Common Core Standards: Literacy - MAthematics



|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..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..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 SS.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 |

|SS.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. |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q1 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|The difference between Algebra I and Algebra II |The difference between Algebra I and Algebra II |The difference between Algebra I and Algebra II |

|Essential Questions |Apply basic algebraic skills |Assignments selected from the AGS texts provided |

|How are cube roots similar to square roots in terms of simplification? |Compare and contrast even and odd number radicals |Completed sample questions from NYS Regents and RCT examinations|

|How can we utilize appropriate algebraic thinking to solve for variables? |Create a series of word problems to represent the different concepts |Glossary of important terms complete with diagrams and examples |

|How will our past knowledge help us in future endeavors? |being explored |Recorded notes of sample problems |

|What are the methods we use to simplify expressions? |Factor and explain the cube roots of numbers and variables | |

|When is it beneficial to express radical expressions with fractional exponents? |Perform algebraic methods | |

|Why are negative results acceptable when dealing with odd numbered radicals? |Review methods used to solve algebra problems | |

|Enduring Understanding |Simplify expressions so that they become more useful for solving | |

| |problems in the real world. | |

| |Utilize different functions to solve for unknowns | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q1 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|Situations in which different types of studies can be used |Situations in which different types of studies can be used |Situations in which different types of studies can be used to |

|to yield meaningful results |to yield meaningful results |yield meaningful results |

|Essential Questions |Determine if the correct type of study has been used by an individual |Assignments selected from the AGS texts provided |

|How can this information be useful in different academic and research areas? |or group when given raw data |Completed sample questions from NYS Regents and RCT examinations|

|What are the attributes of surveys, observations and controlled experiments? |Explore the different types of studies that are used in mathematics |Glossary of important terms complete with diagrams and examples |

|When are the appropriate situations to use each of the previous methods? |and science to make appropriate and accurate generalizations and |Recorded notes of sample problems |

|Enduring Understanding |predictions about populations | |

| |Expose the flaws of each type of study | |

| |Use the characteristics of a population and potential outcome to | |

| |determine the best type of study to use in a given situation | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q1 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|Applying the Pythagorean Theorem to the unit circle |Applying the Pythagorean Theorem to the unit circle |Applying the Pythagorean Theorem to the unit circle |

|Essential Questions |Apply a radius of one to make fractional ratios simpler |Assignments selected from the AGS texts provided |

|What is the unit circle? |Derive the trigonometric identity sin2 + cos2 = 1 from basic |Completed sample questions from NYS Regents and RCT examinations|

|How do the characteristics of the unit circle give us useful information for proofs?|trigonometric ratios and the Pythagorean Theorem |Glossary of important terms complete with diagrams and examples |

|How is the identity sin2 + cos2 = 1 derived from the Pythagorean Theorem? |Explore how the sine and cosine fluctuate with one another as we have |Recorded notes of sample problems |

|Why do the ratios of cosine and sine change because of a constant radius? |a constant hypotenuse | |

|Why are triangles the best choice for inscribing? |Recognize that the defining characteristic of all circles is a | |

|Enduring Understanding |constant radius | |

| |Utilize knowledge of the unit circle and trigonometry to inscribe | |

| |other shapes | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q1 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|A normal distribution curve |A normal distribution curve |A normal distribution curve |

|How is mean determined and how do we use this average to model real world |Analyze data and make predictions from the use of a standard deviation|Assignments selected from the AGS texts provided |

|situations? |curve |Completed sample questions from NYS Regents and RCT examinations|

|What are standard deviations and how are they used to analyze and predict |Calculate the number of individuals within each standard deviation |Glossary of important terms complete with diagrams and examples |

|information and data? |when given a bell curve |Recorded notes of sample problems |

|Enduring Understanding |Determine the mean of a given sample set | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q1 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|Systems of equation and how they are solved |Systems of equation and how they are solved |Systems of equation and how they are solved |

|How is solving a system of three equations similar to and different than solving for|Discover and utilize the imaginary number i to solve and simplify |Assignments selected from the AGS texts provided |

|two equations? |equations with a negative radical |Completed sample questions from NYS Regents and RCT examinations|

|Which attributes of a system can be exploited for solving for unknowns? |Evaluate and apply the best strategy to use when solving a given |Glossary of important terms complete with diagrams and examples |

|When are matricies useful in solving systems of equations? |problem (i.e. graphically, by substitution, by elimination) |Recorded notes of sample problems |

|How can we solve linear quadratic systems graphically and algebraically? |Recall prior information on the solving of systems of two equations | |

|What is the imaginary number i? |Solve for unknowns in linear quadratic systems. | |

|When does the imaginary number occur and how does it help us to answer questions |Understand that matrices are arrays that are useful representation | |

|that were unanswerable in the past? |systems of more than three equations | |

|Enduring Understanding |Utilize strategies used for systems of two equations when solving | |

| |systems of three equations | |

|11 Q1 MATHEMATICS VOCABULARY – |

|Alternative |

|Causation |

|Census |

|Dependent |

|Distribution |

|Expression |

|Formula |

|Independent |

|Maximum |

|Minimum |

|Sample |

|Sequence |

|Standard |

|MATHEMATICS:CCSS.MATH.CONTENT.HSN.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of SS.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 SS.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 SS.MATH.CONTENT..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 SS.MATH.CONTENT..A.2 Use the relation i2 = -1 and the commutative, associative, and distributive properties to |

|add, subtract, and multiply complex numbers. |

|CCSS.MATH.CONTENT..A.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex SS.MATH.CONTENT..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..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..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 |

|SS.MATH.CONTENT..C.7 Solve quadratic equations with real coefficients that have complex SS.MATH.CONTENT..C.8 (+) Extend polynomial identities to the complex numbers. For example, |

|rewrite x2 + 4 as (x + 2i)(x - 2i). |

|CCSS.MATH.CONTENT..C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic SS.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 SS.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 |

|SS.MATH.CONTENT.HSF.LE.A.1.B Recognize situations in which one quantity changes at a constant rate per unit interval relative to SS.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 SS.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 SS.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 SS.MATH.CONTENT.HSF.TF.A.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of |

|trigonometric SS.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 SS.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 SS.MATH.CONTENT.HSF.TF.C.9 (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to |

|solve problems. |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q2 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|How trigonometric ratios are used |How trigonometric ratios are used |How trigonometric ratios are used |

|outside of right triangles |outside of right triangles |outside of right triangles |

|Essential Questions |Derive the Law of Sines to prove that it is true for future use. |Assignments selected from the AGS texts provided |

|What is the Law of Sines? |Recognize the types of situations where the Law of Sines can be |Completed sample questions from NYS Regents and RCT examinations|

|How can we prove the Law of Sines using multiple triangles? |utilized to solve for unknowns |Glossary of important terms complete with diagrams and examples |

|What is the Law of Cosines? |Understand that the ratios need not be found for all angles and sides |Recorded notes of sample problems |

|How can we prove the Law of Cosines using our knowledge of right triangles? |Relate knowledge of geometric proofs to trigonometry. | |

|When is it appropriate to use the Law of Sines vs. Law of Cosines? |Derive the Law of Cosines to prove that it is true for future use. | |

|How can we use trigonometry to find the area of geometric figures? |Recognize the types of situations where the Law of Cosines can be | |

|Enduring Understanding |utilized to solve for unknowns | |

| |Understand that capital letters and lower case letters represent | |

| |angles and sides respectively | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q2 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|The applications and meaning of the imaginary unit i |The applications and meaning of the imaginary unit i |The applications and meaning of the imaginary unit i |

|Essential Questions |Define the imaginary unit as the square root of negative one |Assignments selected from the AGS texts provided |

|How can imaginary numbers with exponents be simplified? |Understand the history and origins that created the need for an |Completed sample questions from NYS Regents and RCT examinations|

|How does the imaginary unit arise in questions related to parabolas? |imaginary number system |Glossary of important terms complete with diagrams and examples |

|What are the practical applications of the imaginary unit? |Create a method to remember the pattern of simplified imaginary |Recorded notes of sample problems |

|What is a + bi form and how is it used for expressions with imaginary and real |numbers | |

|numbers? |Derive the reasons for the pattern of imaginary numbers. | |

|What is the definition of the imaginary unit? |Understand that all numbers can be expressed in the | |

|What is the repeating pattern that appears with imaginary numbers with exponents |form a + bi | |

|between 1 and 4? |Simplify expressions with both imaginary and mixed imaginary and real | |

|Enduring Understanding |numbers | |

| | | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q2 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|Inverse ratios in trigonometry |Inverse ratios in trigonometry |Inverse ratios in trigonometry |

|Essential Questions |Derive trigonometric identities listed on reference sheet |Assignments selected from the AGS texts provided |

|How are cosecant, secant and cotangent different than sine cosine and tangent? |Review basic functions of trigonometry used in right triangles |Completed sample questions from NYS Regents and RCT examinations|

|How are inverse functions useful for simplifying complicated expressions? |Simplify expressions using identities and the fundamental aspects of |Glossary of important terms complete with diagrams and examples |

|How can we use algebraic strategies to simplify trigonometric expressions? |trigonometry |Recorded notes of sample problems |

|What are trigonometric identities? |Understand that cosecant, secant and cotangent are inverse ratios | |

|Enduring Understanding |related to sine, cosine and tangent | |

| |Use these inverse ratios as a method of simplifying expressions by | |

| |creating fractions of 1:1 | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q2 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|Expressing trigonometric functions visually |Expressing trigonometric functions visually |Expressing trigonometric functions visually |

|Essential Questions |Convert degrees to radians and radians to degrees |Assignments selected from the AGS texts provided |

|What are radians and why are they used instead of degrees? |Convert the values of a unit circle from degrees to radians |Completed sample questions from NYS Regents and RCT examinations|

|How do we convert degrees to radians? |Determine the relationship between radians and degrees |Glossary of important terms complete with diagrams and examples |

|Where are the locations of critical values of sine, cosine and tangent on a graph? |Find the critical values on a unit circle |Recorded notes of sample problems |

|What are the domain, range and undefined values for these graphs? |Relate arc length of the unit circle to the interior angles being | |

|How are these graphs on the Cartesian plane related to the unit circle? |created | |

|What is the relationship between arc length and interior angles? |Relate the critical values from the unit circle to the Cartesian plane| |

|Enduring Understanding |by graphing sine, cosine and tangent waves | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q2 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|How quadratic functions are used to represent |How quadratic functions are used to represent |How quadratic functions are used to represent |

|real world situations |real world situations |real world situations |

|Essential Questions |Compare values by utilizing linear quadratic systems |Assignments selected from the AGS texts provided |

|What are the different methods for determining the roots of a quadratic function? |Determine the minimum or maximum of a parabola |Completed sample questions from NYS Regents and RCT examinations|

|What are the potential solution sets of quadratic functions? |Determine the most effective strategy to solve linear quadratic |Glossary of important terms complete with diagrams and examples |

|When is the quadratic equation useful for determining the roots of a function? |systems |Recorded notes of sample problems |

|How do quadratic equations represent motion? |Determine whether or not answers are acceptable based on the | |

|What are the other critical values that can be evaluated? |parameters presented by the question | |

|When are inequalities useful for representing data? |Use inequalities to represent real world situations | |

|How can we utilize linear quadratic systems to Compare two different sets of |Use quadratic functions to represent motion | |

|information? |Use the factoring, quadratic equation and graphing methods for finding| |

|Enduring Understanding |the roots of a quadratic equation | |

| |Utilize the quadratic equation when a discriminant is not a perfect | |

| |square | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q2 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|How ratios are used to show similarities and |How ratios are used to show similarities and |How ratios are used to show similarities and differences in |

|differences in geometric figures |differences in geometric figures |geometric figures |

|Essential Questions |Analyze how proportions and fractions are used to represent real world|Assignments selected from the AGS texts provided |

|How are parallel lines related to proportional measurements of triangles and other |tangible items |Completed sample questions from NYS Regents and RCT examinations|

|polygons? |Review fractions, reduction and similar concepts |Glossary of important terms complete with diagrams and examples |

|How do ratios apply to similar figures, how are differences in lengths of sides |Utilize proportions as a separate entity from geometry |Recorded notes of sample problems |

|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 Understanding | | |

|Knowledge 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. | | |

|11 Q2 MATHEMATICS VOCABULARY – |

|Convert |

|Coordinates |

|Degree |

|Equation |

|Function |

|Identity |

|Laws |

|Linear |

|Roots |

|Simplify |

|System |

|Unit |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q3 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|Using trigonometry to find the area |Using trigonometry to find the area |Using trigonometry to find the area |

|of geometric shapes |of geometric shapes |of geometric shapes |

|Essential Questions |Demonstrate understanding of geometric properties needed to prove |Assignments selected from the AGS texts provided |

|How is the trigonometric formula for the area of a triangle similar to k = ½ b*h |similarity of triangles |Completed sample questions from NYS Regents and RCT examinations|

|What is the proper notation used in advanced mathematics for the labeling of sides |Derive Heron’s formula |Glossary of important terms complete with diagrams and examples |

|and angles of triangles? |Derive the formula for area of a triangle using trigonometry |Recorded notes of sample problems |

|What characteristics of a triangle are needed to find area using the formula k = 1/2|Derive the formula for the area of a triangle using base and height | |

|absinC? |Modify the equation for the trigonometric area of a triangle to suit | |

|What are the characteristics of a parallelogram that relate them to triangles? |the needs of a parallelogram. | |

|How can the formula for triangular area be modified to use with parallelograms? |Relate the properties of triangles and rectangles to the properties of| |

|What is Heron’s Law? |parallelograms | |

|How can Heron’s Law be used to find the area of triangles where angles are not |Solve for the unknown area of a triangle using the formula k= | |

|given? |1/2absinC | |

|Enduring Understanding |Use Heron’s formula to solve for the area of geometric figures when | |

| |angle measures are not given | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q3 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|Referencing triangles to help more accurately |Referencing triangles to help more accurately |Referencing triangles to help more accurately |

|express common answers in trigonometry |express common answers in trigonometry |express common answers in trigonometry |

|Essential Questions |Utilize the unit circle to define the angle measures and trigonometric|Assignments selected from the AGS texts provided |

|What are reference triangles? |ratios found in common right triangles |Completed sample questions from NYS Regents and RCT examinations|

|Why are these common triangles chosen to be used both inside and outside of the |Explain the rationale for the use of common right triangles in |Glossary of important terms complete with diagrams and examples |

|classroom? |practical applications |Recorded notes of sample problems |

|Why are answers expressed in terms of radials more accurate than decimal |Express ratios and side lengths using radicals to more properly answer| |

|approximations? |questions | |

|How are these concepts applicable to the unit circle? |Simplify given equations using radicals to properly express | |

|Enduring Understanding |trigonometric ratios | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q3 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|How identifying formulas helps solve complex |How identifying formulas helps solve complex |How identifying formulas helps solve complex |

|trigonometry problems |trigonometry problems |trigonometry problems |

|Essential Questions |Apply double angle formulas towards solving real world situations |Assignments selected from the AGS texts provided |

|What are the sum and difference formulas? |involving mechanical engineering and optimization. |Completed sample questions from NYS Regents and RCT examinations|

|How are the sum and difference formulas derived? |Apply half angle formulas to real world situations |Glossary of important terms complete with diagrams and examples |

|How are these formulas used to solve for unknowns on a coordinate plane? |Derive double angle formulas for use in future assignments and |Recorded notes of sample problems |

|What are the practical applications of sum and difference formulas? |questions | |

|What are the double angle formulas? |Derive half angle formulas | |

|How are double angle formulas derived? |Derive sum and difference formulas to better understand their use | |

|How can double angle formulas be used to simplify more complex trigonometric |Relate half angle formulas to double angle formulas | |

|expressions and equations? |Simplify complex equations and solve for unknown values using the sum | |

|What are the practical applications of the double angle formulas? |and difference formulas | |

|What are the half angle formulas? |Simplify expressions using double angle formulas | |

|How are half angle formulas derived? |Utilize half angle formulas to simplify statements and solve for | |

|What are the relationships between the double angle formulas and half angle |unknown values | |

|formulas? |Utilize sum and difference formulas to simplify trigonometric | |

|What are the practical applications of half angle formulas? |expressions | |

|Enduring Understanding | | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q3 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|How trigonometric concepts are expressed as functions |How trigonometric concepts are expressed as functions |How trigonometric concepts are expressed as functions |

|Essential Questions |Determine the equations of given trigonometric graphs |Assignments selected from the AGS texts provided |

|How do the functions of f(x) = sin(x), f(x) = cos(x) and f(x) = tan(x) behave when |Explain why the periods of functions show repetition of the same |Completed sample questions from NYS Regents and RCT examinations|

|graphed on a trigonometric plane? |pattern as they pass through 2pi radians |Glossary of important terms complete with diagrams and examples |

|What are the periods of these functions and how are they related to the unit circle?|Express the graphs of trigonometric functions on a coordinate plane |Recorded notes of sample problems |

|What types of natural and manmade phenomena are represented by waves? |Predict the changes in a trigonometric graph when coefficients and | |

|How are the characteristics of the graphs of trigonometric functions reflected in |constants are included in the function | |

|the characteristics of right triangles? |Relate the graphs of trigonometric functions to the unit circle | |

|What are the domains and range of trigonometric functions? |Show a relationship between sine and cosine, showing that their graphs| |

|What are the changes in the graphs of functions when coefficients and constants are |move constantly in fluctuation with one another | |

|involved? | | |

|How can trigonometric equations be obtained using an associated graph? | | |

|Enduring Understanding | | |

|How does it apply to content areas? What content are you currently exploring?  This |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q3 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|How patterns, functions and relationships are |How patterns, functions and relationships are |How patterns, functions and relationships are expressed |

|expressed algebraically and graphically |expressed algebraically and graphically |algebraically and graphically |

|Essential Questions |Apply inverse functions to real world situations |Assignments selected from the AGS texts provided |

|What are the defining characteristics of a sequence? |Apply sigma notation to real world situations involving series and |Completed sample questions from NYS Regents and RCT examinations|

|In what ways can a sequence be expressed? |sample space |Glossary of important terms complete with diagrams and examples |

|What is Sigma notation and what operations does it help us to perform? |Define the characteristics that differ between sequences and patterns |Recorded notes of sample problems |

|What are the practical applications of Sigma notation? |Differentiate between functions and relations | |

|How can arithmetic and geometric sequences and series help us to express an even |Express population growth and decline using arithmetic and geometric | |

|growth or decline? |sequences | |

|What is the proper notation utilized with recursive sequences? |Express sequences visually, algebraically and graphically | |

|What are the differences between relations and functions? |Use Sigma notation to show the total sum of a given series or function| |

|How can we express the inverse of a function? |Use the inverse of a function to make predictions and gather | |

|What are the practical applications of the inverses of functions? |conclusions about the function | |

|Enduring Understanding | | |

|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 |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning  (ie graphic organizers, |

|can be shared through essential questions, content standards, or a brief narrative |resources/ references, direct instruction, collaborative learning, inquiry)  |

|11 Q4 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|How exponential functions represent real world |How exponential functions represent real world situations |How exponential functions represent real world situations |

|situations |Apply constraints and components to the basic form of the function|Assignments selected from the AGS texts provided |

|Essential Questions |and observe changes in the graphed form |Completed sample questions from NYS Regents and RCT examinations |

|What are exponential functions and how do they differ from other functions that have|Demonstrate that in the standard form, exponents do not have |Glossary of important terms complete with diagrams and examples |

|been observed? |negative y values |Recorded notes of sample problems |

|What are the defining characteristics of an exponential function? |Evaluate exponentials | |

|How are asymptotes formed and why do they occur? |Graph and observe exponential functions in the basic form f(x) = | |

|How does the x0=1 effect the form of a exponential growth graph? |abx | |

|Why do exponential functions have no answers in the III and IV quadrants in the |Identify the key characteristics of this graph including the y | |

|general form? |intercept and horizontal asymptote | |

|When do exponential growth and decay occur and how does their occurrence modify our |Model real world situations with decay rates including radio | |

|general exponential function f(x) = abx? |carbon dating and population decay | |

|How does exponential growth in the form f(x) = a(1+r)x represent real world |Model real world situations with growth rates including | |

|situations? |demographic growth, bank account growth and bacterial growth | |

|How does exponential decay in the form f(x) = a(1-r)x represent real world | | |

|situations? | | |

|Enduring Understanding | | |

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

|This can be shared through essential questions, content standards, or a brief |references, direct instruction, collaborative learning, inquiry).  |

|narrative. | |

|11 Q4 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|How logarithms are used as a compliment to |How logarithms are used as a compliment to |How logarithms are used as a compliment to |

|exponential expressions and equations |exponential expressions and equations |exponential expressions and equations |

|Essential Questions |Apply the use of base 10 logarithms to real world situations |Assignments selected from the AGS texts provided |

|What is general conversion forms involving logarithms? |involving science and population growth |Completed sample questions from NYS Regents and RCT examinations |

|In what situations is a base 10 logarithm most useful? |Convert numbers with variables as exponents to logarithmic form in |Glossary of important terms complete with diagrams and examples |

|How are the properties of logarithms related to the properties of exponential |equations and expressions |Recorded notes of sample problems |

|functions? |Derive the natural logarithm e | |

|How can we use logarithms to solve for unknowns in equations? |Invert exponential functions as logarithmic functions | |

|When can we apply logarithms to exponential equations with unlike bases? |Utilize the natural logarithm e, to solve for unknowns | |

|Enduring Understanding | | |

|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 SS.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 domain |

|How does it apply to content areas? What content are you currently exploring?  |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning.  (ie. graphic |

|This can be shared through essential questions, content standards, or a brief |organizers, resources/ references, direct instruction, collaborative learning, inquiry).  |

|narrative. | |

|11 Q4 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|Performing operations on functions to create new |Performing operations on functions to create new |Performing operations on functions to create new |

|or combined outcomes |or combined outcomes |or combined outcomes |

|Essential Questions |Apply inverse functions to real world situations |Assignments selected from the AGS texts provided |

|What is a Composition of Functions and how does it model more complicated real |Compose functions with more than one original function ie (f * g)(x) |Completed sample questions from NYS Regents and RCT examinations |

|world situations? |Determine whether the inverse of a function is a function itself or a|Glossary of important terms complete with diagrams and examples |

|How can we evaluate a Composition of Functions? |relation |Recorded notes of sample problems |

|How are domain and range of Compositions of Functions different than other |Evaluate functions whose answers are the evaluations of other | |

|regular functions that have been observed? |functions. f(g(x)) | |

|What is the Inverse of a Function? |Graph inverse functions on a Cartesian plane | |

|In what ways does the graph of an inverse of a function differ from the original |Observe how inverse functions behave differently than the base | |

|graph? |functions when graphed | |

|When is the inverse of a function a relation? |Prove that (f * g)(x) and (g * f)(x) can, but do not have to have | |

|How do different translations change the graphed form of a function? |different results | |

|Enduring Understanding | | |

| | | |

|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 SS.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?  |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning.  (ie. graphic |

|This can be shared through essential questions, content standards, or a brief |organizers, resources/ references, direct instruction, collaborative learning, inquiry).  |

|narrative. | |

|11 Q4 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|Reasons the formula for a circle creates |Reasons the formula for a circle creates |Reasons the formula for a circle creates |

|a unique shape |a unique shape |a unique shape |

|Essential Questions |Access prior knowledge of the Pythagorean Theorem and apply towards |Assignments selected from the AGS texts provided |

|What is the basic form for the formula of a circle and what components does it |solving for unknowns in a circle |Completed sample questions from NYS Regents and RCT examinations|

|possess? |Apply knowledge of the equation of a circle to the unit circle |Glossary of important terms complete with diagrams and examples |

|How is the formula of a circle related to the Pythagorean Theorem? |Construct a circle from a given equation using a compass or with the |Recorded notes of sample problems |

|From what information can a circle be constructed? |aid of computerized design program | |

|How do we identify the center and radius of a circle when given its equation? |Derive the basic form of the equation of a circle x2+y2 = r2. | |

|Enduring Understanding |Identify the characteristics of a circle including radius, diameter, | |

| |center location using only the equation in non-graphed form | |

| |Use raw data in a given problem to solve and graph for any given | |

| |point on a circle | |

|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 concepts |

|How does it apply to content areas? What content are you currently exploring?  |What are the strategies/tools (Best Practice)? What strategies are being used to support teaching and learning.  (ie. graphic |

|This can be shared through essential questions, content standards, or a brief |organizers, resources/ references, direct instruction, collaborative learning, inquiry).  |

|narrative. | |

|11 Q4 MATHEMATICS |PROCESS |PRODUCT/ASSESSMENT |

|How probability and statistics help make |How probability and statistics help make |How probability and statistics help make predictions about |

|predictions about outcomes for different events |predictions about outcomes for different events |outcomes for different events |

|What are the basic parameters, formula and components of theoretical probability? |Apply prior knowledge of sigma notation to analyze data for large |Assignments selected from the AGS texts provided |

|When are permutations needed for expressing the total number of outcomes in a |sets |Completed sample questions from NYS Regents and RCT examinations|

|given event? |Create ratios for simple probability experiments /events |Glossary of important terms complete with diagrams and examples |

|How are permutations calculated with and without repetition of outcomes and |Derive the basic probability equation as a ratio of desired outcomes |Recorded notes of sample problems |

|arrangements? |divided by total outcomes | |

|What is the difference between a permutation and a combination? When are |Determine the range of potential outcomes of in relationship to a | |

|combinations used as opposed to permutations? |normal distribution curve | |

|How do regressions and binomial theory apply to probability? |Determine whether combinations are to be used for a given situation | |

|How does the Binomial Theorem apply to multiple related outcomes of a given |based on provided information | |

|situation? |Evaluate combinations when repetition is utilized in a given | |

|When can we use sigma notation to measure central tendency? What do measures of |situation | |

|dispersion tell us about the range of a given sample space and potential outcomes?|Express coherent information about the probability of an event using | |

| |permutations, combinations and sigma notation | |

|How can we relate this information to a statistical analysis on a distribution |Make predictions about the possibility of an outcome based on given | |

|curve? |information | |

| |Use permutations to determine the total number of outcomes for a | |

| |complicated event | |

|11 Q4 MATHEMATICS VOCABULARY – |

|Census |

|Combination |

|Difference |

|Diverge |

|Expansion |

|Experiment |

|Population |

|Series |

|Statistics |

|Survey |

|Tendency |

|Variance |

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