Algebra 2 and Trigonometry ® Curriculum Guide - Home -...
Transcript of Algebra 2 and Trigonometry ® Curriculum Guide - Home -...
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
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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
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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
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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.”
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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.