSchool

June 23, 2016

The Parent Notification Policy states “Parent(s) / guardian(s) or adult students are

to be notified, in writing, at any time during a grading period when it is apparent -

that the student may fail or is performing unsatisfactorily in any course or grade

level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during

the grading period when it becomes evident that the student's conduct or effort

grades are unsatisfactory.”

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VISION STATEMENT

True success comes from co-accountability and co-responsibility. In a coherentinstructional system, everyone is responsible for student learning and studentachievement. The question we need to constantly ask ourselves is, "How are ourstudents doing?"

The starting point for an accountability system is a set of standards andbenchmarks for student achievement. Standards work best when they are welldefined and clearly communicated to students, teachers, administrators, andparents. The focus of a standards-based education system is to provide commongoals and a shared vision of what it means to be educated. The purposes of aperiodic assessment system are to diagnose student learning needs, guideinstruction and align professional development at all levels of the system.

The primary purpose of this Instructional Guide is to provide teachers andadministrators with a tool for determining what to teach and assess. Morespecifically, the Instructional Guide provides a "road map" and timeline forteaching and assessing the NYS Mathematics Core Curriculum.

I ask for your support in ensuring that this tool is utilized so students are able tobenefit from a standards-based system where curriculum, instruction, andassessment are aligned. In this system, curriculum, instruction, and assessment aretightly interwoven to support student learning and ensure ALL students have equalaccess to a rigorous curriculum.

We must all accept responsibility for closing the achievement gap and improvingstudent achievement for all of our students.

Dr. Satish Jagnandan

Administrator for Mathematics and Science (K-12)

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PHILOSOPHY OF MATHEMATICS CURRICULUM

The Mount Vernon City School District recognizes that the understanding of mathematics is

necessary for students to compete in today’s technological society. A developmentally

appropriate mathematics curriculum will incorporate a strong conceptual knowledge of

mathematics through the use of concrete experiences. To assist students in the understanding and

application of mathematical concepts, the mathematics curriculum will provide learning

experiences which promote communication, reasoning, and problem solving skills. Students will

be better able to develop an understanding for the power of mathematics in our world today.

Mathematics Curriculum - Algebra 2 and Trigonometry ®

Content Strands Process Strands

1. Number Sense and Operations 1. Problem Solving

2. Algebra 2. Reasoning and Proof

3. Geometry 3. Communication

4. Measurement 4. Connections

5. Probability and Statistics 5. Representation

Students will only become successful in mathematics if they see mathematics as a whole, not as

isolated skills and facts. As we develop mathematics curriculum based upon the standards,

attention must be given to both content and process strands. Likewise, as teachers develop their

instructional plans and their assessment techniques, they also must give attention to the

integration of process and content. To do otherwise would produce students who have temporary

knowledge and who are unable to apply mathematics in realistic settings. Curriculum,

instruction, and assessment are intricately related and must be designed with this in mind. All

three domains must address conceptual understanding, procedural fluency, and problem solving.

If this is accomplished, school districts will produce students who will (1) have mathematical

knowledge, (2) have an understanding of mathematical concepts, and (3) be able to apply

mathematics in the solution of problems.

ALGEBRA 2 AND TRIGONOMETRY ® PACING GUIDE

This guide using AMSCO Algebra 2 and Trigonometry (© 2009) was created to provide teachers with a time frame to complete theNew York State Algebra 2 and Trigonometry ® Mathematics Curriculum.

Unit Unit Title Days

1 The Integers 10

2 The Rational Numbers 10

3 Real Numbers and Radicals 9

4 Relations and Functions 13

5 Quadratic Functions and Complex Numbers 19

6 Sequences and Series 8

7 Exponential Functions 10

8 Logarithmic Functions 13

9 Trigonometric Functions 11

10 More Trigonometric Functions 7

11 Graphs of Trigonometric Functions 10

12 Trigonometric Identities 10

13 Trigonometric Equations 8

14 Trigonometric Applications 8

15 Statistics 13

16 Probability and the Binomial Theorem 11

NYSED ALGEBRA REGENTS: JUNE 17, 2016

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I – The IntegersNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A.N.1 1-1 Whole Numbers,Integers, and the NumberLine

2 #1: What is the set of real numbers (Setr) and its subsets?

Set, set symbol, set R and its subsets,properties of real numbers (commutative,

identity, inverse, associative,distributive), roster method, descriptive

method of describing a set.

SeptHW#1

#2: What are the properties of realnumber (Set R) and how are they appliedin the operations with real numbers?

SeptHW#2

A.N.5 1-2 Writing and SolvingNumber Sentences

5 #3: What are the properties ofequality/inequality and how are theyapplied?

Properties of equality, equation,reflexive, symmetric, multiplicative and

additive properties, transitive;inequality, order relations symbols (<, >,

≤, ≥)

SeptHW#3

A2.N.3 1-3 Adding Polynomials 9 #4: How do we add polynomials? Constant, coefficient, base, exponent,like/similar terms, unlike or dissimilar

terms

SeptHW#4

A.2.A.1 1-4 Solving AbsoluteValue Equations andInequalities

13 #5: How do we solve an absolute valueequation or inequality?

Absolute value, solution, solution set SeptHW#5

A2.A.7 1-5 MultiplyingPolynomials

17 #6: How do we multiply polynomials? Term, power, monomial, binomial,trinomial, polynomial

SeptHW#6

A2.A.7 1-6 FactoringPolynomials

22 #7: How do we factor polynomials? Common factor, greatest common factor,common monomial factor, common

binomial factor, binomial factors, specialproducts, special factors, prime

polynomial

SeptHW#7

A2.A.7 1-7 Quadratic Equationswith Integral Roots

27 #8: How do we find the integral roots ofquadratic equations?

Quadratic equation, standard form,degree.

SeptHW#8

A2.A.4 1-8 Quadratic Inequalities 30 #9: How do we find the solution of aquadratic inequality?

Quadratic inequality SepHW#9

COMMON ASSESSMENT #1 SeptHW#9a

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2 – The Rational NumbersNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.N.3 2-1 Rational Numbers 40 40 #10: What differentiates a rationalfrom irrational number as subsets ofset R?

Rational and irrational numbers,reciprocal, decimal number,terminating decimal, non-

terminating repeating decimal,terminating non-repeating decimal

SeptHW#10

#11: How are the properties of Set Rapplied to the set of rationalnumbers?

SeptHW#11

A2.N.3;A2.A.16

2-2 Simplifying RationalExpressions

44 #12: How do you simplify rationalexpressions?

Rational expression, simplest formor lowest terms, canceling,

numerator, denominator, product,reduction to lowest terms

SeptHW#12

A2.N.3;A2.A.16

2-3 Multiplying and DividingRational Expressions

48 #13: How do you multiply rationalexpressions?#14: How do you divide rationalexpressions?

Factors, multiplier, multiplicand,product, quotient, dividend, divisor

SeptHW#13

A2.N.3;A2.A.16

2-4 Adding and SubtractingRational Expressions

53 #14: How do you add/subtractrational expressions?

Addend, sum, subtrahend, minuend,difference, least common

denominator

SeptHW#14

A2.A.23 2-5 Ratio and Proportion 57 #15: In a proportion, how do youfind a missing mean or extreme?

Ratio, proportion, means, extremes,ratio symbols.

SeptHW#15

A2.A.17 2-6 Complex RationalExpressions

61 #16: How do you simplify a complexfraction?

Complex fraction, complex rationalexpression, least common multiple,

least common denominator,

OctHW#16

A2,A.1,3,23 2-7 Solving Rational Equations 64 #17: How do you find the solution ofa rational equation?

Rational equation, extraneous root OctHW#17

A2,A.1,3,23 2-8 Solving RationalInequalities

70 #18: How do you solve a rationalinequality?

Rational inequality OctHW#18

COMMON ASSESSMENT #2 OctHW#18a

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3 – Real Numbers and RadicalsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.CM.12A2.A.1

3-1 The Real Numbers andAbsolute Value

80 #19: What are real, irrational andrational numbers and how are theyarranged in a number line which can bedescribed using an inequality?

Real numbers, irrational andrational numbers, absolute value,interval notation, absolute value

inequality

OctHW#19

A2.N.1A2.N.2A2.N.3A2.N.4

3-2 Roots and Radicals 84 #20: How do we perform operations onirrational numbers and find its nth root?

Square root, cube root, nth root,radicand, index, principal root,

radical

OctHW#20

A2.N.1A2.N.2A2.N.3A2.N.4

3-3 Simplifying Radicals 88 #21: How do we simplify radicalexpressions with positive integralradicands

Coefficient, index, radicant OctHW#21

A2.A.14A2.N.4

3-4 Adding and SubtractingRadicals

94 #22: How do we add or subtractradicals with both like or unlikeradicands?

Like radicals, unlike radicals,reducible radicals

OctHW#22

A2.A.14A2.N.4

3-5 Multiplying Radicals 98 #23: How do we multiply radicals? Product of radicals, sumcontaining radicals, coefficient of

a radical

OctHW#23

A2.N.2,4A2.A.14

3-6 Dividing Radicals 102 #24: How do you divide radicals? Radical numerator, radicaldenominator

OctHW#24

A2.N.5A2.A.15

3-7 Rationalizing aDenominator

104 #25: How do you rationalize a radicaldenominator to simplify the fraction?

Conjugate, conjugate pair,rationalizing the denominator

OctHW#25

A2.A.22 3-8 Solving Radical Equations 108 #26: How do we solve radicalequations?

Roots, radical equation, OctHW#26

COMMON ASSESSMENT #3 OctHW#26a

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4 – Relations and FunctionsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.A.37A2.A.38A2.A.39A2.A.46

4-1 Relations andFunctions

120 #27: How do we determine when a relation isa function?

Function, relation, one-to-onecorrespondence, domain, range,

dependent variable, independent variable,onto, vertical line test

OctHW#27

A2.A.40 4-2 Function Notation 127 #28: How do we use functional notation andfind the image when the pre-image is givenunder f?

Functional notation forms, rule of pairing OctHW#28

A2.A.5A2.A.41A2.A.51

4-3 Linear Functionsand Direct Variation

130 #29: How do we determine whether a functionin linear and whether onto or one-to-one

Linear function, one-to-one function,horizontal line test,

OctHW#29

A2.A.1 4-4 Absolute ValueFunctions

136 #30: How do you graph an absolute valuefunction?

Absolute value function, many-to-onefunction,

OctHW#30

A2.A.50 4-5 PolynomialFunctions

140 #31: How do we find the roots of a polynomialfunction and how are they linked with thegraph of the function?

Polynomial function, degree, parabola,turning point, vertex, axis of symmetry,

direction of infinite extent, roots ofpolynomial function, double roots

OctHW#31

A2.A.40 4-6 The Algebra ofFunctions

149 #32: How do we perform operations withfunctions

Sum, difference, product, and quotient offunctions

OctHW#32

A2.A.40A2.A.42

4-7 Composition ofFunctions

155 #33: What is the domain of a compositionfunction and how is it formed?

Composition of functions, compositefunction,

Oct 29HW#33

A2.A.43A2.A.44A2.A.45

4-8 Inverse Functions 160 #34: How are inverse functions related to theidentity function?

Identity function, inverse functions,absolute value function and its inverse,

inverse of a quadratic function

OctHW#34

A2.A.48A2.A.49

4-9 Circles 167 #35: How do we graph a circle with a givencenter and radius or with a given equation?

Circle, radius, diameter, standard form,radius-center form

NovHW#35

#36: How do you write the equation of a circlewith a given graph or center and radius?

Circle, radius, diameter, standard form,radius-center form

NovHW#36

A2.A.5A2.A.41A2.A.51

4-10 InverseVariation

174 #37: How do you use inverse proportion tosolve problems on purchases and distance?

Inverse proportion or inverse variation,xy=k parabola

NovHW#37

COMMON ASSESSMENT #4 NovHW#37a

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5 – Quadratic Functions and Complex NumbersNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.A.26 5-1 Real Roots of aQuadratic Equation

187 #38: How do we find roots using completingthe square method?

Perfect squares, completing thesquare

NovHW#38

A2.A.25 5-2 The QuadraticFormula

193 #39: How do we derive the quadratic formulaand use it to find roots of quadratic equations?

Quadratic formula, standardform

NovHW#39

A2.A.2 5-3 The Discriminant 198 #40: How do we use the discriminant todetermine the roots of a quadratic equation?

Coefficients, discriminant NovHW#40

A2.N.6A2.A.7

5-4 The ComplexNumbers

203 #41: What are complex numbers and theirsubsets?

Complex number plane, i,complex numbers, points in the

complex number plane,conjugate pair

NovHW#41

#42: What is i and the powers of i? NovHW#42

A2.N.8A2.A.9

5-5 Operations withComplex Numbers

209 #43: How do we change the square root of anegative number and use algebraic propertiesto perform operations on this group ofnumbers?

Square roots of negativeradicands, sum, difference,

product, and quotient ofcomplex numbers

NovHW#43

A2.N.9 5-6 Complex Roots of aQuadratic Equation

217 #44: How do we find complex roots ofquadratic equations?

Complex roots, negativediscriminant

NovHW#44

A2.A.20A2.A.21

5-7 Sum and Product ofthe Roots of a QuadraticEquation

219 #45: How do we get the sum and product ofroots of a quadratic equation to confirm thatthe roots found are correct?

Sum of roots, product of roots NovHW#45

A2.A.26 5-8 Solving Higher DegreePolynomial Equations

224 #46: How do we find the roots of higherdegree polynomials?

Higher degree polynomials DecHW#46

A2.A.50 5-9 Solutions of Systemsof Equations andInequalities

229 #47: How do we find the solutions of systemsof equations?

Systems of equations, systemsof inequalities

DecHW#47

#48: How do we find the solutions of systemsof inequalities?

Systems of equations, systemsof inequalities

DecHW#48

COMMON ASSESSMENT #5 DecHW#48a

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6 – Sequences and SeriesNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

6-1 Sequences 248 #49: How can we specify the terms of asequence, given its recursive definition?

Sequence, finite and infinitesequence, recursive definition

DecHW#49

6-2 Arithmetic Sequences 252 #50: How do we identify an arithmetic orgeometric sequence and find its nth term?

Arithmetic sequence, geometricsequence, nth term, commondifference, common factor,

arithmetic mean

DecHW#50

6-3 Sigma Notation 257 #51: How do we find a sum using thesigma notation?

Sigma, series, sigma notation,finite series, infinite series

DecHW#51

6-4 Arithmetic Series 262 #52: How do we find the sum of anarithmetic series, find its nth term or firstterm on any term in the sequence?

Arithmetic series DecHW#52

6-5 Geometric Sequences 266 #53: How do we generate a geometricsequence and find the sum of a geometricseries, find its nth term or first term onany term in the sequence?

Geometric sequence, first term,common factor/ratio

DecHW#53

6-6 Geometric Series 270 #54: How do we find the sum of ageometric series?

Geometric series DecHW#54

6-7 Infinite Series 273 #55: How do we determine that anarithmetic series increases without limit,decreases without limit, or approaches alimit?

Limit, without limit, approachesa limit

DecHW#55

COMMON ASSESSMENT #6 DecHW#55a

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7 – Exponential FunctionsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.A.8 7-1 Laws of Exponents 287 #56: How do we write and use the lawsof exponents in simplifying expressions?

Factor, base, exponentexponential form, standard form

DecHW#56

A2.N.1 7-2 Zero and Negative Exponents 289 #57: How do we simplify expressionswith negative exponents?

Zero exponent, negative exponent DecHW#57

A2.N.1A2.A.10

7-3 Fractional Exponents 293 #58: How are expressions with fractionalexponents simplified?

Fractional exponent, coefficientof a radical

JanHW#58

A2.A.12A2.A.53

7-4 Exponential Functions andTheir Graphs

298 #59: How are exponential functionsgraphed manually and using the graphingcalculator?

Exponential function, CartesianPlane, ordered pair, plotting of

points

JanHW#59

A2.A.12 7-5 Solving Equations InvolvingExponents

304 #60: How do we find their solution ofequations involving exponents?

Equations with exponents JanHW#60

A2.A.6A2.A.27

7-6 Solving ExponentialEquations

306 #61: How are exponential equationssolved?

Exponential equations, base,exponent, power

JanHW#61

A2.A.6A2.A.27

7-7 Applications of ExponentialFunctions

308 #62: How do we solve the differentkinds of exponential equation problems?

Exponential equations, base,exponent, power, solutions,

extraneous roots

JanHW#62

COMMON ASSESSMENT #7 JanHW#62a

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8 – Logarithmic FunctionsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.A.19A2.A.54

8-1 Inverse of an ExponentialFunction

320 #63: How do we show the inverse of anexponential function and its graph?

Exponential function, inverse ofexponential function, logarithm

JanHW#63

A2.A.19 8-2 Logarithmic Form of anExponential Equation

324 #64: How do we compare logarithmicform from exponential form and convertone form to the other?

Logarithmic form, exponentialform

JanHW#64

A2.A.19 8-3 Logarithmic Relationships 327 #65: What are the properties of logarithmsand how are they applied?

Properties of logarithms JanHW#65

A2.A.19 8-4 Common Logarithms 332 #66: How numbers in standard formconverted to common logarithmic forms?

Common logarithm JanHW#66

A2.A.19 8-5 Natural Logarithms 336 #67: How do we simplify powers usingnatural logarithms?

Natural logarithm JanHW#67

A2.A.6A2.A.27

8-6 Exponential Equations 340 #68: How do we solve exponentialequations using logarithmic method?

Properties of logarithms;properties of equality; properties

of real numbers

JanHW#68

A2.A.28 8-7 Logarithmic Equations 344 #69: How do we find the solution oflogarithmic equations?

Properties of logarithms;properties of equality; properties

of real numbers

FebHW#69

COMMON ASSESSMENT #8 FebHW#69a

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9 – Trigonometric FunctionsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.A.55A2.A.56

9-1 Trigonometry of the RightTriangle

354 #70: How do we find the parts of aright triangle using the sine, cosine, ortangent function?

Hypotenuse, legs, similartriangles, sine, cosine, tangent,

acute angle, right angle.

FebHW#70

A2.A.56A2.A.62

9-2 Angles and Arcs asRotations

357 #71: How do we determine that anglesare coterminal, quadrantal, or both?

Angle, initial side, terminal side,angle in standard position,

angular speed, quadradrantalangles, coterminal angles

FebHW#71

A2.A.60 9-3 The Unit Circle, Sine, andCosine

362 #72: How do we use the unit circle tofind the sine, cosine, and coordinatesof the terminal side of an angle instandard position?

Unit circle, sine function, cosinefunction

FebHW#72

A2.A.55A2.A.56

9-4 The Tangent Function 368 #73: How can we use the tangentfunction to solve any right trianglewhen the sine and cosine are known?

Tangent function FebHW#73

A2.A.55A2.A.58A2.A.59

9-5 The ReciprocalTrigonometric Functions

374 #74: How can we solve a right trianglewhen the reciprocal of the sine, cosineor tangent are known?

Secant, cosecant, cotangent FebHW#74

A2.A.56 9-6 Function Values of SpecialAngles

378 #75: How do we find the sixtrigonometric functions of specialangles?

Special angles, isoscelestriangle, 30-60 degree right

triangle

FebHW#75

A2.A.66 9-7 Function Values from theCalculator

381 #76: How do we use the calculator todetermine the measure of an angleusing degree or radian unit of angularmeasure?

Degree, radian, central angle,arc, radius, sector

FebHW#76

A2.A.57A2.A.66

9-8 Reference Angles and theCalculator

386 #77: How do we express functionvalues of angles greater than 90degrees as function values of positiveacute angles?

Reference angle, negative angle,positive angle,

first/second/third/fourthquadrant angle

FebHW#77

COMMON ASSESSMENT #9 FebHW#77a

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10 – More Trigonometric FunctionsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.A.61A2.M.1A2.M.2

10-1 Radian Measure 400 #78: How do we convert radian measureto degree measure and vise-versa?

Radian measure, degreemeasure, Pi,

FebHW#78

A2.A.62 10-2 Trigonometric FunctionValues and Radian Measure

406 #79: How do we use radian measure tofind exact values of trigonometricfunctions?

Pi-radian/degree equivalents,arc, central angle

FebHW#79

A2.A.67 10-3 Pythagorean Identities 411 #80: Given a trigonometric function of anangle, how do we find the othertrigonometric functions using any of thePythagorean identities?

Pythagorean identities FebHW#80

A2.A.63 10-4 Domain and Range ofTrigonometric Functions

414 #81: How do we find the domain andrange of any given trigonometric function?

Domain and range of atrigonometric function

FebHW#81

A2.A.63A2.A.64

10-5 Inverse TrigonometricFunctions

419 #82: How do we find the inverse of atrigonometric function?

Inverse of a trigonometricfunction, restrict the domain,arcsine, arccosine, arc-tangent, arc-cotangent, arc-secant, arc-cosecant

MarHW#82

A2.A.58A2.A.59

10-6 Cofunctions 425 #83: How do we express the function ofan angle in terms of its cofunction angle?

Cofunction, cofunction pairs MarHW#83

COMMON ASSESSMENT #10 MarHW#83a

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11 – Graphs of Trigonometric FunctionsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.A.70 11-1 Graph of the Sine Function 435 #84: How do we graph the sine function anddescribe its cycle and period?

Sine graph MarHW#84

A2.A.70 11-2 Graph of the Cosine Function 442 #85: How do we graph the cosine functionand determine its amplitude, period, phaseshift, and frequency?

Cosine curve MarHW#85

A2.A.69 11-3 Amplitude, Period, and PhaseShift

447 #86: How do we determine the amplitude,period, and phase shift of a sine or cosinegraph?

Cycle, period, amplitude,phase shift, frequency

MarHW#86

A2.A.72 11-4 Writing the Equation of a Sineor Cosine Graph

455 #87: How do we write the equation of a sineor cosine graph?

Y=a sin (bx+c)Y= a cos (bx+c)

MarHW#87

A2.A.71 11-5 Graph of the Tangent Function 460 #88: How do we graph the tangent functionand describe its amplitude, period, domainand range?

Cycle, period, amplitude,phase shift, frequency

MarHW#88

A2.A.63A2.A.65

11-6 Graphs of the ReciprocalFunctions

463 #89: How do we graph the reciprocalfunctions of sine, cosine, and tangent?

Reciprocal functions MarHW#89

A2.A.65 11-7 Graphs of InverseTrigonometric Functions

468 #90: How are the graphs of the inversetrigonometric functions drawn?

Y = arcsin xY = arcos xY = arctan x

MarHW#90

A2.A.70A2.A.71

11-8 Sketching TrigonometricGraphs

472 #91: How do we sketch trigonometric graphswith a given interval and the trigonometricequation?

Interval, a, b, and c inY=a sin (bx+c) andY= a cos (bx+c)

MarHW#91

COMMON ASSESSMENT #11 MarHW#91a

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12 – Trigonometric IdentitiesNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.A.58 12-1 Basic Identities 483 #92: How do we derive and apply the basicidentities?

Pythagorean, reciprocal, quotientidentities

MarHW#92

A2.A.58A2.A.67

12-2 Proving an Identity 485 #93: How do we use the basic identities toprove other identities?

Pythagorean, reciprocal, quotientidentities

MarHW#93

A2.A.76 12-3 Cosine (A - B) 488 #94: Given two angles, how are these twoangles used to find the cosine of theirdifference?

Cos(A - B)=CosAcosB+sinAsinB MarHW#94

A2.A.76 12-4 Cosine (A + B) 493 #95: Given two angles, how are these twoangles used to find the cosine of their sum?

Cos(A + B) = CosAcosB -sinAsinB

MarHW#95

A2.A.76 12-5 Sine (A - B) and Sine(A + B)

496 #96: Given two angles, how are these twoangles used to find the sine of their sum ordifference?

sin(A -B) = sinAcosB – cosAsinBsin(A + B) = sinAcosB +

cosAsinB

MarHW#96

A2.A.76 12-6 Tangent (A - B) andTangent (A + B)

500 #97: Given two angles, how are these twoangles used to find the tangent of their sum ordifference?

tan(A + B) = CosAcosB -inAsinB

MarHW#97

A2.A.77 12-7 Functions of 2A 504 #98: How do you find the function of twice anangle using the double angle identity?

Double angle identity MarHW#98

A2.A.77 12-8 Functions of Half anAngle

508 #99: How do you find the function of half anangle using the half angle identity?

Half angle identities AprHW#99

COMMON ASSESSMENT #12 AprHW#99a

20

13 – Trigonometric EquationsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.A.68 13-1 First-Degree TrigonometricEquations

519 #100: How do we find the solution of afirst degree linear trigonometric equation?

Linear trigonometric equation,solution

AprHW#100

A2.A.68 13-2 Using Factoring to SolveTrigonometric Equations

526 #101: How do you use factoring to solvea trigonometric function?

Product, factors AprHW#101

A2.A.68 13-3 Using the QuadraticFormula to Solve TrigonometricEquations

530 #102: How and when is the quadraticformula used to solve a trigonometricequations?

Constant, coefficient, quadraticequation, quadratic formula

AprHW#102

A2.A.68 13-4 Using Substitution to SolveTrigonometric EquationsInvolving More Than OneFunction

534 #103: How do you use substitution to findthe solution of more than one function?

Trigonometric identities,substitution, solution

AprHW#103

A2.A.68 13-5 Using Substitution to SolveTrigonometric EquationsInvolving Different AngleMeasures

538 #104: How do you use substitution tosolve trigonometric equations involvingdifferent angular measures?

Trigonometric identities,substitution, solution

AprHW#104

COMMON ASSESSMENT #13 AprHW#104a

21

14 – Trigonometric ApplicationsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.G.44A2.A.45A2.A.46

14-1 Similar Triangles 548 #105: How are similar triangles used towrite the coordinates of a point in termsof its distance from the origin as well asthe sine and cosine of an angle in standardposition?

Similar triangles- two angles, threesides, two sides and the included

angle, hypotenuse and one leg of aright triangle

AprHW#105

A2.A.73 14-2 Law of Cosines 552 #106: How do you find distances,directions, and forces using the cosinelaw?

Cosine law, distance, direction,force, magnitude of a force

AprHW#106

A2.A.73 14-3 Using the Law of Cosinesto Find Angle Measure

557 #107: How do you use the cosine law tofind angular measure and direction?

Cosine law AprHW#107

A2.A.74 14-4 Area of a Triangle 559 #108: How do you find the area of atriangular figure when two sides and theincluded angle are known?

Area of a triangle, side-angle-siderelationship

AprHW#108

A2.A.73 14-5 Law of Sine 564 #109: How and when is the Law of Sinesused to solve any triangle?

Sine law, angle opposite to a side AprHW#109

A2.A.75 14-6 The Ambiguous Case 569 #110: How is the ambiguous case used todetermine the shape and number oftriangles involved in a given situation?

Ambiguous case, SSAcorrespondence

AprHW#110

A2.A.73A2.A.74

14-7 Solving Triangles 575 #111: How are triangles solved usingtrigonometric function laws?

Angle of elevation/depression,resultant, force, bearing, heading

AprHW#111

COMMON ASSESSMEN #14 MayHW#111a

22

15 - StatisticsNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.S.1A2.S.2

15-1 Gathering Data 588 #112: How do we show data using a stem-and-leaf diagram, frequency distribution, andhistogram?

Statistics, data, inivariate statistics,census, survey, controlled experiment,observational studies, population, sample,stem-and-leaf, frequency distributiontable, tally

MayHW#112

A2.A.3 15-2 Measures ofCentral Tendency

596 #113: How do we find the measures of centraltendency in a set of data?

Measure of central tendency, mean,arithmetic mean, average, median, mode,quartiles, first/lower quartile, secondquartile/median, third/upper quartile,statistical summary, box-and-whiskerplot

MayHW#113

A2.S.3 15-3 Measures ofCentral Tendency forGrouped Data

605 #114: How do we find the measures of centraltendency for grouped data?

Frequency distribution table, cumulativefrequency, percentile,

MayHW#114

A2.S.4 15-4 Measures ofDispersion

614 #115: How do we find the measure ofdispersion to show the spread of individual dataon both sides of the mean?

Measure of dispersion, range,interquartile range, outlier

MayHW#115

A2.S.4 15-5 Variance andStandard Deviation

619 #116: How do we calculate the variance andstandard deviation of a set of data?

Variance, standard deviation MayHW#116

A2.S.5 15-6 NormalDistribution

628 #117: How does the standard deviation in anormal curve describe the spread of the data

Normal curve, Gaussian or normaldistribution, z-score, empirical rule,probability density function, frequencycurve,

MayHW#117

A2.S.1A2.S.2

15-7 BivariateStatistics

634 #118: How do we show a bivariate statistics ina scatter plot and produce a line of best fit?

Bivariate statistics, scatter plot,correlation, line of best fit, regression line

MayHW#118

A2.S.7 15-8 CorrelationCoefficient

641 #119: How do we find and use correlationcoefficients?

Correlation, positive/negative correlation,Pearson correlation coefficient

MayHW#119

A2.S.6 15-9 Non-LinearRegression

647 #120: How do we determine and useregression functions?

Independent variable, dependent variable,regression models

MayHW#120

A2.S.7 15-10 Interpolationand Extrapolation

655 #121: When do we use interpolation andextrapolation process?

Interpolation, extrapolation MayHW#121

COMMON ASSESSMENT #15 MayHW#121a

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16 – Probability and the Binomial TheoremNYSPI # Topic/Lesson Textbook

PageAim Vocabulary Date

A2.S.12 16-1 The CountingPrinciple

673 #122: How do you use the counting principle todetermine the number of outcomes occur in twogiven activities?

Sample space, event, outcome,dependent event, independent event,counting principle

MayHW#122

A2.S.9A2.S.10A2.S.11A2.S.12

16-2 Permutations andCombinations

678 #123: How do we find permutations of a givensample space?

Arrangement, factorial,permutation, combination

MayHW#123

#124: How do we find the number ofcombinations from a given sample space?

MayHW#124

A2.S.13A2.S.14

16-3 Probability 687 #125: How is theoretical probability found? Theoretical probability, randomvariable, empirical probability.Distribution, complement

MayHW#125

#126: How is empirical probability calculated? MayHW#126

A2.S.15 16-4 Probability withTwo Outcomes

695 #127: How do we use the binomial probabilityformula to make predictions?

Bernoulli or binomial experiment,binomial probability formula

MayHW#127

A2.S.15A2.S.16

16-5 BinomialProbability and theNormal Curve

701 #128: How do we find binomial probabilitiesdefined by restrictions like “at least” or “at most”?

At least, at most MayJun

HW#128A2.A.36A2.S.15A2.S.16

16-6 The BinomialTheorem

708 #129: How do you apply the binomial theorem toexpand a binomial raised to a power n?

Pascal’s triangle, binomial theorem JunHW#129

COMMON ASSESSMENT #16 JunHW#129a

Based on the formative and summative assessments, teachers should focus on the performance indicators wherestudents’ performances were at levels 1 and 2.

June

NYS ALGEBRA 2 & TRIGONOMETRY REGENTS

24

SUGGESTED LISTOF

MATHEMATICALLANGUAGE

Suggested List ofMathematical LanguageThe Suggested List ofMathematical Language ispresented for Regents-approved course entitledAlgebra 2 &Trigonometry. This list isintended to engage NewYork State educators andstudents in building amathematical language.The list contains terms thatare defined in the Glossary(http://www.emsc.nysed.gov/3-8/glossary.htm).

Algebra 2 &Trigonometry

Problem Solving algebraically alternate approach collaborate conjecture constraint critique equivalent evaluate explain formulate generalization graphically interpret multiple

representations numerically observe parameter strategy verbally

Reasoning and Proof argument axiom conclusion conjecture counterexample discover exact answer explain explore general case inductive reasoning informal indirect

proof investigate justify refute specific result theorem

Communication accuracy appropriate challenge chart coherent comprehension conjecture decoding diagram equation formula function graph interpretation logical argument mathematical

representation numerical tables organize outline rationale reflect standard notation strategy symbol technical writing

terminology validity verbal explanation written explanation

Connections concept conclusion formulate multiple

representation physical model procedure quantitative model representation

Representation algebraic

representation apply chart communicate compare concept diagram equation explore graph graphical

representation investigate mathematical

phenomena multiple

representations organize physical object physical phenomena recognize record social phenomena symbol table technology translate

25

Number Sense andOperations

a+bi form absolute value complex fraction complex number conjugate direct variation e fractional exponent i imaginary number index of a radical inverse variation irrational number negative exponent nth root operation pi powers of i principal square root procedure radical radical form radicand rational number rationalize a

denominator real number scientific notation sigma sigma notation

Algebra abscissa absolute value absolute value

equation absolute value

function absolute value

inequality adjacent angles adjacent sides algebraic expression algebraic

representation

ambiguous case amplitude analyze angle angle in standard

position angle of depression angle of elevation antilogarithm approximate value arc length arccosine arcsine arctangent area of a

parallelogram usingSAS

area of a triangleusing SAS

arithmetic sequence arithmetic series asymptote base base of a logarithmic

function base of an

exponential function binomial expansion binomial theorem center-radius

equation of a circle central angle circle circular functions coefficient cofunctions common base(s) common difference common factor common logarithm common ratio completing the

square complex fractional

expressions composition of

functions compound interest

constant function cosecant cosine cotangent coterminal angles degree of a

polynomial difference of two

perfect squares direct variation discriminant domain double and half angle

formulas fortrigonometricfunctions

double root e equation equivalent forms exact value expand a binomial explicit definition exponential form exponential function extraneous root factor fractional exponent frequency (of a

periodic function) function function notation geometric sequence geometric series graphical solution of

equations greatest common

factor (GCF) growth factor half-life horizontal-line test i identities initial side of an

angle inverse function inverse trigonometric

functions

26

inverse variation Law of Cosines Law of Sines laws of exponents laws of logarithms linear equation linear expression linear system logarithm logarithmic form lowest terms nature of the roots negative exponent nth root nth term one cycle of a

trigonometricfunction

one-to-one function onto opposite side in a

right triangle ordinate parabola parameter period (of a function) periodic function phase shift polynomial

expression polynomial function powers of i Pythagorean

identities quadrantal angle quadratic equation quadratic formula quadratic inequality quadratic trinomial radian radical equation radical expression radius range (of a function) rational coefficient rational equation rational expression rational inequality

rationalizedenominators

reciprocaltrigonometricfunctions

recursive definition reference angle relation replacement set represent restricted domain resultant right triangle

trigonometry root of an equation secant (of an angle) sigma notation sine solution set standard position (of

an angle) subset sum and product of

roots of a quadraticequation

sum of a geometricseries

sum of an arithmeticseries

sum or differenceformulas fortrigonometricfunctions

system of equations/inequalities

tangent (of an angle) technology terminal side of an

angle transformation transformations of

functions andrelations

trigonometricequation

trigonometricfunctions

unit circle variable

vector vertical line test zero of a function zero product property

Geometry absolute value absolute value

equation absolute value

inequality angle in standard

position angle of depression angle of elevation area of a

parallelogram usingSAS

area of a triangleusing SAS

circle coefficient function generalize geometric

representation of thecircular

function graph of a relation graphical

representation graphical solution of

equations investigate ordered pair parabola rational coefficient rectangular

coordinates relation root of an equation sector of a circle slope triangle vertex visualization

Measurement arc length

27

degree measure measure of central

angle minute radian measure

Statistics and Probability at least at most Bernouli experiments biased sample bimodal binomial probability

formula bivariate data central tendency combination compound event conjecture controlled

experiment correlation

coefficient Counting Principle exactly experimental

probability extrapolate frequency (of a data

set) frequency

distribution grouped frequency

distributions index in statistics interpolate interquartile range least squares

regression line line of best fit linear regression mean measure of central

tendency measures of

dispersion median mode

normal curve normal distribution observation outlier Pascal's Triangle percentile permutation probability quartiles random sample range (of a data set) regression equation regression model sample space scatter plot standard deviation

(population) standard deviation

(sample) statistics survey technology theoretical

probability univariate data variance (population) variance (sample)

28

WORD WALLS ARE DESIGNED …

to promote group learning support the teaching of important general principles about words and how they work Foster reading and writing in content area Provide reference support for children during their reading and writing Promote independence on the part of young students as they work with

words Provide a visual map to help children remember connections between words

and the characteristics that will help them form categories Develop a growing core of words that become part of their vocabulary

Important Notice A Mathematics Word Wall must be present in every mathematics classroom. The Suggested List of Mathematical Language for Algebra 2 &

Trigonometry ® level instruction must be incorporated into theMathematics Word Wall.

Math Word Wall

Create a math wordwall

Place math words onyour current wordwall but highlightthem in some way.

29

SETUP OF THE MATHEMATICS CLASSROOM

I. Prerequisites for a Mathematics Classroom Teacher Schedule Class List Seating Chart Code of Conduct / Discipline Grade Level Mathematics Standards Power Performance Indicators - PPI (Grades 3 – 10) Updated Mathematics Student Work Mathematics Grading Policy Mathematics Diagrams, Charts, Posters, etc. Grade Level Number Line Grade Level Mathematics Word Wall Mathematics Portfolios Mathematics Center with Manipulatives (Grades K - 12)

II. Updated Student WorkA section of the classroom must display recent student work. This can be of anytype of assessment, graphic organizer, and writing activity. Teacher feedback mustbe included on student’s work.

III. Board Set-UpEvery day, teachers must display the NYS Standard (Performance Indicator),Aim, Do Now and Homework. At the start of the class, students are to copy thisinformation and immediately begin on the Do Now.

IV. Spiraling HomeworkHomework is used to reinforce daily learning objectives. The secondary purposeof homework is to reinforce objectives learned earlier in the year. Theassessments are cumulative, spiraling homework requires students to reviewcoursework throughout the year.

Student’s Name: School:

Teacher’s Name: Date:

Aim #:

NYS Performance Indicator:

Do Now:

30

SECONDARY MATHEMATICS GRADING POLICY

This course of study includes different components, each of which are assigned the

following percentages to comprise a final grade. I want you--the student--to understand

that your grades are not something that I give you, but rather, a reflection of the work

that you give to me.

COMPONENTS

1. Common Assessments → 35%

2. Quizzes → 20%

3. Homework → 20%

4. Notebook and/or Journal → 10%

5. Classwork / Class Participation → 15%

o Class participation will play a significant part in the determination of your

grade. Class participation will include the following: attendance, punctuality

to class, contributions to the instructional process, effort, contributions during

small group activities and attentiveness in class.

Important Notice

As per MVCSD Board Resolution 06-71, the Parent Notification Policy states

“Parent(s) / guardian(s) or adult students are to be notified, in writing, at any time during

a grading period when it is apparent - that the student may fail or is performing

unsatisfactorily in any course or grade level. Parent(s) / guardian(s) are also to be

notified, in writing, at any time during the grading period when it becomes evident that

the student's conduct or effort grades are unsatisfactory.”

31

SAMPLE NOTEBOOK SCORING RUBRIC

Student Name:

_________________________________________________

Teacher Name:

__________________________________________

Criteria 4 3 2 1 Points

Completion ofRequired Sections

All requiredsections arecomplete.

One requiredsection ismissing.

Two or threerequired sections

are missing.

More than threerequired sections

are missing.

Missing SectionsNo sections of

the notebook aremissing.

One sections ofthe notebook is

missing.

Two sections of thenotebook are

missing.

Three or moresections of thenotebook are

missing.

Headers / Footers

No requiredheader(s) and/or

footer(s) aremissing within

notebook.

One or tworequired

header(s) and/orfooter(s) are

missing withinnotebook.

Three or fourrequired header(s)and/or footer(s) are

missing withinnotebook.

More than fourrequired header(s)and/or footer(s) are

missing withinnotebook.

Organization

All assignmentand/or notes arekept in a logical

or numericalsequence.

One or twoassignments

and/or notes arenot in a logical or

numericalsequence.

Three or Fourassignments and/ornotes are not in a

logical ornumericalsequence.

More than fourassignments and/ornotes are not in a

logical ornumericalsequence.

NeatnessOverall notebookis kept very neat.

Overall notebookis kept in asatisfactorycondition.

Overall notebook iskept in a below

satisfactorycondition.

Overall notebook isunkept and very

disorganized.

Total

Teacher’s Comments:

32

CLASSROOM AESTHETICS

“PRINT–RICH” ENVIRONMENT CONDUCIVE TO LEARNING

TEACHER NAME: _________________________________________________________

COURSE / PERIOD: _________________________________________________________

ROOM: _________________________________________________________

CHECKLISTYES NO

Teacher Schedule

Class List

Seating Chart

Code of Conduct / Discipline

Grade Level Mathematics Standards

Power Performance Indicators - PPI (Grades 3 - 10)

Mathematics Grading Policy

Mathematics Diagrams, Posters, Displays, etc.

Grade Level Number Line

Updated Student Work (Projects, Assessments, Writing, etc.)

Updated Student Portfolios

Updated Grade Level Mathematics Word-Wall

Mathematics Centers with Manipulatives

Organization of Materials

Cleanliness

Principal Signature: _________________________________________ Date: ____________

Asst. Pri. Signature: _________________________________________ Date: ____________

33

SYSTEMATIC DESIGN OF A MATHEMATICS LESSON

What are the components of a Mathematics Block?

ComponentFluency Practice Information processing theory supports the view that automaticity in math facts is

fundamental to success in many areas of higher mathematics. Without the ability to retrievefacts directly or automatically, students are likely to experience a high cognitive load as theyperform a range of complex tasks. The added processing demands resulting from inefficientmethods such as counting (vs. direct retrieval) often lead to declarative and procedural errors.Accurate and efficient retrieval of basic math facts is critical to a student’s success inmathematics.

Opening Exercise - Whole Group This can be considered the motivation or Do Now of the lesson It should set the stage for the day's lesson Introduction of a new concept, built on prior knowledge Open-ended problemsConceptual Development - Whole Group (Teacher Directed, Student Centered) Inform students of what they are going to do. Refer to Objectives. Refer to the Key Words

(Word Wall) Define the expectations for the work to be done Provide various demonstrations using modeling and multiple representations (i.e. model a

strategy and your thinking for problem solving, model how to use a ruler to measure items,model how to use inch graph paper to find the perimeter of a polygon,)

Relate to previous work Provide logical sequence and clear explanations Provide medial summaryApplication Problems - Cooperative Groups, Pairs, Individuals, (Student Interaction &Engagement, Teacher Facilitated) Students try out the skill or concept learned in the conceptual development Teachers circulate the room, conferences with the students and assesses student work (i.e.

teacher asks questions to raise the level of student thinking) Students construct knowledge around the key idea or content standard through the use of

problem solving strategies, manipulatives, accountable/quality talk, writing, modeling,technology applied learning

Student Debrief - Whole Group (Teacher Directed, Student Centered) Students discuss their work and explain their thinking Teacher asks questions to help students draw conclusions and make references Determine if objective(s) were achieved Students summarize what was learned Allow students to reflect, share (i.e. read from journal)Homework/Enrichment - Whole Group (Teacher Directed, Student Centered) Homework is a follow-up to the lesson which may involve skill practice, problem solving

and writing

34

Homework, projects or enrichment activities should be assigned on a daily basis. SPIRALLING OF HOMEWORK - Teacher will also assign problems / questions pertaining to

lessons taught in the past

Remember: Assessments are on-going based on students’ responses.Assessment: Independent Practice (It is on-going! Provide formal assessment whennecessary / appropriate) Always write, use and allow students to generate Effective Questions for optimal learning Based on assessment(s), Re-teach the skill, concept or content using alternative strategies

and approaches

Important Notice

All lessons must be numbered with corresponding homework. For example, lesson #1 will

corresponded to homework #1 and so on.

Writing assignments at the end of the lesson (closure) bring great benefits. Not only do they

enhance students' general writing ability, but they also increase both the understanding of

content while learning the specific vocabulary of the disciplines.

Spiraling Homework

o Homework is used to reinforce daily learning objectives. The secondary purpose of

homework is to reinforce objectives learned earlier in the year. The assessments are

cumulative, spiraling homework requires students to review coursework throughout the

year.

Manipulative must be incorporated in all lessons. With students actively involved in

manipulating materials, interest in mathematics will be aroused. Using manipulative

materials in teaching mathematics will help students learn:

a. to relate real world situations to mathematics symbolism.

b. to work together cooperatively in solving problems.

c. to discuss mathematical ideas and concepts.

d. to verbalize their mathematics thinking.

e. to make presentations in front of a large group.

f. that there are many different ways to solve problems.

g. that mathematics problems can be symbolized in many different ways.

h. that they can solve mathematics problems without just following teachers' directions.