MATHEMATICS:CCSS.MATH.CONTENT.HSN.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. CCSS.MATH.CONTENT.HSN.RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. CCSS.MATH.CONTENT.HSN.RN.B.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. CCSS.MATH.CONTENT.HSN.Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CCSS.MATH.CONTENT.HSN.CN.A.1: Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real. CCSS.MATH.CONTENT.HSN.CN.A.2: Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. CCSS.MATH.CONTENT.HSA.SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. CCSS.MATH.CONTENT.HSA.APR.C.4: Prove polynomial identities and use them to describe numerical relationships. CCSS.MATH.CONTENT.HSA.CED.A.1:Create equations and inequalities in one variable and use them to solve problems.CCSS.MATH.CONTENT.HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. CCSS.MATH.CONTENT.HSA.CED.A.3:Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. CCSS.MATH.CONTENT.HSA.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. CCSS.MATH.CONTENT.HSA.REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. CCSS.MATH.CONTENT.HSA.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. CCSS.MATH.CONTENT.HSA.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. CCSS.MATH.CONTENT.HSA.REI.B.4: Solve quadratic equations in one variable. CCSS.MATH.CONTENT.HSA.REI.B.4.A: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form. CCSS.MATH.CONTENT.HSA.REI.B.4.B: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. CCSS.MATH.CONTENT.HSA.REI.C.8: (+) Represent a system of linear equations as a single matrix equation in a vector variable. CCSS.MATH.CONTENT.HSA.REI.C.9: (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). CCSS.MATH.CONTENT.HSF.LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. CCSS.MATH.CONTENT.HSF.LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context CCSS.MATH.CONTENT.HSS.ID.A.2:Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. CCSS.MATH.CONTENT.HSS.ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). CCSS.MATH.CONTENT.HSS.ID.A.4:Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.CCSS.MATH.CONTENT.HSS.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. CCSS.MATH.CONTENT.HSS.IC.B.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. CCSS.MATH.CONTENT.HSS.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. CCSS.MATH.CONTENT.HSS.IC.B.6: Evaluate reports based on data.

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11 Q1 MATHEMATICS PROCESS PRODUCT/ASSESSMENTThe difference between Algebra I and Algebra IIEssential QuestionsHow are cube roots similar to square roots in terms of simplification?How can we utilize appropriate algebraic thinking to solve for variables?How will our past knowledge help us in future endeavors?What are the methods we use to simplify expressions?When is it beneficial to express radical expressions with fractional exponents?Why are negative results acceptable when dealing with odd numbered radicals?Enduring Understanding

The difference between Algebra I and Algebra IIApply basic algebraic skills Compare and contrast even and odd number radicalsCreate a series of word problems to represent the different concepts being explored Factor and explain the cube roots of numbers and variables Perform algebraic methods Review methods used to solve algebra problems Simplify expressions so that they become more useful for solving problems in the real world.Utilize different functions to solve for unknowns

The difference between Algebra I and Algebra IIAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q1 MATHEMATICS PROCESS PRODUCT/ASSESSMENTSituations in which different types of studies can be usedto yield meaningful resultsEssential QuestionsHow can this information be useful in different academic and research areas?What are the attributes of surveys, observations and controlled experiments?When are the appropriate situations to use each of the previous methods?Enduring Understanding

Situations in which different types of studies can be usedto yield meaningful resultsDetermine if the correct type of study has been used by an individual or group when given raw dataExplore the different types of studies that are used in mathematics and science to make appropriate and accurate generalizations and predictions about populationsExpose the flaws of each type of studyUse the characteristics of a population and potential outcome to determine the best type of study to use in a given situation

Situations in which different types of studies can be used to yield meaningful resultsAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q1 MATHEMATICS PROCESS PRODUCT/ASSESSMENTApplying the Pythagorean Theorem to the unit circleEssential QuestionsWhat is the unit circle?How do the characteristics of the unit circle give us useful information for proofs?How is the identity sin2 + cos2 = 1 derived from the Pythagorean Theorem?Why do the ratios of cosine and sine change because of a constant radius?Why are triangles the best choice for inscribing?Enduring Understanding

Applying the Pythagorean Theorem to the unit circleApply a radius of one to make fractional ratios simpler Derive the trigonometric identity sin2 + cos2 = 1 from basic trigonometric ratios and the Pythagorean TheoremExplore how the sine and cosine fluctuate with one another as we have a constant hypotenuseRecognize that the defining characteristic of all circles is a constant radiusUtilize knowledge of the unit circle and trigonometry to inscribe other shapes

Applying the Pythagorean Theorem to the unit circleAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q1 MATHEMATICS PROCESS PRODUCT/ASSESSMENTA normal distribution curveHow is mean determined and how do we use this average to model real world situations?What are standard deviations and how are they used to analyze and predict information and data?Enduring Understanding

A normal distribution curveAnalyze data and make predictions from the use of a standard deviation curveCalculate the number of individuals within each standard deviation when given a bell curveDetermine the mean of a given sample set

A normal distribution curveAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q1 MATHEMATICS PROCESS PRODUCT/ASSESSMENTSystems of equation and how they are solvedHow is solving a system of three equations similar to and different than solving for two equations?Which attributes of a system can be exploited for solving for unknowns?When are matricies useful in solving systems of equations?How can we solve linear quadratic systems graphically and algebraically?What is the imaginary number i?When does the imaginary number occur and how does it help us to answer questions that were unanswerable in the past?Enduring Understanding

Systems of equation and how they are solvedDiscover and utilize the imaginary number i to solve and simplify equations with a negative radicalEvaluate and apply the best strategy to use when solving a given problem (i.e. graphically, by substitution, by elimination)Recall prior information on the solving of systems of two equationsSolve for unknowns in linear quadratic systems.Understand that matrices are arrays that are useful representation systems of more than three equationsUtilize strategies used for systems of two equations when solving systems of three equations

Systems of equation and how they are solvedAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

11 Q1 MATHEMATICS VOCABULARY –AlternativeCausationCensusDependentDistributionExpressionFormulaIndependentMaximumMinimumSampleSequenceStandard

MATHEMATICS:CCSS.MATH.CONTENT.HSN.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.CCSS.MATH.CONTENT.HSN.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.CCSS.MATH.CONTENT.HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. CCSS.MATH.CONTENT.HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.CCSS.MATH.CONTENT.HSN.CN.A.1 Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.CCSS.MATH.CONTENT.HSN.CN.A.2 Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.CCSS.MATH.CONTENT.HSN.CN.A.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.CCSS.MATH.CONTENT.HSN.CN.B.4 (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. CCSS.MATH.CONTENT.HSN.CN.B.5 (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°.CCSS.MATH.CONTENT.HSN.CN.B.6 (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.CCSS.MATH.CONTENT.HSN.CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.CCSS.MATH.CONTENT.HSN.CN.C.8 (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).CCSS.MATH.CONTENT.HSN.CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.CCSS.MATH.CONTENT.HSA.APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. CCSS.MATH.CONTENT.HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.CCSS.MATH.CONTENT.HSF.LE.A.1.A Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.CCSS.MATH.CONTENT.HSF.LE.A.1.B Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.CCSS.MATH.CONTENT.HSF.LE.A.1.C Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.CCSS.MATH.CONTENT.HSF.TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.CCSS.MATH.CONTENT.HSF.TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.CCSS.MATH.CONTENT.HSF.TF.A.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number.CCSS.MATH.CONTENT.HSF.TF.A.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.CCSS.MATH.CONTENT.HSF.TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*CCSS.MATH.CONTENT.HSF.TF.B.6 (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.CCSS.MATH.CONTENT.HSF.TF.B.7 (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*CCSS.MATH.CONTENT.HSF.TF.C.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.CCSS.MATH.CONTENT.HSF.TF.C.9 (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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11 Q2 MATHEMATICS PROCESS PRODUCT/ASSESSMENTHow trigonometric ratios are usedoutside of right trianglesEssential QuestionsWhat is the Law of Sines?How can we prove the Law of Sines using multiple triangles?What is the Law of Cosines?How can we prove the Law of Cosines using our knowledge of right triangles?When is it appropriate to use the Law of Sines vs. Law of Cosines?How can we use trigonometry to find the area of geometric figures?Enduring Understanding

How trigonometric ratios are usedoutside of right trianglesDerive the Law of Sines to prove that it is true for future use.Recognize the types of situations where the Law of Sines can be utilized to solve for unknownsUnderstand that the ratios need not be found for all angles and sidesRelate knowledge of geometric proofs to trigonometry.Derive the Law of Cosines to prove that it is true for future use.Recognize the types of situations where the Law of Cosines can be utilized to solve for unknownsUnderstand that capital letters and lower case letters represent angles and sides respectively

How trigonometric ratios are usedoutside of right trianglesAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q2 MATHEMATICS PROCESS PRODUCT/ASSESSMENTThe applications and meaning of the imaginary unit iEssential QuestionsHow can imaginary numbers with exponents be simplified?How does the imaginary unit arise in questions related to parabolas?What are the practical applications of the imaginary unit?What is a + bi form and how is it used for expressions with imaginary and real numbers?What is the definition of the imaginary unit?What is the repeating pattern that appears with imaginary numbers with exponents between 1 and 4?Enduring Understanding

The applications and meaning of the imaginary unit iDefine the imaginary unit as the square root of negative oneUnderstand the history and origins that created the need for an imaginary number systemCreate a method to remember the pattern of simplified imaginary numbersDerive the reasons for the pattern of imaginary numbers.Understand that all numbers can be expressed in the form a + biSimplify expressions with both imaginary and mixed imaginary and real numbers

The applications and meaning of the imaginary unit iAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q2 MATHEMATICS PROCESS PRODUCT/ASSESSMENTInverse ratios in trigonometryEssential QuestionsHow are cosecant, secant and cotangent different than sine cosine and tangent?How are inverse functions useful for simplifying complicated expressions?How can we use algebraic strategies to simplify trigonometric expressions?What are trigonometric identities?Enduring Understanding

Inverse ratios in trigonometryDerive trigonometric identities listed on reference sheetReview basic functions of trigonometry used in right trianglesSimplify expressions using identities and the fundamental aspects of trigonometryUnderstand that cosecant, secant and cotangent are inverse ratios related to sine, cosine and tangentUse these inverse ratios as a method of simplifying expressions by creating fractions of 1:1

Inverse ratios in trigonometryAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q2 MATHEMATICS PROCESS PRODUCT/ASSESSMENTExpressing trigonometric functions visuallyEssential QuestionsWhat are radians and why are they used instead of degrees?How do we convert degrees to radians?Where are the locations of critical values of sine, cosine and tangent on a graph?What are the domain, range and undefined values for these graphs?How are these graphs on the Cartesian plane related to the unit circle?What is the relationship between arc length and interior angles?Enduring Understanding

Expressing trigonometric functions visuallyConvert degrees to radians and radians to degreesConvert the values of a unit circle from degrees to radiansDetermine the relationship between radians and degreesFind the critical values on a unit circleRelate arc length of the unit circle to the interior angles being createdRelate the critical values from the unit circle to the Cartesian plane by graphing sine, cosine and tangent waves

Expressing trigonometric functions visuallyAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q2 MATHEMATICS PROCESS PRODUCT/ASSESSMENTHow quadratic functions are used to representreal world situationsEssential QuestionsWhat are the different methods for determining the roots of a quadratic function?What are the potential solution sets of quadratic functions?When is the quadratic equation useful for determining the roots of a function?How do quadratic equations represent motion?What are the other critical values that can be evaluated?When are inequalities useful for representing data?How can we utilize linear quadratic systems to Compare two different sets of information?Enduring Understanding

How quadratic functions are used to representreal world situationsCompare values by utilizing linear quadratic systemsDetermine the minimum or maximum of a parabolaDetermine the most effective strategy to solve linear quadratic systemsDetermine whether or not answers are acceptable based on the parameters presented by the questionUse inequalities to represent real world situationsUse quadratic functions to represent motionUse the factoring, quadratic equation and graphing methods for finding the roots of a quadratic equationUtilize the quadratic equation when a discriminant is not a perfect square

How quadratic functions are used to representreal world situationsAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q2 MATHEMATICS PROCESS PRODUCT/ASSESSMENTHow ratios are used to show similarities and differences in geometric figuresEssential QuestionsHow are parallel lines related to proportional measurements of triangles and other polygons?How do ratios apply to similar figures, how are differences in lengths of sides proportional, but angles remain constant. How do we set up equations featuring fractions when given word problems?What are proportions and ratios?What can we do to translate, dilate, and verify similarity on a coordinate plane?Enduring UnderstandingKnowledge of proportions can be applied to geometric shapes, enhancing prior knowledge of both algebra and geometry. Knowledge of geometry and the coordinate plane is used to rotate, translate and dilate figures, applying proportions.

How ratios are used to show similarities and differences in geometric figuresAnalyze how proportions and fractions are used to represent real world tangible itemsReview fractions, reduction and similar conceptsUtilize proportions as a separate entity from geometry

How ratios are used to show similarities and differences in geometric figuresAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

11 Q2 MATHEMATICS VOCABULARY – ConvertCoordinatesDegreeEquationFunctionIdentityLawsLinearRootsSimplifySystemUnit

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11 Q3 MATHEMATICS PROCESS PRODUCT/ASSESSMENTUsing trigonometry to find the area of geometric shapesEssential QuestionsHow is the trigonometric formula for the area of a triangle similar to k = ½ b*hWhat is the proper notation used in advanced mathematics for the labeling of sides and angles of triangles?What characteristics of a triangle are needed to find area using the formula k = 1/2 absinC?What are the characteristics of a parallelogram that relate them to triangles?How can the formula for triangular area be modified to use with parallelograms?What is Heron’s Law?How can Heron’s Law be used to find the area of triangles where angles are not given?Enduring Understanding

Using trigonometry to find the area of geometric shapesDemonstrate understanding of geometric properties needed to prove similarity of trianglesDerive Heron’s formulaDerive the formula for area of a triangle using trigonometryDerive the formula for the area of a triangle using base and heightModify the equation for the trigonometric area of a triangle to suit the needs of a parallelogram.Relate the properties of triangles and rectangles to the properties of parallelogramsSolve for the unknown area of a triangle using the formula k= 1/2absinCUse Heron’s formula to solve for the area of geometric figures when angle measures are not given

Using trigonometry to find the area of geometric shapesAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q3 MATHEMATICS PROCESS PRODUCT/ASSESSMENTReferencing triangles to help more accuratelyexpress common answers in trigonometryEssential QuestionsWhat are reference triangles?Why are these common triangles chosen to be used both inside and outside of the classroom?Why are answers expressed in terms of radials more accurate than decimal approximations?How are these concepts applicable to the unit circle?Enduring Understanding

Referencing triangles to help more accuratelyexpress common answers in trigonometryUtilize the unit circle to define the angle measures and trigonometric ratios found in common right trianglesExplain the rationale for the use of common right triangles in practical applicationsExpress ratios and side lengths using radicals to more properly answer questionsSimplify given equations using radicals to properly express trigonometric ratios

Referencing triangles to help more accuratelyexpress common answers in trigonometryAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q3 MATHEMATICS PROCESS PRODUCT/ASSESSMENTHow identifying formulas helps solve complextrigonometry problemsEssential QuestionsWhat are the sum and difference formulas?How are the sum and difference formulas derived?How are these formulas used to solve for unknowns on a coordinate plane?What are the practical applications of sum and difference formulas?What are the double angle formulas?How are double angle formulas derived?How can double angle formulas be used to simplify more complex trigonometric expressions and equations?What are the practical applications of the double angle formulas?What are the half angle formulas?How are half angle formulas derived?What are the relationships between the double angle formulas and half angle formulas?What are the practical applications of half angle formulas?Enduring Understanding

How identifying formulas helps solve complextrigonometry problemsApply double angle formulas towards solving real world situations involving mechanical engineering and optimization.Apply half angle formulas to real world situationsDerive double angle formulas for use in future assignments and questionsDerive half angle formulasDerive sum and difference formulas to better understand their useRelate half angle formulas to double angle formulasSimplify complex equations and solve for unknown values using the sum and difference formulasSimplify expressions using double angle formulasUtilize half angle formulas to simplify statements and solve for unknown valuesUtilize sum and difference formulas to simplify trigonometric expressions

How identifying formulas helps solve complextrigonometry problemsAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q3 MATHEMATICS PROCESS PRODUCT/ASSESSMENTHow trigonometric concepts are expressed as functionsEssential QuestionsHow do the functions of f(x) = sin(x), f(x) = cos(x) and f(x) = tan(x) behave when graphed on a trigonometric plane?What are the periods of these functions and how are they related to the unit circle?What types of natural and manmade phenomena are represented by waves?How are the characteristics of the graphs of trigonometric functions reflected in the characteristics of right triangles?What are the domains and range of trigonometric functions?What are the changes in the graphs of functions when coefficients and constants are involved?How can trigonometric equations be obtained using an associated graph?Enduring Understanding

How trigonometric concepts are expressed as functionsDetermine the equations of given trigonometric graphsExplain why the periods of functions show repetition of the same pattern as they pass through 2pi radiansExpress the graphs of trigonometric functions on a coordinate planePredict the changes in a trigonometric graph when coefficients and constants are included in the functionRelate the graphs of trigonometric functions to the unit circleShow a relationship between sine and cosine, showing that their graphs move constantly in fluctuation with one another

How trigonometric concepts are expressed as functionsAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

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11 Q3 MATHEMATICS PROCESS PRODUCT/ASSESSMENTHow patterns, functions and relationships are expressed algebraically and graphicallyEssential QuestionsWhat are the defining characteristics of a sequence?In what ways can a sequence be expressed?What is Sigma notation and what operations does it help us to perform?What are the practical applications of Sigma notation?How can arithmetic and geometric sequences and series help us to express an even growth or decline?What is the proper notation utilized with recursive sequences?What are the differences between relations and functions?How can we express the inverse of a function?What are the practical applications of the inverses of functions?Enduring Understanding

How patterns, functions and relationships are expressed algebraically and graphicallyApply inverse functions to real world situationsApply sigma notation to real world situations involving series and sample spaceDefine the characteristics that differ between sequences and patternsDifferentiate between functions and relationsExpress population growth and decline using arithmetic and geometric sequencesExpress sequences visually, algebraically and graphicallyUse Sigma notation to show the total sum of a given series or functionUse the inverse of a function to make predictions and gather conclusions about the function

How patterns, functions and relationships are expressed algebraically and graphicallyAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

11 Q3 MATHEMATICS VOCABULARY –

Mathematics CCSS.MATH.CONTENT.HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. CCSS.MATH.CONTENT.HSF.LE.A.1.A Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. CCSS.MATH.CONTENT.HSF.LE.A.1.C Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. CCSS.MATH.CONTENT.HSF.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). CCSS.MATH.CONTENT.HSF.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. CCSS.MATH.CONTENT.HSF.LE.A.4 For exponential models, express as a logarithm the solution to abct = dwhere a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. CCSS.MATH.CONTENT.HSF.LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context.How does it apply to content areas? What content are you currently exploring? This can be shared through essential questions, content standards, or a brief narrative

What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning (ie graphic organizers, resources/ references, direct instruction, collaborative learning, inquiry)

11 Q4 MATHEMATICS PROCESS PRODUCT/ASSESSMENTHow exponential functions represent real world situationsEssential QuestionsWhat are exponential functions and how do they differ from other functions that have been observed?What are the defining characteristics of an exponential function?How are asymptotes formed and why do they occur?How does the x0=1 effect the form of a exponential growth graph?Why do exponential functions have no answers in the III and IV quadrants in the general form? When do exponential growth and decay occur and how does their occurrence modify our general exponential function f(x) = abx?How does exponential growth in the form f(x) = a(1+r)x represent real world situations?How does exponential decay in the form f(x) = a(1-r)x represent real world situations?Enduring Understanding

How exponential functions represent real world situationsApply constraints and components to the basic form of the function and observe changes in the graphed formDemonstrate that in the standard form, exponents do not have negative y valuesEvaluate exponentials Graph and observe exponential functions in the basic form f(x) = abx

Identify the key characteristics of this graph including the y intercept and horizontal asymptote Model real world situations with decay rates including radio carbon dating and population decayModel real world situations with growth rates including demographic growth, bank account growth and bacterial growth

How exponential functions represent real world situationsAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

Mathematics CCSS.MATH.CONTENT.HSN.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. CCSS.MATH.CONTENT.HSF.BF.B.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. CCSS.MATH.CONTENT.HSF.IF.C.7.E Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.How does it apply to content areas? What content are you currently exploring? This can be shared through essential questions, content standards, or a brief narrative.

What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning. (ie. graphic organizers, resources/ references, direct instruction, collaborative learning, inquiry).

11 Q4 MATHEMATICS PROCESS PRODUCT/ASSESSMENTHow logarithms are used as a compliment toexponential expressions and equationsEssential QuestionsWhat is general conversion forms involving logarithms? In what situations is a base 10 logarithm most useful?How are the properties of logarithms related to the properties of exponential functions?How can we use logarithms to solve for unknowns in equations?When can we apply logarithms to exponential equations with unlike bases?Enduring Understanding

How logarithms are used as a compliment toexponential expressions and equationsApply the use of base 10 logarithms to real world situations involving science and population growthConvert numbers with variables as exponents to logarithmic form in equations and expressionsDerive the natural logarithm eInvert exponential functions as logarithmic functionsUtilize the natural logarithm e, to solve for unknowns

How logarithms are used as a compliment toexponential expressions and equationsAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

Mathematics CCSS.MATH.CONTENT.HSA.SSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. CCSS.MATH.CONTENT.HSA.APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x). CCSS.MATH.CONTENT.HSA.APR.C.4 Prove polynomial identities and use them to describe numerical relationships. CCSS.MATH.CONTENT.HSA.APR.C.5 Know and apply the Binomial Theorem for the expansion of (x + y)nin powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.CCSS.MATH.CONTENT.HSF.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. CCSS.MATH.CONTENT.HSF.BF.B.3Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. CCSS.MATH.CONTENT.HSF.BF.B.4 Find inverse functions.CCSS.MATH.CONTENT.HSF.BF.B.4.A Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. CCSS.MATH.CONTENT.HSF.BF.B.4.B Verify by composition that one function is the inverse of another. CCSS.MATH.CONTENT.HSF.BF.B.4.C Read values of an inverse function from a graph or a table, given that the function has an inverse. CCSS.MATH.CONTENT.HSF.BF.B.4.D Produce an invertible function from a non-invertible function by restricting the domainHow does it apply to content areas? What content are you currently exploring? This can be shared through essential questions, content standards, or a brief narrative.

What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning. (ie. graphic organizers, resources/ references, direct instruction, collaborative learning, inquiry).

11 Q4 MATHEMATICS PROCESS PRODUCT/ASSESSMENTPerforming operations on functions to create newor combined outcomesEssential QuestionsWhat is a Composition of Functions and how does it model more complicated real world situations?How can we evaluate a Composition of Functions?How are domain and range of Compositions of Functions different than other regular functions that have been observed?What is the Inverse of a Function?In what ways does the graph of an inverse of a function differ from the original graph?When is the inverse of a function a relation?How do different translations change the graphed form of a function?Enduring Understanding

Performing operations on functions to create newor combined outcomesApply inverse functions to real world situationsCompose functions with more than one original function ie (f * g)(x)Determine whether the inverse of a function is a function itself or a relationEvaluate functions whose answers are the evaluations of other functions. f(g(x))Graph inverse functions on a Cartesian planeObserve how inverse functions behave differently than the base functions when graphedProve that (f * g)(x) and (g * f)(x) can, but do not have to have different results

Performing operations on functions to create newor combined outcomesAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

Mathematics CCSS.MATH.CONTENT.HSG.GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. CCSS.MATH.CONTENT.HSG.GPE.A.3 (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.CCSS.MATH.CONTENT.HSG.GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. CCSS.MATH.CONTENT.HSG.C.A.1 Prove that all circles are similar. CCSS.MATH.CONTENT.HSG.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.CCSS.MATH.CONTENT.HSG.C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.How does it apply to content areas? What content are you currently exploring? This can be shared through essential questions, content standards, or a brief narrative.

What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning. (ie. graphic organizers, resources/ references, direct instruction, collaborative learning, inquiry).

11 Q4 MATHEMATICS PROCESS PRODUCT/ASSESSMENTReasons the formula for a circle createsa unique shapeEssential QuestionsWhat is the basic form for the formula of a circle and what components does it possess?How is the formula of a circle related to the Pythagorean Theorem?From what information can a circle be constructed?How do we identify the center and radius of a circle when given its equation?Enduring Understanding

Reasons the formula for a circle createsa unique shapeAccess prior knowledge of the Pythagorean Theorem and apply towards solving for unknowns in a circleApply knowledge of the equation of a circle to the unit circleConstruct a circle from a given equation using a compass or with the aid of computerized design programDerive the basic form of the equation of a circle x2+y2 = r2.Identify the characteristics of a circle including radius, diameter, center location using only the equation in non-graphed formUse raw data in a given problem to solve and graph for any given point on a circle

Reasons the formula for a circle creates a unique shapeAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

Mathematics CCSS.MATH.CONTENT.HSS.ID.B.6.C Fit a linear function for a scatter plot that suggests a linear association. CCSS.MATH.CONTENT.HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. CCSS.MATH.CONTENT.HSS.ID.C.9 Distinguish between correlation and causation. CCSS.MATH.CONTENT.HSS.IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. CCSS.MATH.CONTENT.HSS.IC.A.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. CCSS.MATH.CONTENT.HSS.IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. CCSS.MATH.CONTENT.HSS.IC.B.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. CCSS.MATH.CONTENT.HSS.IC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. CCSS.MATH.CONTENT.HSS.IC.B.6 Evaluate reports based on data. CCSS.MATH.CONTENT.HSS.MD.B.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. CCSS.MATH.CONTENT.HSS.MD.B.5.A Find the expected payoff for a game of chance. CCSS.MATH.CONTENT.HSS.MD.B.5.B Evaluate and compare strategies on the basis of expected values. CCSS.MATH.CONTENT.HSS.MD.B.6 Use probabilities to make fair decisions CCSS.MATH.CONTENT.HSS.MD.B.7 Analyze decisions and strategies using probability conceptsHow does it apply to content areas? What content are you currently exploring? This can be shared through essential questions, content standards, or a brief narrative.

What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning. (ie. graphic organizers, resources/ references, direct instruction, collaborative learning, inquiry).

11 Q4 MATHEMATICS PROCESS PRODUCT/ASSESSMENTHow probability and statistics help make predictions about outcomes for different eventsWhat are the basic parameters, formula and components of theoretical probability?When are permutations needed for expressing the total number of outcomes in a given event?How are permutations calculated with and without repetition of outcomes and arrangements? What is the difference between a permutation and a combination? When are combinations used as opposed to permutations? How do regressions and binomial theory apply to probability? How does the Binomial Theorem apply to multiple related outcomes of a given situation? When can we use sigma notation to measure central tendency? What do measures of dispersion tell us about the range of a given sample space and potential outcomes? How can we relate this information to a statistical analysis on a distribution curve?

How probability and statistics help make predictions about outcomes for different eventsApply prior knowledge of sigma notation to analyze data for large sets Create ratios for simple probability experiments /events Derive the basic probability equation as a ratio of desired outcomes divided by total outcomes Determine the range of potential outcomes of in relationship to a normal distribution curve Determine whether combinations are to be used for a given situation based on provided information Evaluate combinations when repetition is utilized in a given situation Express coherent information about the probability of an event using permutations, combinations and sigma notationMake predictions about the possibility of an outcome based on given information Use permutations to determine the total number of outcomes for a complicated event

How probability and statistics help make predictions about outcomes for different eventsAssignments selected from the AGS texts providedCompleted sample questions from NYS Regents and RCT examinationsGlossary of important terms complete with diagrams and examples Recorded notes of sample problems

11 Q4 MATHEMATICS VOCABULARY – CensusCombinationDifferenceDivergeExpansionExperimentPopulationSeriesStatisticsSurveyTendencyVariance