ࡱ> UXRST bjbj  4hUL -#####k%o+C,lmoooooo"ĭoQ,g%k%,,o##p333,<##m3,m33=|#0'3.|PY֧0J.tJJ5$,,3,,,,,oo#1t,,,,,,,J,,,,,,,,, : Mathematics:  HYPERLINK "http://www.corestandards.org/Math/Content/HSG/CO/A/1" CCSS.Math.Content.HSG-CO.A.1Know 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.  HYPERLINK "http://www.corestandards.org/Math/Content/HSG/CO/B/6" CCSS.Math.Content.HSG-CO.B.6Use 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.  HYPERLINK "http://www.corestandards.org/Math/Content/HSG/CO/B/7" CCSS.Math.Content.HSG-CO.B.7Use 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.  HYPERLINK "http://www.corestandards.org/Math/Content/HSG/CO/B/8" CCSS.Math.Content.HSG-CO.B.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.  HYPERLINK "http://www.corestandards.org/Math/Content/HSG/CO/C/9" CCSS.Math.Content.HSG-CO.C.9Prove 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 segments endpoints.  HYPERLINK "http://www.corestandards.org/Math/Content/HSG/CO/C/10" CCSS.Math.Content.HSG-CO.C.10Prove 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.  HYPERLINK "http://www.corestandards.org/Math/Content/HSG/CO/D/12" CCSS.Math.Content.HSG-CO.D.12Make 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.  HYPERLINK "http://www.corestandards.org/Math/Content/HSG/MG/A/1" CCSS.Math.Content.HSG-MG.A.1Use 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTGeometry and how it applies to real-world situations Essential Questions Geometric principles found in locations around the world Geometric 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 situations Analyze and identify of proportions, angles and measurements Complete a project based on historical architecture Complete assignments to strengthen skills Complete sample questions from NYS Regents/RCT exams Create a glossary of terms with diagrams & examples Engage in class discussions Identify key areas of content Record notes & sample problems for reference Use appropriate language in writing and in conversations Geometry and how it applies to real-world situations Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTUsing different types of measurement to represent ideas Essential Questions Absolute value and coordinate figures Applying degrees Converting units of measurement Measuring three dimensional figures Using appropriate units of measurement Enduring Understanding Using different types of measurement to represent ideas Apply knowledge of two dimensional figures to three dimensional figures for surface area, volume and creation of appropriate formulas Convert 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 concepts Review absolute value to measure geometric figures that fall into negative quadrants Use & 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 proofsUsing different types of measurement to represent ideas Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTThe process of proving congruence of different figures Essential Questions Algebraic proofs Congruence of Parallel lines and transversals Congruence of triangles Rules of congruence Using postulates to prove simple statements Enduring Understanding The process of proving congruence of different figures Create 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 polygons Prove figures to be congruent, first with algebra for vertical and horizontal angles, continued onto polygons Review examples of Regents questions Use given information as well as a list of postulates to prove geometric figures congruent to one another Utilize study guide of postulates to identify congruent triangles Analyze appropriate logical and organizational methods for proofsThe process of proving congruence of different figures Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTWays in which modeling is used to better represent data and help solve difficult problems Essential Questions Enduring Understanding Ways in which modeling is used to better represent data and help solve difficult problems Model and measure to scale a location of choice Utilize appropriate tools to create sketches and measure to scale different figures Utilize appropriate tools to measure two and three dimensional figuresWays in which modeling is used to better represent data and help solve difficult problems Assignments Glossary of terms with diagrams & examples Projects Worksheets  10 Q1 MATH VOCABULARY Acute Adjacent Axis Base Complementary Congruent Degree Distance Meters Midpoint Obtuse Parallel Perimeter Perpendicular Point Proof Segment Space Supplementary Surface Vertex Mathematics: CCSS.Math.Content.HSG-C.A.1Prove that all circles are similar. CCSS.Math.Content.HSG-C.A.2Identify 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.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. CCSS.Math.Content.HSG-CO.A.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. CCSS.Math.Content.HSG-CO.A.5Given 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.7Use 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.8Explain 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.9Prove 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 segments endpoints. CCSS.Math.Content.HSG-CO.C.10Prove 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. 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTThe reasons why the properties of shapes with circular bases are similar/different than other figures observed Essential Questions How 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 circles What is pi? Enduring Understanding The 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 than other figures observed Apply measurements to determine area, volume, surface, circumference and diameter Complete assignments Complete sample questions from NYS Regents & RCT exams Engage in class discussions Manipulate equations as needed Record notes & sample problems Use appropriate language in writing and in conversationsThe reasons why the properties of shapes with circular bases are similar/different than other figures observed Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTCombining the properties of geometry and algebra to define the characteristics of plots on a coordinate plane Essential Questions How 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 algebra to define the characteristics of plots on a coordinate plane Create equations using real world examples of parallel and perpendicular lines to show how individuals utilize these skills across a variety of different fields Determine perpendicular lines, parallel lines & intercept points Plot points and create lines to understand the values of slope, x and y intercepts in the formula y=mx+b Review the properties of a coordinate planeCombining the properties of geometry and algebra to define the characteristics of plots on a coordinate plane Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTUsing our understanding of congruence to prove different characteristics of triangles Essential Questions How 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 prove different characteristics of triangles Determine the appropriate characteristics of triangles Prove triangles through the appropriate steps Prove whether or not triangles meet the appropriate criteria for similarity or congruence Recognize the characteristics of triangles Using our understanding of congruence to prove different characteristics of triangles Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTThe characteristics of other quadrilaterals Essential Questions How 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 Understanding Algebra 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 quadrilaterals Apply knowledge of proved Explore the properties each type of quadrilateral possesses Solve problems related to real world situations Undertake single or multi step/variable questions The characteristics of other quadrilaterals Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTHow ratios are used to show similarities and differences in geometric figures Essential Questions How 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 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.How ratios are used to show similarities and differences in geometric figures Analyze how proportions and fractions are used to represent real world tangible items Review fractions, reduction and similar concepts Utilize proportions as a separate entity from geometry How ratios are used to show similarities and differences in geometric figures Assignments Glossary of terms with diagrams & examples Projects Worksheets  10 Q2 MATH VOCABULARY Altitude Auxiliary Concurrent Congruent Contradiction Corresponding Dilation Enlargement Equilateral Indirect Median Perpendicular Proportion Ratio Reduction Reflection Rotation Scale Transformation Translation Mathematics: CCSS.Math.Content.HSG-GPE.B.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.HYPERLINK "http://www.corestandards.org/Math/Content/HSG/GPE/B/7"CCSS.Math.Content.HSG-GPE.B.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.&CCSS.Math.Content.HSG-SRT.C.6Understand 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.7Explain and use the relationship between the sine and cosine of complementary angles.CCSS.Math.Content.HSG-SRT.C.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.& CCSS.Math.Content.HSG-CO.A.2Represent 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.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.CCSS.Math.Content.HSG-CO.A.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.CCSS.Math.Content.HSG-CO.A.5Given 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.12Make 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 formulaA= 1/2absin(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.HYPERLINK "http://www.corestandards.org/Math/Content/HSG/SRT/D/11"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.2Identify 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.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. How does it apply to content areas? What content are you currently exploring? This can be shared through essential questions, content standards, or a brief narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTApplying prior knowledge of geometric principals to trigonometry Essential Questions How 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 trigonometry Apply prior knowledge towards the Pythagorean theorem Apply the same idea over a variety of different areas Create a glossary of terms with diagrams & examples Complete sample questions from NYS Regents/RCT exams Use appropriate language in writing and in conversations Create altitudes on given right triangles Determine how ratios between angles can be expressed Engage in class discussions Express knowledge of ratios Identify triangles found in different situations Record notes & sample problems Relate the use of ratios to Pythagorean triples Show how inequalities can be applied outside of linear and quadratic equations Utilize new formulasApplying prior knowledge of geometric principals to trigonometry Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTTrigonometry and applying it to problem solving Essential Questions How 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 Understanding The 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 solving Apply concepts to solve logical and real world problems Apply inverse functions to find solutions Solve for unknowns through graphing and algebra Use defined mathematical laws and inequalities to solve problems featuring non-right triangles Utilize knowledge of trigonometry to solve basic physics problems involving vectors Utilize technology when appropriateTrigonometry and applying it to problem solving Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTUsing algebraic principles to manipulate images Found on a coordinate plane Essential Questions How 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 Understanding Reflections can be expressed both graphically and algebraically. The location of a figures 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 images Found on a coordinate plane Express a figure algebraically both before and after a rotation Identify situations where symmetry is expressed on a coordinate plane and in the real world Use dilations to maintain the ratios and proportions of a figure, while changing the overall sizeUsing algebraic principles to manipulate images Found on a coordinate plane Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTWorking with the unique properties of circles Essential Questions How 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 Understanding Although 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 circles Apply concepts of algebra and ratios to geometry problems involving circles Create new arcs Create ratios and arcs to solve for unknowns Explore concentric and congruent circles Manipulate new tools for measuring Solve for unknown values Study given arcsWorking with the unique properties of circles Assignments Glossary of terms with diagrams & examples Projects Worksheets  10 Q3 MATH VOCABULARY Arc Central Circumference Circumscribe Composition Concentric Depression Diameter Elevation Inscribed Inverse Magnitude Mean Radius Ratio Resultant Rotation Segment Symmetry Transformation Translation Mathematics: CCSS.MATH.CONTENT.HSS.CP.B.6 Find the conditional probability ofAgivenBas the fraction ofB's outcomes that also belong toA, 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. HYPERLINK "http://www.corestandards.org/Math/Content/HSS/CP/B/9/"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 formulaA= 1/2absin(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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTRelating knowledge of triangles and angles to circles Essential Questions How 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 Understanding While a circles center point, diameter and circumference may change, the ratios that exist are similar in all circles.Relating knowledge of triangles and angles to circles Apply the appropriate ratios of tangents, secants, interior angles and chords when given particular circumstances Create appropriate illustrations of tangents, secants and cosecants Derive the equation of a circle Enhance understanding of trigonometry and trigonometry ratios by applying them to circular figures Record notes & sample problems Relate aspects previously learned in trigonometry to circular figures Solve problems related to a circular equation, graphing with appropriate technology for given circumstances Use appropriate language in writing and in conversations Complete questions from NYS Regents/RCT exams Utilize special equations for circles at appropriate times Engage in class discussions Relating knowledge of triangles and angles to circles Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTThe practical applications of determining the area of polygons and circles Essential Questions How 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 Understanding Pi is a fixed ratio between the circumference and diameter of a circle.The practical applications of determining the area of polygons and circles Construct inscribed polygons inside of a circle Demonstrate an appropriate understanding of proportions when solving for unknowns in two similar polygons Derive formulas for polygons Determine area using characteristics of both circle & polygon Dissect regular polygons into smaller parts which can be more easily measured and help to derive formulas Relate these actions to the distance formula and perform actions both on and off of a Cartesian plane Review prior knowledge in determining the area of polygons Use trigonometry to solve for unknown values of inscribed figuresThe practical applications of determining the area of polygons and circles Assignments Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTApplying the concepts of trigonometry and area toward solving advanced problems relating to volume and surface area Essential Questions How 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 area Derive 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 area Glossary 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 narrativeWhat 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 MATHPROCESSPRODUCT/ASSESSMENTApplying probability and measurement to geometry Essential Questions What 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? 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