HWM Geometry Curriculum Overview 2017

Transcription

1 HWM Geometry Curriculum Overview 2017 Overview Standards for Mathematical Content Unit Focus Standards for Mathematical Practice Unit I Basic of Geometry September Unit 2 Reasoning and Proof October G-CO.A.1 G-CO.D.12 G-GPE.B.7 G-MG.A.1 (Preparing for) G-CO.C.9 G-CO.C.10 G-CO.C.11 Experiment with transformations in the plane Make geometric constructions Use coordinates to prove simple geometric theorems algebraically Apply geometric concepts in modeling situation Prove geometric theorems MP.1 Make sense of problems and persevere in solving them. Unit 3 Parallel and Perpendicular lines October G-CO.A.1 G-CO.C.9 G-CO.D.12 G-GPE.B.5 G-GPE.B.6 Experiment with transformations in the plane Prove geometric theorems Make geometric constructions Use coordinates to prove simple geometric theorems algebraically MP.2 Reason abstractly and quantitatively. Unit 4 Transformations November Unit 5 Congruent Triangles December G-CO.A.2 G-CO.A.3 G-CO.A.4 G-CO.A.5 G-CO.B.6 G-SRT.A.1 G-SRT.A.2 G-CO.C.10 G-CO.B.7 G-CO.B.8 G-CO.B.10 G-CO.D G-SRT.B.5 G-GPE.B.4 Experiment with transformations in the plane Understand congruence in terms of rigid motions Understand similarity in terms of similarity transformations Prove geometric theorems Understand congruence in terms of rigid motions Make geometric constructions Prove theorems involving similarity MP.3 Construct viable arguments & critique the reasoning of others.

2 Unit 6 Relationships with Triangles January G-CO.C.9 G-CO.C.10 G-MG.A.1 G-CO.D.12 Prove Geometric theorems Apply geometric concepts in modeling situations Make geometric constructions MP.4 Model with mathematics. Unit 7 Quadrilaterals and Other Polygons February Unit 8 Similarity March G-CO.C.11 G-SRT.B.5 G-MG.A.1 G-MG.A.3 G- SRT.A.2 G- SRT.A.3 G-MG.A.3 G-MG.A.1 G-SRT.B.5 G-SRT.B.4 G-GPE.B.5 Prove geometric theorems Prove theorems involving similarity Apply geometric concepts in modeling situations Understand similarity in terms of similarity transformations Apply geometric concepts in modeling situations Prove theorems involving similarity Use coordinates to prove simple geometric theorems algebraically MP.5 Use appropriate tools strategically. Unit 9 Right Triangles and Trigonometry April Unit 10 Circles May Unit 11 Circumference, Area and Volume G-SRT.B.4 G-SRT.B.5 G-SRT.C.7 G-SRT.C.6 G-SRT.C.8 G-SRT.D.9 G-SRT.D.10 G-SRT.D.11 G-CO.A.1 G-C.A.1 G-C.A.2 G-C.A.3 G-C.A.4 G-CO.D.13 G-GPE.A.1 G-GPE.B.4 G-GMD.A.1 G-GMD.A.2 G-GMD.A.3 Prove theorems involving similarity Define trigonometric ratios and solve problems involving right triangles Apply trigonometry to general triangles Experiment with transformations in the plane Understand and apply theorems about circles Make geometric constructions Translate between the geometric description and the equation for a conic section Use coordinates to prove simple geometric theorems algebraically Explain volume formulas and use them to solve problems Find arc lengths and areas of sectors of circles MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning

3 June G-C.B.5 G-GMD.B.4 G-MG.A.1 G-MG.A.2 G-MG.A.3 Visualize relationships between two-dimensional and three-dimensional objects Apply geometric concepts in modeling situations HWM Geometry Curriculum 2017

4 Content Standards Suggested Standards for Mathematical Practice Unit 1 Basic of Geometry Critical Knowledge & Skills G-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 G-CO.D.12 Make formal geometric constructions with a variety of tools and methods G-GPE.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 G-MG.A. 1 Use geometric shapes, their measures, and their properties to describe objects Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning Students are able to: Name points, lines and planes Name segments and rays Sketch intersections of lines and planes Solve real life problems involving lines and planes Use ruler postulate Use segment addition postulate Name angles Measure and classify angles Identify congruent angles Identify complementary and supplementary angles Identify linear pairs and vertical angles Students are able to: Copy segments and compare segments for congruence Find segment lengths using midpoints and segment bisectors Bisect angles Students are able to: Use midpoint formula Use distance formula Find perimeters and areas of polygons in the coordinate plane Students are able to: Classify Polygons

5 Unit 1 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy

6 working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Content Standards Suggested Standards for Mathematical Practice Unit 2 Reasoning and Proof Critical Knowledge & Skills (Preparing for) G-CO.C.9 Prove theorems about lines and angles. G-CO.C.10 Prove theorems about triangles. G-CO.C.11 Prove theorems about parallelograms Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use Student will be able to: Write conditional statements use definitions written as conditional statements Write biconditional statements make truth tables Use inductive reasoning use deductive reasoning identifying postulates using diagrams Sketch and interpret diagrams Justify steps on solving an equation Write two-column proofs Name and prove properties of congruence Write flowchart proofs to prove geometric constructions write paragraph proofs to prove geometric relationships

7 of structure. MP.8 Look for and express regularity in repeated reasoning Unit 2 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills

8 Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Unit 3 Parallel and Perpendicular lines Suggested Standards for Critical Knowledge & Skills Mathematical Practice G-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 G-CO.C.9 Prove theorems about lines and angles. Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the Identify lines and planes identify parallel and perpendicular lines Identify pairs of angles formed by transversals Use properties of parallel lines Prove theorems about parallel lines Use corresponding angles converse Use transitive property of parallel lines find distance from a point to a line prove theorems about perpendicular lines

9 G-CO.D.12 Make formal geometric constructions with a variety of tools and methods G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning construct parallel lines construct perpendicular lines Use slope to partition directed line segments use slope to find the distance from a point to a line Use slope to partition directed line segments Write equations of parallel and perpendicular lines Unit 3 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy

10 Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Suggested Standards for Mathematical Practice Unit 4 Transformations Critical Knowledge & Skills

11 G-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). G-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself G-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments G-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 G-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. G-SRT.A.1a - A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning perform translations perform compositions Perform reflections perform glide reflections identify lines of symmetry perform rotations perform compositions with rotations identify rotational symmetry identify congruent figures Describe congruence transformations perform translations perform compositions Perform reflections perform glide reflections identify lines of symmetry perform compositions with rotations identify rotational symmetry identify congruent figures Describe congruence transformations Identify and perform dilations

12 line passing through the center unchanged. G-SRT.A.1b - The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-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. Solve real life problems involving scale factors and dilation perform similarity transformations Describe similarity transformations prove that figures are similar Unit 4 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Accommodations and Modifications ELL, Special Education, Gifted and Talented

13 Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Suggested Standards for Mathematical Practice Unit 5 Congruent Triangles Critical Knowledge & Skills G-CO.C.10 Prove theorems about triangles G-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 Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. classify triangles by sides and angles find interior and exterior angle measures Identify and use corresponding parts Use Third angle Theorem

14 pairs of sides and corresponding pairs of angles are congruent. G-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. G-CO.C.10 - Prove theorems about triangles. G-CO.D.12 Make formal geometric constructions with a variety of tools and methods G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning Use SAS congruence theorem Use base angles theorem use isosceles and equilateral triangles Use SSS congruence theorem Use ASA congruence theorem Use AAS congruence theorem construct equilateral triangle construct triangle using SAS construct triangles using SSS construct triangles using ASA Use congruent triangles prove constructions Place figures in a coordinate plane Write coordinate proof Unit 5 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test

15 District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Unit 6 Relationships with Triangles

16 Content Standards G-CO.C.9 Prove theorems about lines and angles G-CO.C.10 Prove theorems about triangles. G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects G-CO.D.12 Make formal geometric constructions with a variety of tools and methods Suggested Standards for Mathematical Practice Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning Critical Knowledge & Skills Use perpendicular bisectors to find measures Use angle bisectors to find measures and direct relationships Write equations to perpendicular bisectors Use medians and fin centroids of triangles Use altitudes and find orthocenters of triangles Use midsegments of triangles in the coordinate plane Use the triangle midsegment theorem to find distances Write indirect proofs List sides and angles of triangle in order by size Use Triangle Inequality Theorem to find possible side lengths Compare measures in Triangles Solve problems using the Hinge Theorem Use geometric shapes, their measures, and their properties to describe objects Use and find the circumcenter of a triangle use and find the incenter of a triangle Circumscribe a circle about a triangle Unit 6 Geometry

17 District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy

18 with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Content Standards Unit 7 Quadrilaterals and Other Polygons Suggested Standards for Critical Knowledge & Skills Mathematical Practice G-CO.C.11 Prove theorems about parallelograms. G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures G-MG.A.1Use geometric shapes, their measures, and their properties to describe objects G-MG.A.3 Apply geometric methods to solve design problems Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated Use interior angle measures of polygons Use the exterior angles measures of polygons Use properties to find side lengths and angles of parallelograms Use parallelograms in the coordinate plane Identify and verify parallelograms Show that a quadrilateral is a parallelogram in the coordinate plane Use properties of special parallelograms use properties of diagonals of special parallelograms use coordinate geometry to identify special types of parallelograms Use properties of trapezoids Use the Trapezoid Midsegment theorem to find distances Use properties of kites Identify quadrilaterals Use geometric shapes, their measures, and their properties to describe objects Apply geometric methods to solve design problems

19 reasoning Unit 7 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy

20 to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Content Standards G- 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. G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. G-MG.A.1Use geometric shapes, their measures, and their properties to describe objects G-MG.A.3 Apply geometric methods to solve design problems Suggested Standards for Mathematical Practice Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools Unit 8 Similarity Critical Knowledge & Skills Use similarity statements Find corresponding lengths in similar polygons Find perimeters and areas of similar polygons Decide whether polygons are similar Use angle angle similarity theorems Use SSS Similarity Theorem Use SAS similarity theorem Apply geometric methods to solve design problems Use geometric shapes, their measures, and their properties to describe objects

21 G-SRT.B.4 Prove theorems about triangles G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Use triangle Proportionality Theorem and its converse Use other proportionality theorems Prove slope criteria using similar triangles Unit 8 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth

22 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Unit 9 Right Triangles and Trigonometry Suggested Standards for Critical Knowledge & Skills Mathematical Practice G-SRT.B.4 Prove theorems about triangles. G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and Use Pythagorean theorem Use converse of the Pythagorean theorem Classify triangles Identify similar triangles use geometric means

23 problems. G-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. G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. G-SRT.D.9 Derive the formula for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. G-SRT.D.10 Prove the Laws of Sines and Cosines and use them to solve problems. G-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). quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning Use Pythagorean theorem Use converse of the Pythagorean theorem Find side lengths in special right triangles use tangent ratio Us inverse trigonometric ratios solve right triangles use tangent ratio Use sine and cosine ratios Find the sine and cosine measures in special right triangles Use sine and cosine ratios Find the sine and cosine measures in special right triangles Find areas of triangles Use law of sines and cosines to solve problems Use law of sines and cosines to solve problems Unit 9 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test

24 District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy

25 Content Standards Suggested Standards for Mathematical Practice Unit 10 Circles Critical Knowledge & Skills G-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. G-C.A.1 Prove that all circles are similar G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle G-C.A.4 Construct a tangent line from a point outside a given circle to the circle. G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle G-GPE.A.1 Derive the equation of a circle Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning identify special segments and lines draw and identify common tangents use properties of tangents Prove that all circles are similar Identify and describe relationships among inscribed angles, radii, and chords. identify special segments and lines draw and identify common tangents use properties of tangents identify congruent arcs find arc measures Use chords of circles to find lengths and arc measures Find angle and arc measures Use circumscribed angles Use segments of chords, tangents and secants Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle Use inscribed angles Use inscribed polygons Construct a tangent line from a point outside a given circle to the circle. identify special segments and lines draw and identify common tangents use properties of tangents Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Derive the equation of a circle of given center and radius using the Pythagorean

26 G-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically Theorem; complete the square to find the center and radius of a circle given by an equation. Write and graph equations of circles Use coordinates to prove simple geometric theorems algebraically. Write coordinate proofs involving circles Unit 10 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills

27 Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Unit 11 Circumference, Area and Volume Suggested Standards for Critical Knowledge & Skills Mathematical Practice G-GMD.A.1Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. G-GMD.A.2 Give an informal argument using Cavalieri s principle for the formulas for the volume of a sphere and other solid figures. G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Mathematical practices addressed throughout the unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others.. Use formula for circumference use arc length to find measures Use formula for area of a circle use formula for population density Find surface areas of right cones Find and use volumes of cones Find surface areas of spheres Find volume of spheres Find areas of rhombuses and kites find angle measures in regular polygons Find area of regular polygons Find volume of spheres Find and use volumes of pyramids Find and use volumes of prisms and cylinders

28 G-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 G-GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of twodimensional objects. G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects G-MG.A.2 Apply concepts of density based on area and volume in modeling situations G-MG.A.3 Apply geometric methods to solve design problems. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning Measure angles in radians Find and use areas of sectors classify solids describe cross sections sketch and describe solids of revolution Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). Apply concepts of density based on area and volume in modeling situation Use formula for density Apply geometric methods to solve design problems Unit 11 Geometry District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources

29 Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan Academy Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy