PreCalculus Curriculum Guide - SharpSchoolmvcsd.sharpschool.net/UserFiles/Servers/Server_87286/File/Satish... · mount vernon city school district precalculus curriculum guide this

MOUNT VERNON CITY SCHOOL DISTRICT

PreCalculus

Curriculum Guide

THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE NYSPRECALCULUS CURRICULUM IN MOUNT VERNON. THIS PROVIDESAN OUTLINE OF THE DISTRICT’S EXPECTATIONS AND POLICIES.

2015-16

2

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 PRECALCULUS PACING GUIDE ……………………...………….......7

VIII. WORD WALLS ARE DESIGNED TO ………...………….......22

IX. SETUP OF A MATHEMATICS CLASSROOM …………... 23

X. SECONDARY GRADING POLICY …………... 24

XI. SAMPLE NOTEBOOK RUBRIC …………... 25

XII. CLASSROOM AESTHETICS …………... 26

XIII. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON …………... 27

This document was prepared by the Mount Vernon City School District Curriculum and

Instruction Department in conjunction with the Mathematics Articulation Committee.

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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.

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. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

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

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

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PRE-CALCULUS PACING GUIDEThis guide using A Graphical Approach to Pre-calculus with Limits (ISBN #: 0-201-73513-X) was created to provide teachers with atime frame to complete the Pre-Calculus Curriculum. The following applicable instructional strategies under the Strategy / Activitycolumn of the pacing guide below will be used, as needed, in each lesson: Identify similarities/differences, summarize and take notes,reinforce effort and provide recognition, give homework and practice work, provide nonlinguistic representations, use cooperativelearning, set objectives and provide feedback, generate and test hypotheses, and provide cues or questions and advance organizers.

Chapter Chapter Title Date

1 Chapter 1: Linear Functions, Equations, and Inequalities Sept. 8 – Sept. 30

2 Chapter 2: Analysis of Graphs of Functions Oct. 1 – Oct. 30

3 Chapter 3: Polynomial Functions Nov 2 - Nov. 25

4 Chapter 4: Rational, Power, and Root Functions Dec. 1 – Dec. 23

5 Chapter 5: Inverse, Exponential, and Logarithmic Functions Jan. 4 – Jan. 22

6 Chapter 6: Analytic Geometry Feb. 2 – Feb. 12

7 Chapter 7: Matrices and Systems of Equations and Inequalities Feb. 22 – Mar. 18

8 Chapter 8: Trigonometric Functions and Applications Mar. 28 – Apr. 15

9 Chapter 9: Trigonometric Identities and Equations Apr. 18 – April 30

10 Chapter 10: Applications of Trigonometry; Vectors May 2 – May 13

11 Chapter 11: Sequences, Binomial Theorem May 15 – May 31

12 Chapter 12: Limits, Derivative, and Definite Integrals June 1 - June 10

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Chapter 1: Linear Functions, Equations, and InequalitiesPages 1 – 88, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date1-1 Real Numbersand CoordinateSystems

#1: What is the set of Real Numbers, its subsets,and properties, and how are its properties used?

Set, Set of realnumbers(Set R),subsets of set R,

Cartesian CoordinateSystem, distance,

midpoint

Review the complex numbersystem, recall its subsets, showsimilarities of Set R and the setof complex numbers, reviewthe Cartesian Plane, find thedistance and midpoint of twogiven points

Sept

1-1 Real Numbersand CoordinateSystems

#2: How is the Cartesian Coordinate System usedto plot points, draw lines, and find midpoints anddistance between two points found?

Sept

1-2 Introduction toRelations andFunctions

#3: How is the set-builder notation used todescribe groups, write and graph intervals?

Set builder notation,interval, intervalnotation, relation,function, domain,range, functional

notation

Concept mapping, organizer,modeling, group work withinstant feedback, individualactivity.

Sept

1-2 Introduction toRelations andFunctions

# 4: How do you describe, identify, illustrate, anddifferentiate between a relation and a function?

Sept

1-3 Linear Functions #5: How is a linear function expressed,determined, written and graphed?

Linear function,slope, intercept,

standard form, slope-intercept form

Mini-lesson, partner work,summarization, 4-problem quiz,homework

Sept

1-4 Equation ofLines and LinearModels

#6: How are the different linear function formsused in determining the graph of equation of aline?

Point-slope form,parallel lines,

perpendicular lines,linear regression

Concept mapping, illustrativeexample, group work,individual work/ summarizing,homework

Sept

#7: How are parallel or perpendicular linesdetermined

Sept

9

Chapter 1: Linear Functions, Equations, and InequalitiesPages 1 – 88, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date1-5 Linear Equationsand Inequalities

#8: How do you differentiate an identity from aconditional equation and how do you find thesolutions of two linear equations graphically andalgebraically?

Linear equation,identity, linear

inequality, three-partinequality

List/define the two groups ofequations with examples, mini-lesson with studentparticipation on the algebraicand graphical methods offinding solutions of ; individualpractice; 4-problem assessment;homework

Sept

# 9: How is a linear inequality solved andgraphed, and how is the solution set of two linearinequalities solved graphically?

Sept

1-6 Applications ofLinear Functions

#10: What are direct and inverse variations? Direct variation,inverse variation

Define terms, illustrate the typeand operation procedures andapply the concepts; individualwork, review.

Sept

#11: How do you differentiate direct from inversevariation?

Sept

COMMON ASSESSMENT # 1 Sept

10

Chapter 2: Analysis of Graphs of FunctionsPages 89 –169, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date2-1: Graphs ofBasic Functionsand Relations;Symmetry

#12: How is a continuous function determined asdecreasing, increasing, or constant?

Increasing function,decreasing function,constant function,identity function,

symmetry, squaringfunction, cubingfunction, evenfunction, odd

function

Do now; mini-lesson, studentactivity, assessment,reinforcement

Oct

#13: Why is a squaring function symmetric withrespect to the y-axis and a cubing function symmetricwith respect to the origin?

Oct

#14: How do you determine the domain and range ofsquare root and cube root functions?

Oct

# 15: How do you graph an absolute value function? Oct

#16: Why is the relation x=y2 symmetric with respectto the x-Axis and when is a function even or odd?

Oct

2-2 Vertical andHorizontal Shiftsof Graphs

#17: When does a vertical or horizontal shift occursin a given function y=f(x)?

Vertical shift,horizontal shift,combinations of

vertical andhorizontal shift


Oct

#18: How do shifts affect the domain and the range ofa function?

Oct

2-3 Stretching,Shrinking, andReflecting Graphs

#19: What is stretching and shrinking, and when doesvertical stretching or shrinking occur?

Stretching, shrinkingreflection, vertical

stretch, verticalshrink


Oct

# 20: How is the graph of a function reflected acrossthe x-axis, and how do you describe combinations oftransformations of graphs?

Oct

2-4 AbsoluteValue Functions:Graphs, Equations,and Inequalities

#21: How are the properties of absolute valuefunctions used in simplifying equations andinequalities?

Absolute valueequation, absolutevalue inequality


Oct

2-5 Piece-WiseDefined Functions

#22: How do you find the function values of apiecewise-defined function and how do you graph it?

Piecewise definedfunction, greatestinteger function


Oct

#23: How do you evaluate and graph a greatestinteger function?

Oct

11

Chapter 2: Analysis of Graphs of FunctionsPages 89 –169, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date2-6 Operations andComposition

#24: What are the operations of function rules, andhow are they used to evaluate combinations offunctions?

Operations onfunctions, thedifference quotient,composition offunctions


Oct

#25: How do you find the difference quotient andevaluate composite functions?

Oct

COMMON ASSESSMENT #2 Oct

12

Chapter 3: Polynomial FunctionsPages 172 - 270, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date3-1: ComplexNumbers

# 26: How do we recognize imaginary and complexnumbers?

Imaginary numbers,complex numbers,

conjugate, conjugate pair

Do now; mini-lesson,student activity, assessment,reinforcement

Nov

#27: How do we add and multiply complex numbers? Nov

3-2: QuadraticFunctions andGraphs

#28: How is a quadratic equation in standard form solvedwhen the quadratic equation is not factorable?

Completing the square,vertex formula, extrema or

extreme values


Nov

# 29: What is the vertex formula of a quadratic function andhow is this linked with extreme or extreme values making upthe minimum or maximum point?

Nov

3-3: QuadraticEquations

#30: How do you use the zero product property to solvequadratic equations and how is it related to the quadraticformula?

Zero product property,quadratic formula,

discriminant


Nov

3-4: QuadraticInequalities

#31: How do you find the solution set of quadraticinequalities?

Quadratic inequality,solution set


Nov

3-5: HigherDegreePolynomialFunctions andGraphs

#32: What are higher-degree polynomials and how can theirextrema be found?

Turning point, localminimum point, localmaximum point, localminima, local maxima


Nov

3-6: Theory ofPolynomialFunctions

#33: How do you use the intermediate value theorem to findthe zero/s of a polynomial?

x-intercept, real zeros,solutions of a polynomial,synthetic division, factor

theorem, remaindertheorem, fundamental

theorem of algebra, numberof zeros theorem, rational

zeros theorem


Nov

#34: How do you divide a polynomial by (x-a) using thesynthetic division method?

Nov

#35: What are the remainder theorem and the factor theoremand how are they related with each other?

Nov

#36: How do you determine the zeros of a polynomialnumber of zeros theorem and the rational zeros theorem

Nov

3-7: PolynomialEquations andInequalities

#37: How do you apply the complex nth roots theorem todetermine the number of roots and find those roots?

Complex nth roots theorem Do now; mini-lesson,student activity, assessment,reinforcement

Nov

COMMON ASSESSMENT #3 Nov

13

Chapter 4: Rational, Power, and Root FunctionsPages 272 – 339, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date4-1: RationalFunctions andGraphs

#38: How do you graph a rational function and itsasymptote, if any?

Rational function,reciprocal functions,asymptote( vertical

and horizontal, pointof discontinuity


Dec

#39: How do you graph reciprocal functions and identifythe equation of their vertical, horizontal or obliqueasymptote?

Dec

#40: How do you find a point of discontinuity of a functionand show its graph?

Dec

4-2: RationalEquations,Inequalities,Applications,and Models

#41: How do you solve rational equations? Rational equation,associated inequality,

direct and indirectvariations, joint

variation, combinedvariation


Dec

#42: How do you solve rational equations and theirassociated inequalities?

Dec

#43: How do you direct or inverse variation (simple,combined, or joint)?

Dec

4-3: FunctionsDefined byPowers andRoots

#44: When does a power function become a root functionand how do you describe its graph?

Root function, index,odd index, even

index, circle,parabola


Dec

#45: How do you graph a root function when the index isodd or even?

Dec

#46: How do you find the equations and draw the graphscircles and horizontal parabolas using root functions?

Dec

4-4:Equations,Inequalities,andApplicationsInvolving RootFunctions

#47: How do you find the solution and solution sets ofpower functions? and inequalities

Power property,extraneous root,

coefficient


Dec

#48: How do you find the solution sets of inequalities? Dec

COMMON ASSESSMENT #4 Dec

14

Chapter 5: Inverse, Exponential, and Logarithmic FunctionsPages 342 - 417, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date5-1: InverseFunctions

#49: What are inverse operations and how are theydifferentiated?

One-to-one function,inverse function,horizontal line test,reflection

Do now; mini-lesson, studentactivity, assessment, reinforcement

Dec

#50: Hoe do you determine whether a function or its inverse isa one-to-one function and how are their graphs related?

Dec

#51: How do you graph and compare a given function and itsinverse?

Dec

5-2:ExponentialFunctions

#52: How do you graph an exponential function with a positivebase?

Exponential function,number e, compoundinterest,


Jan

#53: How do you compare the graphs o the functions with thesame base but their exponents are either greater than 1 orbetween 0 and 1?

Jan

#54: How do we find the solution of exponential equations? Jan

# 55: How do we use the irrational number e to find compoundinterest?

Jan

5-3: Logarithmsand theirProperties

#56: What is a logarithmic function and how is it compared toan exponential function?

Logarithm, base,exponent, properties oflogarithm, logarithmicform


Jan

#57: What are common logarithm and natural logarithm andhow are they differentiated?

Jan

58: How are the properties of logarithms used to performoperations and solve equations?

Jan

#59: How do you change logarithmic expressions from onebase to another?

Jan

5-4:LogarithmicFunctions

#60: How do you graph a logarithmic function f(x) = loga x andhow do you determine the domain of the logarithm?

Exponential form,inverse of f(x)


Jan

#61: How do you find the inverse of an exponential functionexpressed in terms of logarithm?

Jan

5-5:Exponential andLogarithmicEquations andInequalities

#62: How do you solve exponential equations whose membersare of different bases?

Properties ofexponential andlogarithmic functions,natural logarithm


Jan

#63: How do you solve exponential inequalities? Jan

#64: How do you solve exponential and logarithmic equationsinvolving formulas?

Jan

COMMON ASSESSMENT #5 Jan

15

Chapter 6: Analytic GeometryPages 419 - 464, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date6-1: Circles #65: How do you find the center and radius of a circle

and draw it graph?Circle, radius,diameter, locus of apoint, distance betweentwo points, midpoint

Do now; mini-lesson,student activity,assessment, reinforcement

Feb

#66: How do you derive the equation of a circle whengraph is given and when the center and radius are known?

Feb

6-2: Parabolas #67: How do you change the equation of a parabola tostandard form, find its vertex, axis of symmetry, focus,focal distance, and determine the direction of its infiniteextent?

Vertex, focus, focaldistance, standardform, general form


Feb

#68: How do you graph a parabola when the vertex andthe focal distance are known?

Feb

6-3: Ellipses #69: How do you change the equation of an ellipse fromgeneral form to standard form and get the center, minorand major axes, and its semi-minor and semi-major axes?

Center, vertices, minorand major axes, semi-minor and semi-majoraxes, standard form ofthe equation


Feb

#70: How do you derive the equation of an ellipse whenthe center and the length of the two axes are known?

Feb

6-4:Hyperbolas

#71: How do you change the equation of a hyperbolafrom general form to standard form, get the center,transverse and conjugate axes, the length of the semi-transverse and semi-conjugate axes, and draw its graph?

Center, asymptotes,transverse andconjugate axes, semi-transverse and semi-conjugate axes,standard equation form


Feb

#72: How do you derive the equation of a hyperbolawhen the center and the lengths of the two axes areknown?

Feb

6-5:ParametricEquations

#73: How do you change a parametric equation to itsrectangular equivalent form and vise-versa and how arethey graphed?

Parametric equation,rectangular equationform, general form,


Feb

COMMON ASSESSMENT #6 Feb

16

Chapter 7: Matrices and Systems of Equations and InequalitiesPages 466 - 563, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date7-1: Systems ofequations

# 74: How do your solve linear equations usingelimination and substitution method?

Linear equation,system of linearequation, nonlinearequation, nonlinearsystem


Feb

Aim #75: How do you solve nonlinear systems ofequations?

Feb

7-2: Solution oflinear systemsby EchelonMethod

#76: How do you find the solution set of a linear system ofequations in three variables using the echelon method?

Linear system ofequations in threevariables, echelonmethod


Feb

7-3: Solution ofLinear Systemsby RowTransformation

#77: How do you find the solution set of a system of linearequations in three variables using the matrix rowtransformation method?

Matris, elenment,entry, augmentedmatrix, maindiagonal, secondarydiagonal


Mar

7-4: MatrixProperties andOperations

#78: What are the different kinds of matrices and how arethe matrix properties applied in matrix operations?

Dimension of amatrix, row matrix,column matrix,square matrix, mbyn matrix,, inverse ofa matrix


Mar

#79: How are matrices added and subtracted? Mar#80: How do you find the product of a scalar by a matrixand a matrix by another matrix?

Mar

7-5:Determinantsand Cramer’sRule

#81: How do you find a determinant and how is it relatedto Cramer’s rule?

Determinant,Cramer’s rule,square matrix, nxnmatrix, coefficientmatrix


Mar

#82: How do you use determinants to solve system ofequations?

Mar

7-6: PartialFractions

#83: How do you find the partial fraction decompositionof a given fraction?

Partial fraction,partial fractiondecomposition,


Mar

COMMON ASSESSMENT #7 Mar

17

Chapter 8: Trigonometric Functions and ApplicationsPages 566 - 671, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date8-1: Anglesand Arcs

#84: How are angles and arcs measured? Point, line, angle, initial side,terminal side, positive angle,

negative angle, angle instandard position, degree,

radian, arc kinds of angles,complementary and

supplementary angles,quadrantal angles, co-

terminal angles


Mar

#85: How is radian measure converted to degree measureand vise-versa?

Mar

#86: How are coterminal, quadrantal, and angles isstandard position identified?

Mar

# 87: How do you find arc lengths, area of sectors, angularspeed and linear speed?

Mar

8-2: UnitCircle

#88: What is the unit circle and its relationship with thecircular functions?

Unit circle, circular functions,identities


Mar

#89: What are the special trigonometric functions ofspecial angles?

Mar

8-3: Graph ofSine andCosine

#90: How do you graph the sine and the cosine functions? Sine, cosine, periodicfunction, period, amplitude,frequency, secant, cosecant,

tangent, cotangent


Mar#91: How do you find the period, frequency and amplitudeof the sine and cosine functions?

Mar

#92: How do you graph the secant and cosecant functions? Mar#93: How do you graph the tangent and cotangentfunctions?

Apr

#94: How do you graph the function resulting from thesum or difference of two other functions?

Apr

8-4: Functionof Angles

#95: How do you find the trigonometr5ic functions ofquadrantal angles and angles in standard position?

Sin, cos, tan, cot, sec, csc,quadrantal angles,


Apr

8-5: TheFundamentalIdentities

#96: How do you derive identities and use them to proveother identities?

reciprocal identities,Pythagorean identities,

ratio(quotient) identities


Apr

8-6:EvaluatingTrigonometricFunctions

#97: How do you find trigonometric values of specialangles, and use co-function identities and reference anglesto evaluate trigonometric expressions and angular measure?

Co0functions, special angles,reference angle


Apr

18

8-7:Applications ofRight Triangles

#98: How do you solve right triangles to significant digits? Significant digit, angles ofelevation and depression,

bearing, heading, airspeed,linear speed.


Apr

#99: How do you find angles of elevation and depression,bearing, heading, and airspeed, linear speed?

Apr

COMMON ASSESSMENT #8 Apr

Chapter 9: Trigonometric Identities and EquationsPages 673 - 737, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date9-1:TrigonometricIdentities

#100: How are proved identities used to prove or verifyother identities?

Quotient,Pythagorean, co-function, reciprocaland negative-numberidentities


Apr

9-2: The Sumand DifferenceIdentities

#101: How do you derive and use the sum anddifference identities, double-angle identities, half-angleidentities, and product-to-sum identities?

Cosine sum anddifference identities


Apr

9-3: InverseCircularFunctions

#102: How are the inverse of sine, cosine, and tangentfunctions found?

Sin-1, cos--1, tan-1 ,cot-1 , sec -1, csc -1


Apr

#103: How are the inverse of cotangent, secant, andcosecant functions found?

Apr

9-4:TrigonometricEquations andInequalities

# 104: How do you solve trigonometric equations andinequalities by linear method and factoring method?

Linear method,factoring method,quadratic formula


Apr

#105: How do you solve trigonometric equations usingthe quadratic formula and/or trigonometric identities?

Apr

COMMON ASSESSMENT #9 Apr

19

Chapter 10: Applications of Trigonometry; VectorsPages 739 - 814, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date10-1: Law of Sines #106: How do we find the remaining measures and

lengths of a triangle when two angles and one side areknown?

Sine law, givenangles, given side


May

10-2: Law ofCosines, AreaFormulas(Heron’sformula and SASformula)

#107: How do we find any missing part of a triangleusing the Cosine Law and calculate its area?

Area of a triangleformula, Cosine Law


May

10-3: Vectors andteir Applications

#108: How do we apply the Laws of sine and cosine insolving vector problems?

Vector, direction,scalar, magnitude,vector quantities,resultant,parallelogram rule


May

10-4:Trigonometric orPolar Form ofComplex Numbers

#109: In the Complex Number Plane, how do youconvert coordinates in rectangular form to polar formand vise-versa?

Rectangular form,polar/trigonometricform, cis notation


May

#110: How do you find the product or quotient ofcomplex numbers in trigonometric or polar form?

10-5: Powers andRoots of ComplexNumbers

#111: How do you find the powers of a complexnumber using De Moivre’s Theorem?

De Moivre’sTheorem


May

10-6: PolarEquations andGraphs

#112: How do you differentiate rectangularcoordinates from polar coordinates and illustrate thesimilarities and differences of these two sets ofcoordinates?

Polar coordinates,rectangularcoordinates, polarequation, rectangularequation, polarcoordinate system


May

#113: How do you graph polar equations?#114: How do you convert polar equations to polarequations?

COMMON ASSESSMENT #10 Mar

20

Chapter 11: Sequences, Binomial TheoremStatistics and Probability, Pages 816 - 888, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date11-1: Sequencesand Series

#115: How do we specify the terms of a sequence byusing a formula to find the nth term of a sequence

Sequence. Series, terms ofthe sequence


May

11-2:ArithmeticSequence andSeries

#116: How do we generate an arithmetic sequenceand find its nth term?

Arithmetic sequence, firstterm, common difference,

nth term, arithmetic series,sum of an arithmetic series


May

#117: How do we find the sum of an arithmeticseries?

May

11-3: GeometricSequence andSeries

#118: How do we generate a geometric sequence andfind its nth term?

Geometric sequence, firstterm, common ratio/factor,nth term, geometric series,sum of a geometric series


May

#119: How do we find the sum of a geometric series? May

11-4: BinomialTheorem

#120: How can we find any given term in a binomialexpansion using the Binomial Theorem?

Binomial Theorem,Pascal’s triangle, nth termof a binomial expansion


May

#121: How can we find any given term in a binomialexpansion using the Pascal’s triangle?

May

11-5: CountingTheory

#122: How is the counting principle related topermutation and how do your find the permutation ofn objects taken r at a time?

Counting Principle,permutation, n-factorial,combination, binomial

coefficient


May

#123: How do you find the number of combination ofn objects taken r at a time?

May

# 124: How do you differentiate and distinguishpermutation from combination?

May

11-6:Probability

#125: How do we find the probability of independent,dependent, and mutually exclusive events?

Outcomes, sample space,event, probability,

complement, union,intersection, Venn diagram,

odds, mutually exclusiveevent, binomial experiment


May

COMMON ASSESSMENT #11

21

Chapter 12: Limits, Derivative, and Definite IntegralsPages 890 –935, Precalculus, 3rd Edition, by Hornsby, Lial, & Rockswold

Lesson Aim Vocabulary Strategy/Activity Date12-1:Introduction toLimits

#126: What is limit of a function and how do youdetermine whether there is a limit or not?

Limit of a function, limitnotation, polynomial fundtion,piece-wise-defined function,trigonometric function

Do now; mini-lesson,student activity,assessment,reinforcement

Jun

12-2:Techniques forCalculatingLimits

#127: How do you find the limits of various typesof function using the conditions under which limitsfail to exist?

Rules for limits, infinity, andinfinity symbol


Jun

#128: What are the techniques of calculating limitsusing the rules for limits?

12-3: One-sidedLimits

#129: How do you find a one-hand limit? Right-hand limit, left-handlimit, one-sided limit, two-sided limits


Jun

#130: How do you find two-sided limits and limitsat infinity?

12-4: TangentLines

#131: How do you find the tangent line of the graphof a function at a given point?

Tangent line Do now; mini-lesson,student activity,assessment,reinforcement

Jun

12-5:Derivatives

#132: How do you find the derivative of a functionat a given point and how is it interpreted in relationto rate of change?

Differentiation, derivative, rateof change


Jun

12-6: Areaunder a Curve

#133: How do you find the approximate area of afigure or region under a curve by the trapezoidal andmidpoint rules?

Area of region under a curve,trapezoidal rule, midpoint rule


Jun

12-7: DefiniteIntegral

#134: How do we apply the definition of definiteintegral to find the area of a region under a curve?

Integral, definite integral,integration, lower limit ofintegration, upper limit ofintegration


Jun

COMMON ASSESSMENT #12 Jun

22

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 all mathematics class rooms.

Math Word Wall

Create a math wordwall

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

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 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 Opening Exercise (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 #:

Objective:

Opening Exercise (Do Now):

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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


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


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:

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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: ____________

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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

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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.

Documents

PreCalculus Curriculum Guide - SharpSchoolmvcsd.sharpschool.net/UserFiles/Servers/Server_87286/File/Satish... · mount vernon city school district precalculus curriculum guide this