Common Core Standards: Literacy - MAthematics



|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 |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)  |

|10 Q1 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Geometry and how it applies to real-world situations |Geometry and how it applies to real-world situations |Geometry and how it applies to real-world situations |

|Essential Questions |Analyze and identify of proportions, angles and measurements |Assignments |

|Geometric principles found in locations around the world |Complete a project based on historical architecture |Glossary of terms with diagrams & examples |

|Geometric principles found in the school |Complete assignments to strengthen skills |Projects |

|(IE parallel, perpendicular, congruent on a map of Manhattan city streets). |Complete sample questions from NYS Regents/RCT exams |Worksheets |

|Enduring Understanding |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 | |

|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)  |

|10 Q1 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Using different types of measurement to represent |Using different types of measurement to represent |Using different types of measurement to represent ideas |

|ideas |ideas |Assignments |

|Essential Questions |Apply knowledge of two dimensional figures to three dimensional |Glossary of terms with diagrams & examples |

|Absolute value and coordinate figures |figures for surface area, volume and creation of appropriate formulas |Projects |

|Applying degrees |Convert simple units of measurement (inches to feet, cm to m to km) in|Worksheets |

|Converting units of measurement |order to best suit different situations (measuring height of people in| |

|Measuring three dimensional figures |feet not miles) | |

|Using appropriate units of measurement |Identify new areas as well as refresh algebra concepts | |

|Enduring Understanding |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 proofs | |

|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)  |

|10 Q1 MATH |PROCESS |PRODUCT/ASSESSMENT |

|The process of proving congruence |The process of proving congruence |The process of proving congruence |

|of different figures |of different figures |of different figures |

|Essential Questions |Create personal study guides based on rules of congruence for |Assignments |

|Algebraic proofs |different geometric figures including, but not limited to parallel |Glossary of terms with diagrams & examples |

|Congruence of Parallel lines and transversals |lines, angles, vertical angles, horizontal angles and polygons |Projects |

|Congruence of triangles |Prove figures to be congruent, first with algebra for vertical and |Worksheets |

|Rules of congruence |horizontal angles, continued onto polygons | |

|Using postulates to prove simple statements |Review examples of Regents’ questions | |

|Enduring Understanding |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 proofs | |

|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)  |

|10 Q1 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Ways in which modeling is used to better represent |Ways in which modeling is used to better represent |Ways in which modeling is used to better represent data and help|

|data and help solve difficult problems |data and help solve difficult problems |solve difficult problems |

|Essential Questions |Model and measure to scale a location of choice |Assignments |

| |Utilize appropriate tools to create sketches and measure to scale |Glossary of terms with diagrams & examples |

|Enduring Understanding |different figures |Projects |

| |Utilize appropriate tools to measure two and three dimensional figures|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.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 |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)  |

|10 Q2 MATH |PROCESS |PRODUCT/ASSESSMENT |

|The reasons why the properties of shapes with |The reasons why the properties of shapes with |The reasons why the properties of shapes with |

|circular bases are similar/different than |circular bases are similar/different than |circular bases are similar/different than |

|other figures observed |other figures observed |other figures observed |

|Essential Questions |Apply measurements to determine area, volume, surface, circumference |Assignments |

|How do we use the appropriate tools when measuring circular figures? |and diameter |Glossary of terms with diagrams & examples |

|How do we utilize different equations for area, volume, surface area, diameter and |Complete assignments |Projects |

|circumference? |Complete sample questions from NYS Regents & RCT exams |Worksheets |

|How does pi apply to all circles |Engage in class discussions | |

|What is pi? |Manipulate equations as needed | |

|Enduring Understanding |Record notes & sample problems | |

|The historical concept of pi, its origins and meaning serves as a means of |Use appropriate language in writing and in conversations | |

|application. Appropriate tools are necessary to measure circumference and diameter | | |

|of various real world objects to show that pi as a ratio is constant. | | |

|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)  |

|10 Q2 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Combining the properties of geometry and algebra |Combining the properties of geometry and algebra |Combining the properties of geometry and algebra |

|to define the characteristics of plots |to define the characteristics of plots |to define the characteristics of plots |

|on a coordinate plane |on a coordinate plane |on a coordinate plane |

|Essential Questions |Create equations using real world examples of parallel and |Assignments |

|How are ‘concepts’ physically represented in our surroundings? |perpendicular lines to show how individuals utilize these skills |Glossary of terms with diagrams & examples |

|How are coordinates plotted on axis? |across a variety of different fields |Projects |

|How do we find intercept points and intersecting point of two lines? |Determine perpendicular lines, parallel lines & intercept points |Worksheets |

|How do we prove lines parallel or perpendicular? |Plot points and create lines to understand the values of slope, x and | |

|What is the formula for a line, how do its components represent the different |y intercepts in the formula y=mx+b | |

|characteristics of that line? |Review the properties of a coordinate plane | |

|When and where can these concepts apply to real world situations? | | |

|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)  |

|10 Q2 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Using our understanding of congruence to prove |Using our understanding of congruence to prove |Using our understanding of congruence to prove |

|different characteristics of triangles |different characteristics of triangles |different characteristics of triangles |

|Essential Questions |Determine the appropriate characteristics of triangles |Assignments |

|How do we use our knowledge of congruence of angles and lengths to show that |Prove triangles through the appropriate steps |Glossary of terms with diagrams & examples |

|triangles are congruent or not congruent? |Prove whether or not triangles meet the appropriate criteria |Projects |

|How is proving the characteristics of triangles similar and different to congruence |for similarity or congruence |Worksheets |

|in lines and individual angles. |Recognize the characteristics of triangles | |

|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 | | |

|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)  |

|10 Q2 MATH |PROCESS |PRODUCT/ASSESSMENT |

|The characteristics of other quadrilaterals |The characteristics of other quadrilaterals |The characteristics of other quadrilaterals |

|Essential Questions |Apply knowledge of proved |Assignments |

|How can we apply our knowledge of angles, lengths and triangles to solving geometric|Explore the properties each type of quadrilateral possesses |Glossary of terms with diagrams & examples |

|problems involving polygons? |Solve problems related to real world situations |Projects |

|How do the characteristics of polygons allow us to apply mathematical reasoning to |Undertake single or multi step/variable questions |Worksheets |

|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. | | |

|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)  |

|10 Q2 MATH |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 |

|How are parallel lines related to proportional measurements of triangles and other |tangible items |Glossary of terms with diagrams & examples |

|polygons? |Review fractions, reduction and similar concepts |Projects |

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

|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. | | |

|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.6 Find the point on a directed line segment between two given points that partitions the segment in a given SS.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 SS.Math.Content.HSG-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary |

|SS.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 SS.Math.Content.HSG-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, |

|perpendicular lines, parallel lines, and line SS.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 SS.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 |

|SS.Math.Content.HSG-SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve SS.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 |

|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?  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)  |

|10 Q3 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Applying prior knowledge of geometric principals to |Applying prior knowledge of geometric principals to trigonometry |Applying prior knowledge of geometric principals to trigonometry|

|trigonometry |Apply prior knowledge towards the Pythagorean theorem |Assignments |

|Essential Questions |Apply the same idea over a variety of different areas |Glossary of terms with diagrams & examples |

|How can we apply the use of ratios to Pythagorean Triples? |Create a glossary of terms with diagrams & examples Complete sample |Projects |

|How does geometric mean help us to understand the dimensions of similar triangles? |questions from NYS Regents/RCT exams Use appropriate language in |Worksheets |

|How does the converse of the Pythagorean Theorem allow us to classify triangles |writing and in conversations | |

|without knowing their angles? |Create altitudes on given right triangles | |

|What types of triangles can be treated differently as individual applications? |Determine how ratios between angles can be expressed | |

|Enduring Understanding |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 formulas | |

|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)  |

|10 Q3 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Trigonometry and applying it to problem solving |Trigonometry and applying it to problem solving |Trigonometry and applying it to problem solving |

|Essential Questions |Apply concepts to solve logical and real world problems |Assignments |

|How are trigonometric principles used to solve for unknown? |Apply inverse functions to find solutions |Glossary of terms with diagrams & examples |

|How do we apply laws of sine/cosine to solve problems in non-right triangles? |Solve for unknowns through graphing and algebra |Projects |

|How do we apply trigonometry towards solving problems involving vectors? |Use defined mathematical laws and inequalities to solve problems |Worksheets |

|What ratios are represented by sine, cosine and tangent? |featuring non-right triangles | |

|When are secant, cosecant and cotangent used to solve for unknown values? |Utilize knowledge of trigonometry to solve basic physics problems | |

|When can we apply these ratios towards solving real world problems? |involving vectors | |

|Enduring Understanding |Utilize technology when appropriate | |

|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. | | |

|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)  |

|10 Q3 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Using algebraic principles to manipulate images |Using algebraic principles to manipulate images |Using algebraic principles to manipulate images |

|Found on a coordinate plane |Found on a coordinate plane |Found on a coordinate plane |

|Essential Questions |Express a figure algebraically both before and after a rotation |Assignments |

|How are figures dilated to make them either larger or smaller, yet still remaining |Identify situations where symmetry is expressed on a coordinate plane |Glossary of terms with diagrams & examples |

|in consistent ratio? |and in the real world |Projects |

|How are lines reflected over a given line? |Use dilations to maintain the ratios and proportions of a figure, |Worksheets |

|How are lines reflected over the x and y axis? |while changing the overall size | |

|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 | | |

|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. | | |

|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)  |

|10 Q3 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Working with the unique properties of circles |Working with the unique properties of circles |Working with the unique properties of circles |

|Essential Questions |Apply concepts of algebra and ratios to geometry problems involving |Assignments |

|How are ratios applied when determining arcs and angles? |circles |Glossary of terms with diagrams & examples |

|How do we recall prior knowledge of circumference and diameter to solve problems now|Create new arcs |Projects |

|involving measurement of angles? |Create ratios and arcs to solve for unknowns |Worksheets |

|What are concentric circles and congruent circles and how do we use their properties|Explore concentric and congruent circles | |

|to solve mathematical and real world problems? |Manipulate new tools for measuring | |

|What tools are best suited for measuring angles and arcs? |Solve for unknown values | |

|Enduring Understanding |Study given arcs | |

|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. | | |

|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 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 |

|SS.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 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. CCSS.MATH.CONTENT.HSG.C.A.4 (+) Construct a tangent line from a point outside a given circle to the |

|SS.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 |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)  |

|10 Q4 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Relating knowledge of triangles and angles to circles |Relating knowledge of triangles and angles to circles |Relating knowledge of triangles and angles to circles |

|Essential Questions |Apply the appropriate ratios of tangents, secants, interior angles|Assignments |

|How can circles be constructed using appropriate tools with and without technology? |and chords when given particular circumstances |Glossary of terms with diagrams & examples |

|How can the equation of a circle be manipulated to change size while maintaining the|Create appropriate illustrations of tangents, secants and |Projects |

|same ratios? |cosecants |Worksheets |

|How can we apply aspects of trigonometry towards questions involving circles? |Derive the equation of a circle | |

|What are tangents and how are they used to solve problems involving multiple |Enhance understanding of trigonometry and trigonometry ratios by | |

|circles? |applying them to circular figures | |

|What are the appropriate ratios for angles in circles? |Record notes & sample problems | |

|What is the appropriate form for the equation of a circle? |Relate aspects previously learned in trigonometry to circular | |

|When are special segments of a circle used appropriately for solving problems? |figures | |

|Enduring Understanding |Solve problems related to a circular equation, graphing with | |

|While a circle’s center point, diameter and circumference may change, the ratios |appropriate technology for given circumstances | |

|that exist are similar in all circles. |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 | |

|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)  |

|10 Q4 MATH |PROCESS |PRODUCT/ASSESSMENT |

|The practical applications of determining the area |The practical applications of determining the area |The practical applications of determining the area |

|of polygons and circles |of polygons and circles |of polygons and circles |

|Essential Questions |Construct inscribed polygons inside of a circle |Assignments |

|How can proportions be used to solve problems involving similar polygons? |Demonstrate an appropriate understanding of proportions when solving |Glossary of terms with diagrams & examples |

|How can regular polygons inscribed inside of circles aid in the solving of problems |for unknowns in two similar polygons |Projects |

|with trigonometry? |Derive formulas for polygons |Worksheets |

|How do these general formulas relate to determining the area of compound figures? |Determine area using characteristics of both circle & polygon | |

|What are the basic formulas for determining area of polygons? |Dissect regular polygons into smaller parts which can be more easily | |

|What is Pi and how is it derived? |measured and help to derive formulas | |

|When can inscribing regular polygons inside of a circle be useful for solving real |Relate these actions to the distance formula and perform actions both | |

|world problems? |on and off of a Cartesian plane | |

|Why are area formulas similar and how are they derived from the basic form of base *|Review prior knowledge in determining the area of polygons | |

|height? |Use trigonometry to solve for unknown values of inscribed figures | |

|Enduring Understanding | | |

|Pi is a fixed ratio between the circumference and diameter of a circle. | | |

|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)  |

|10 Q4 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Applying the concepts of trigonometry and area toward solving advanced problems |Applying the concepts of trigonometry and area toward solving advanced|Applying the concepts of trigonometry and area toward solving |

|relating to volume and surface area |problems relating to volume and surface area |advanced problems relating to volume and surface area |

|Essential Questions |Derive formulas for volume and surface area by recalling prior |Glossary of terms with diagrams & examples |

|How can we derive the basic formulas for surface area from known area formulas? |knowledge based on area. |Projects |

|What are the equations for surface area of polygon based figures? |Understand that all prism related figures have the same basic formula |Worksheets |

|How does surface area increase efficiency in engineering models? |of area of base * height. | |

|How do the formulas of figures with circular bases differ from other equations? |Solve for variables and unknowns related to volume and surface area. | |

|When can trigonometric properties of circles be applied to three dimensional |Understand that surface area is a critical measurement for engineering| |

|figures? |design, increasing efficiency and minimizing size. | |

|What is the relationship between determining distance across the surface of a sphere|Apply trigonometric properties to three dimensional figures with both | |

|and latitude and longitude? |circular and noncircular bases. | |

|Enduring Understanding |Relate the concepts of surface distance to latitude and longitude in | |

| |science and social studies. | |

|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)  |

|10 Q4 MATH |PROCESS |PRODUCT/ASSESSMENT |

|Applying probability and measurement to geometry |Applying probability and measurement to geometry |Applying probability and measurement to geometry |

|Essential Questions |Access prior knowledge of trigonometry to help divide circles and |Assignments |

|What are the key representations and vocabulary associated with probability? |polygons into smaller equal and unequal parts |Glossary of terms with diagrams & examples |

|How can probability be related to the sides of polygons? |Divide polygons and circles into smaller equal and unequal segments to |Projects |

|In what ways can a circle be divided into equal and unequal parts so that it might |represent data in a given set |Worksheets |

|be a proper representation of a given probability set? |Graph and display data appropriately | |

|How is probability expressed in terms of independent and dependent variables? |Identify independent and dependent variables in scientific and | |

|How are mutually exclusive events represented graphically? |empirical studies | |

|Enduring Understanding |Represent mutually exclusive events using symbols and graphic | |

| |representations | |

| |Use appropriate unites of measurement for given problems | |

| |Utilize appropriate vocabulary, terminology and symbols when speaking | |

| |and writing about probability and measurement | |

|10 Q4 MATH VOCABULARY – |

|Altitude |

|Center |

|Central |

|Combination |

|Congruent |

|Diagram |

|Oblique |

|Permutation |

|Probability |

|Sample |

|Sector |

|Segment |

|Semicircle |

|Simulation |

|Solid |

|Statistics |

|Value |

|Variable |

|Volume |

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