Mathematics: CCSS.Math.Content.HSG-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. CCSS.Math.Content.HSG-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. CCSS.Math.Content.HSG-CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. CCSS.Math.Content.HSG-CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CCSS.Math.Content.HSG-CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. CCSS.Math.Content.HSG-CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. CCSS.Math.Content.HSG-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. CCSS.Math.Content.HSG-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

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) 

10 Q1 MATH PROCESS PRODUCT/ASSESSMENTGeometry and how it applies to real-world situationsEssential QuestionsGeometric principles found in locations around the worldGeometric principles found in the school(IE parallel, perpendicular, congruent on a map of Manhattan city streets).Enduring Understanding

Geometry and how it applies to real-world situationsAnalyze and identify of proportions, angles and measurementsComplete a project based on historical architecture Complete assignments to strengthen skills Complete sample questions from NYS Regents/RCT examsCreate a glossary of terms with diagrams & examples Engage in class discussionsIdentify key areas of content Record notes & sample problems for referenceUse appropriate language in writing and in conversations 

Geometry and how it applies to real-world situationsAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q1 MATH PROCESS PRODUCT/ASSESSMENTUsing different types of measurement to representideasEssential QuestionsAbsolute value and coordinate figuresApplying degreesConverting units of measurementMeasuring three dimensional figuresUsing appropriate units of measurementEnduring Understanding

Using different types of measurement to representideasApply knowledge of two dimensional figures to three dimensional figures for surface area, volume and creation of appropriate formulasConvert simple units of measurement (inches to feet, cm to m to km) in order to best suit different situations (measuring height of people in feet not miles)Identify new areas as well as refresh algebra conceptsReview ‘absolute value’ to measure geometric figures that fall into negative quadrantsUse & manipulate different tools (protractors, rulers, compass) to correctly measure using appropriate units (feet, meters, degrees)Use degrees for creation of algebraic formulas based on complimentary/supplementary angles, polygons, transversals and geometric proofs

Using different types of measurement to represent ideasAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q1 MATH PROCESS PRODUCT/ASSESSMENTThe process of proving congruenceof different figuresEssential QuestionsAlgebraic proofsCongruence  of Parallel lines and transversalsCongruence of trianglesRules of congruenceUsing postulates to prove simple statementsEnduring Understanding

The process of proving congruence of different figuresCreate personal study guides based on rules of congruence for different geometric figures including, but not limited to parallel lines, angles, vertical angles, horizontal angles and polygonsProve figures to be congruent, first with algebra for vertical and horizontal angles, continued onto polygonsReview examples of Regents’ questionsUse given information as well as a list of postulates to prove geometric figures congruent to one anotherUtilize study guide of postulates to identify congruent triangles Analyze appropriate logical and organizational methods for proofs

The process of proving congruence of different figuresAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q1 MATH PROCESS PRODUCT/ASSESSMENTWays in which modeling is used to better representdata and help solve difficult problemsEssential Questions

Enduring Understanding

Ways in which modeling is used to better represent data and help solve difficult problemsModel and measure to scale a location of choiceUtilize appropriate tools to create sketches and measure to scale different figuresUtilize appropriate tools to measure two and three dimensional figures

Ways in which modeling is used to better represent data and help solve difficult problemsAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

10 Q1 MATH VOCABULARY –AcuteAdjacentAxisBaseComplementaryCongruentDegreeDistanceMetersMidpointObtuse ParallelPerimeterPerpendicularPointProofSegmentSpaceSupplementarySurfaceVertex

Mathematics: 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-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.CCSS.Math.Content.HSG-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.CCSS.Math.Content.HSG-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. CCSS.Math.Content.HSG-CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. CCSS.Math.Content.HSG-CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CCSS.Math.Content.HSG-CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. CCSS.Math.Content.HSG-CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point . CCSS.Math.Content.HSG-CO.C.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

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) 

10 Q2 MATH PROCESS PRODUCT/ASSESSMENTThe reasons why the properties of shapes with circular bases are similar/different thanother figures observedEssential QuestionsHow do we use the appropriate tools when measuring circular figures? How do we utilize different equations for area, volume, surface area, diameter and circumference?How does pi apply to all circlesWhat is pi?Enduring UnderstandingThe historical concept of pi, its origins and meaning serves as a means of application. Appropriate tools are necessary to measure circumference and diameter of various real world objects to show that pi as a ratio is constant.

The reasons why the properties of shapes with circular bases are similar/different thanother figures observedApply measurements to determine area, volume, surface, circumference and diameterComplete assignments Complete sample questions from NYS Regents & RCT examsEngage in class discussions Manipulate equations as neededRecord notes & sample problems Use appropriate language in writing and in conversations

The reasons why the properties of shapes with circular bases are similar/different thanother figures observedAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q2 MATH PROCESS PRODUCT/ASSESSMENTCombining the properties of geometry and algebrato define the characteristics of plotson a coordinate planeEssential QuestionsHow are ‘concepts’ physically represented in our surroundings?How are coordinates plotted on axis?How do we find intercept points and intersecting point of two lines?How do we prove lines parallel or perpendicular?What is the formula for a line, how do its components represent the different characteristics of that line?When and where can these concepts apply to real world situations?Enduring Understanding

Combining the properties of geometry and algebrato define the characteristics of plotson a coordinate planeCreate equations using real world examples of parallel and perpendicular lines to show how individuals utilize these skills across a variety of different fieldsDetermine perpendicular lines, parallel lines & intercept pointsPlot points and create lines to understand the values of slope, x and y intercepts in the formula y=mx+bReview the properties of a coordinate plane

Combining the properties of geometry and algebrato define the characteristics of plotson a coordinate planeAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q2 MATH PROCESS PRODUCT/ASSESSMENTUsing our understanding of congruence to provedifferent characteristics of trianglesEssential QuestionsHow do we use our knowledge of congruence of angles and lengths to show that triangles are congruent or not congruent?How is proving the characteristics of triangles similar and different to congruence in lines and individual angles.What are the acceptable methods for proving the congruence of two triangles?What are the defining properties and characteristics of triangles What is the appropriate form for a triangle proof?Enduring Understanding

Using our understanding of congruence to provedifferent characteristics of trianglesDetermine the appropriate characteristics of trianglesProve triangles through the appropriate stepsProve whether or not triangles meet the appropriate criteria for similarity or congruenceRecognize the characteristics of triangles 

Using our understanding of congruence to provedifferent characteristics of trianglesAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q2 MATH PROCESS PRODUCT/ASSESSMENTThe characteristics of other quadrilateralsEssential QuestionsHow can we apply our knowledge of angles, lengths and triangles to solving geometric problems involving polygons?How do the characteristics of polygons allow us to apply mathematical reasoning to corresponding problems? How do we apply the properties of quadrilaterals to real world problem solving situations?Enduring UnderstandingAlgebra problems involve recognition of characteristics of different shapes as well as applications of the general rules of algebra. Algebra can be utilized to create equations based on real world situations.

The characteristics of other quadrilateralsApply knowledge of proved Explore the properties each type of quadrilateral possesses Solve problems related to real world situationsUndertake single or multi step/variable questions 

The characteristics of other quadrilateralsAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q2 MATH 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 figuresAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

10 Q2 MATH VOCABULARY –AltitudeAuxiliaryConcurrentCongruentContradictionCorrespondingDilationEnlargementEquilateralIndirectMedianPerpendicularProportionRatioReductionReflectionRotationScaleTransformationTranslation

Mathematics: 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-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.★CCSS.Math.Content.HSG-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.CCSS.Math.Content.HSG-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.CCSS.Math.Content.HSG-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★CCSS.Math.Content.HSG-CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).CCSS.Math.Content.HSG-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.CCSS.Math.Content.HSG-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.CCSS.Math.Content.HSG-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.CCSS.Math.Content.HSG-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.CCSS.Math.Content.HSG-SRT.D.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.CCSS.Math.Content.HSG-SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.CCSS.Math.Content.HSG-SRT.D.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).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.

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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) 

10 Q3 MATH PROCESS PRODUCT/ASSESSMENTApplying prior knowledge of geometric principals to trigonometryEssential QuestionsHow can we apply the use of ratios to Pythagorean Triples?How does geometric mean help us to understand the dimensions of similar triangles?How does the converse of the Pythagorean Theorem allow us to classify triangles without knowing their angles?What types of triangles can be treated differently as individual applications?Enduring Understanding

Applying prior knowledge of geometric principals to trigonometryApply prior knowledge towards the Pythagorean theoremApply the same idea over a variety of different areasCreate a glossary of terms with diagrams & examples Complete sample questions from NYS Regents/RCT exams Use appropriate language in writing and in conversationsCreate altitudes on given right trianglesDetermine how ratios between angles can be expressedEngage in class discussionsExpress knowledge of ratios Identify triangles found in different situations Record notes & sample problemsRelate the use of ratios to Pythagorean triples Show how inequalities can be applied outside of linear and quadratic equationsUtilize new formulas

Applying prior knowledge of geometric principals to trigonometryAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q3 MATH PROCESS PRODUCT/ASSESSMENTTrigonometry and applying it to problem solvingEssential QuestionsHow are trigonometric principles used to solve for unknown?How do we apply laws of sine/cosine to solve problems in non-right triangles?How do we apply trigonometry towards solving problems involving vectors?What ratios are represented by sine, cosine and tangent?When are secant, cosecant and cotangent used to solve for unknown values?When can we apply these ratios towards solving real world problems?Enduring UnderstandingThe secant, cosecant and cotangents are inverted forms of trigonometric functions. Sine, cosine and tangent are applied in problems involving right triangles to solve for the unknown.

Trigonometry and applying it to problem solvingApply concepts to solve logical and real world problemsApply inverse functions to find solutionsSolve for unknowns through graphing and algebraUse defined mathematical laws and inequalities to solve problems featuring non-right trianglesUtilize knowledge of trigonometry to solve basic physics problems involving vectorsUtilize technology when appropriate

Trigonometry and applying it to problem solvingAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q3 MATH PROCESS PRODUCT/ASSESSMENTUsing algebraic principles to manipulate imagesFound on a coordinate planeEssential QuestionsHow are figures dilated to make them either larger or smaller, yet still remaining in consistent ratio?How are lines reflected over a given line?How are lines reflected over the x and y axis?How can figures be rotated about a given point?What are reflections and how is symmetry expressed on a coordinate plane?When can we utilize lines of symmetry and how are these lines expressed algebraically?When using transformations, to where can figures be moved on a coordinate plane?Enduring UnderstandingReflections can be expressed both graphically and algebraically. The location of a figure’s reflection can also be predicted when a figure is rotated about a given point. Understanding how to manipulate individual points and full equations to transform figures from one place to another on a coordinate plane while retaining all properties except position can aid in real life manipulation of concrete objects.

Using algebraic principles to manipulate imagesFound on a coordinate planeExpress a figure algebraically both before and after a rotationIdentify situations where symmetry is expressed on a coordinate plane and in the real worldUse dilations to maintain the ratios and proportions of a figure, while changing the overall size

Using algebraic principles to manipulate imagesFound on a coordinate planeAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q3 MATH PROCESS PRODUCT/ASSESSMENTWorking with the unique properties of circlesEssential QuestionsHow are ratios applied when determining arcs and angles?How do we recall prior knowledge of circumference and diameter to solve problems now involving measurement of angles?What are concentric circles and congruent circles and how do we use their properties to solve mathematical and real world problems?What tools are best suited for measuring angles and arcs?Enduring UnderstandingAlthough all circles have the same ratios involving diameter and circumference, concentric and congruent circles have other essential aspects that allow us to solve for unknown values. There are ratios that can be created involving ratio and arc which can be used to solve for unknowns. Knowledge of algebra and ratios can be enhanced by applying these concepts to geometry problems involving circles. Compasses are used to measure and create arcs.

Working with the unique properties of circlesApply concepts of algebra and ratios to geometry problems involving circlesCreate new arcsCreate ratios and arcs to solve for unknownsExplore concentric and congruent circles Manipulate new tools for measuring Solve for unknown valuesStudy given arcs

Working with the unique properties of circlesAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

10 Q3 MATH VOCABULARY – ArcCentralCircumferenceCircumscribeCompositionConcentricDepressionDiameterElevationInscribedInverseMagnitudeMeanRadiusRatioResultantRotationSegmentSymmetryTransformationTranslation

Mathematics: CCSS.MATH.CONTENT.HSS.CP.B.6 Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.CCSS.MATH.CONTENT.HSS.CP.B.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. CCSS.MATH.CONTENT.HSS.CP.B.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.     CCSS.MATH.CONTENT.HSS.CP.B.9   (+) Use permutations and combinations to compute probabilities of compound events and solve problems. CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. CCSS.MATH.CONTENT.HSG.CO.C.11Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals . CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. CCSS.MATH.CONTENT.HSG.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. CCSS.MATH.CONTENT.HSG.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. CCSS.MATH.CONTENT.HSG.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. CCSS.MATH.CONTENT.HSG.SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. CCSS.MATH.CONTENT.HSG.SRT.D.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. CCSS.MATH.CONTENT.HSG.SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems. CCSS.MATH.CONTENT.HSG.SRT.D.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). 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. CCSS.MATH.CONTENT.HSG.C.A.4 (+) Construct a tangent line from a point outside a given circle to the circle.CCSS.MATH.CONTENT.HSG.C.B.5      Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. CCSS.MATH.CONTENT.HSG.GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. CCSS.MATH.CONTENT.HSG.GMD.A.2 (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. CCSS.MATH.CONTENT.HSG.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*CCSS.MATH.CONTENT.HSG.GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. CCSS.MATH.CONTENT.HSG.MG.A.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*CCSS.MATH.CONTENT.HSG.MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*

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) 

10 Q4 MATH PROCESS PRODUCT/ASSESSMENTRelating knowledge of triangles and angles to circlesEssential QuestionsHow can circles be constructed using appropriate tools with and without technology?How can the equation of a circle be manipulated to change size while maintaining the same ratios?How can we apply aspects of trigonometry towards questions involving circles?What are tangents and how are they used to solve problems involving multiple circles?What are the appropriate ratios for angles in circles?What is the appropriate form for the equation of a circle?When are special segments of a circle used appropriately for solving problems?Enduring UnderstandingWhile a circle’s center point, diameter and circumference may change, the ratios that exist are similar in all circles.

Relating knowledge of triangles and angles to circlesApply the appropriate ratios of tangents, secants, interior angles and chords when given particular circumstancesCreate appropriate illustrations of tangents, secants and cosecantsDerive the equation of a circleEnhance understanding of trigonometry and trigonometry ratios by applying them to circular figuresRecord notes & sample problemsRelate aspects previously learned in trigonometry to circular figuresSolve problems related to a circular equation, graphing with appropriate technology for given circumstancesUse appropriate language in writing and in conversations Complete questions from NYS Regents/RCT examsUtilize special equations for circles at appropriate times Engage in class discussions 

Relating knowledge of triangles and angles to circlesAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q4 MATH PROCESS PRODUCT/ASSESSMENTThe practical applications of determining the areaof polygons and circlesEssential QuestionsHow can proportions be used to solve problems involving similar polygons?How can regular polygons inscribed inside of circles aid in the solving of problems with trigonometry?How do these general formulas relate to determining the area of compound figures?What are the basic formulas for determining area of polygons?What is Pi and how is it derived?When can inscribing regular polygons inside of a circle be useful for solving real world problems?Why are area formulas similar and how are they derived from the basic form of base * height?Enduring UnderstandingPi is a fixed ratio between the circumference and diameter of a circle.

The practical applications of determining the areaof polygons and circlesConstruct inscribed polygons inside of a circleDemonstrate an appropriate understanding of proportions when solving for unknowns in two similar polygonsDerive formulas for polygonsDetermine area using characteristics of both circle & polygonDissect regular polygons into smaller parts which can be more easily measured and help to derive formulasRelate these actions to the distance formula and perform actions both on and off of a Cartesian planeReview prior knowledge in determining the area of polygonsUse trigonometry to solve for unknown values of inscribed figures

The practical applications of determining the areaof polygons and circlesAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q4 MATH PROCESS PRODUCT/ASSESSMENTApplying the concepts of trigonometry and area toward solving advanced problems relating to volume and surface areaEssential QuestionsHow can we derive the basic formulas for surface area from known area formulas?What are the equations for surface area of polygon based figures?How does surface area increase efficiency in engineering models?How do the formulas of figures with circular bases differ from other equations?When can trigonometric properties of circles be applied to three dimensional figures? What is the relationship between determining distance across the surface of a sphere and latitude and longitude?Enduring Understanding

Applying the concepts of trigonometry and area toward solving advanced problems relating to volume and surface areaDerive formulas for volume and surface area by recalling prior knowledge based on area.Understand that all prism related figures have the same basic formula of area of base * height.Solve for variables and unknowns related to volume and surface area.Understand that surface area is a critical measurement for engineering design, increasing efficiency and minimizing size.Apply trigonometric properties to three dimensional figures with both circular and noncircular bases.Relate the concepts of surface distance to latitude and longitude in science and social studies.

Applying the concepts of trigonometry and area toward solving advanced problems relating to volume and surface areaGlossary of terms with diagrams & examples Projects Worksheets

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) 

10 Q4 MATH PROCESS PRODUCT/ASSESSMENTApplying probability and measurement to geometryEssential QuestionsWhat are the key representations and vocabulary associated with probability?How can probability be related to the sides of polygons?In what ways can a circle be divided into equal and unequal parts so that it might be a proper representation of a given probability set?How is probability expressed in terms of independent and dependent variables?How are mutually exclusive events represented graphically?Enduring Understanding

Applying probability and measurement to geometryAccess prior knowledge of trigonometry to help divide circles and polygons into smaller equal and unequal partsDivide polygons and circles into smaller equal and unequal segments to represent data in a given setGraph and display data appropriatelyIdentify independent and dependent variables in scientific and empirical studiesRepresent mutually exclusive events using symbols and graphic representationsUse appropriate unites of measurement for given problemsUtilize appropriate vocabulary, terminology and symbols when speaking and writing about probability and measurement

Applying probability and measurement to geometryAssignmentsGlossary of terms with diagrams & examples Projects Worksheets

10 Q4 MATH VOCABULARY – AltitudeCenterCentralCombinationCongruent DiagramObliquePermutationProbability Sample Sector SegmentSemicircle SimulationSolidStatisticsValueVariableVolume