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
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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 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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
Nov
3-4: QuadraticInequalities
#31: How do you find the solution set of quadraticinequalities?
Quadratic inequality,solution set
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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,
Do now; mini-lesson, studentactivity, assessment, reinforcement
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
Do now; mini-lesson, studentactivity, assessment, reinforcement
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)
Do now; mini-lesson, studentactivity, assessment, reinforcement
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
Do now; mini-lesson, studentactivity, assessment, reinforcement
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
Do now; mini-lesson,student activity,assessment, reinforcement
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
Do now; mini-lesson,student activity,assessment, reinforcement
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
Do now; mini-lesson,student activity,assessment, reinforcement
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,
Do now; mini-lesson,student activity,assessment, reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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,
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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,
Do now; mini-lesson, studentactivity, assessment,reinforcement
Apr
8-5: TheFundamentalIdentities
#96: How do you derive identities and use them to proveother identities?
reciprocal identities,Pythagorean identities,
ratio(quotient) identities
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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.
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson, studentactivity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity, assessment,reinforcement
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
Do now; mini-lesson,student activity,assessment, reinforcement
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
Do now; mini-lesson,student activity,assessment, reinforcement
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
Do now; mini-lesson,student activity,assessment, reinforcement
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
Do now; mini-lesson,student activity,assessment, reinforcement
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
Do now; mini-lesson,student activity,assessment, reinforcement
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
Do now; mini-lesson,student activity,assessment, reinforcement
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
Do now; mini-lesson,student activity,assessment,reinforcement
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
Do now; mini-lesson,student activity,assessment,reinforcement
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
Do now; mini-lesson,student activity,assessment,reinforcement
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
Do now; mini-lesson,student activity,assessment,reinforcement
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
Do now; mini-lesson,student activity,assessment,reinforcement
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.”
- 25 -
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:
- 26 -
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: ____________
- 27 -
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
- 28 -
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.