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SCHOOL DISTRICT OF THE CHATHAMS CURRICULUM PROFILE Content Area(s): Mathematics Course/Grade Level(s): Concepts in Geometry (9, 10) I. Course Overview This course provides an understanding of the practical uses of geometry. Skills are developed in the traditional topics of Euclidean geometry. Problem-solving aspects of this course call upon the skills developed in Algebra 1. In connection with the Common Core Standards, this course examines the concepts of; Congruence, Similarity, Right Triangles, Trigonometry, Circles, Expressing Geometric Properties with Equations, Geometric Measurement and Dimension, and Modeling with Geometry. This course with also incorporate the 8 Standards for Mathematical Practices as identified by the Common Core. II. Units of Study Unit 1 – Basics of Geometry Unit 2 – Linear and Planar Relationships Unit 3 – Perpendicular and Parallel Lines Unit 4 – Congruent Triangles Unit 5 – Properties of Triangles Unit 6 – Quadrilaterals Unit 7 – Transformations Unit 8 – Similarity Unit 9 – Right Triangle and Trigonometry Unit 10 – Circles Unit 11 – Area of Polygons and Circles Unit 12 – Surface Area and Volume III. Essential Questions (The open-ended, provocative questions that help frame inquiry) Unit 1 – How do you identify and define mathematical patterns? What is the vocabulary that is necessary to study geometry? What is the distance formula and how do you apply it? How do you classify angles? How do you bisect a segment or an angle? What are vertical, supplementary and complimentary angles? How do you find the perimeter and area of common plane figures? SCHOOL DISTRICT OF THE CHATHAMS CURRICULUM PROFILE Unit 2 – What is a conditional statement? What is a bi-conditional statement? How do you apply laws of logics to determine a conclusion? How do you apply rules of algebra to justify relationships? How do you justify statements about congruent relationships? How do you prove properties about special angle pairs? Unit 3 – What relationships are formed by lines and transversals? How do you apply properties of parallel lines? What is the relationship between slope and pairs of lines? Unit 4 – How can you classify triangles? How do you define two triangles as being congruent? How can you prove (methods) that two triangles are congruent? What are properties of isosceles, equilateral and right triangles? Unit 5 – What are angles bisectors and perpendicular bisectors? What is a median and centroid of a triangle? What is an altitude and orthocenter of a triangle? What is an angle bisector and incenter of a triangle? What is a perpendicular bisector and circumcenter of a triangle? What is the triangle inequality theorem? Unit 6 – How do you classify polynomials? What are the properties of a parallelogram? What are the properties of rhombuses, rectangles and squares? What are the properties of a trapezoid? How can you identify special quadrilaterals? How can you find the area of special quadrilaterals? Unit 7 – What are the 3 basic rigid transformations? What is a reflection and the properties associated with it? What is a rotation and the properties associated with it? What is a translation and the properties associated with it? Unit 8 – What are ratios and proportions and how can they be applied to the real world? How can you identify similar polygons? How can you identify similar triangles? How can proportionality theorems be used to calculate segment length? Unit 9 – Given a right triangle, how does an altitude create similar right triangles? What is a geometric mean? How can you apply the Pythagorean Theorem to similar right triangles? What is the converse of the Pythagorean Theorem? How do you find the side lengths of special right triangles? What are the sine, cosine and tangent? How do you solve a right triangle? SCHOOL DISTRICT OF THE CHATHAMS CURRICULUM PROFILE Unit 10 – What are the special lines and segments related to a circle? What are the properties of arcs and chords? What are the properties of inscribed angles? What are the properties of angles formed by secants and tangents in circles? What are the lengths of segments formed by secants and tangents in circles? What is the equation of a circle? Unit 11 – What are the measures of interior and exterior angles of polygons? How do you find the area of a regular polygon? What is the relationship between perimeters of similar figures? What is the relationship between areas of similar figures? How do you find circumference and arc length of a circle? How do you find the area of a circle and sector of a sector? Unit 12 – What is Euler’s Theorem? How do you find the surface area of a pyramids or cones? How do you find the volume of prisms and cylinders? How do you find the volume of pyramids or cones? How do you find the surface area and volume of a sphere? How do you apply the scale factor of similar figures? IV. Learning Objectives Common Core State Standards for Mathematics: Congruence • Experiment with transformations in the plane • Understand congruence in terms of rigid motions • Prove geometric theorems • Make geometric constructions Similarity, Right Triangles and Trigonometry • Understand similarity in terms of similarity transformations • Prove theorems involving similarity • Define trigonometric ratios and solve problems involving right triangles • Apply trigonometry to general triangles Circles • Understand and apply theorems about circles • Find arc lengths and areas of sectors of circles Expressing Geometric Properties with Equations • Translate between the geometric description and the equation for a conic section • Use coordinates to prove simple geometric theorems algebraically Geometric Measurement and Dimension • Explain volume formulas and use them to solve problems • Visualize relationships between two dimensional and three-dimensional objects Modeling with Geometry • Apply geometric concepts in modeling situations SCHOOL DISTRICT OF THE CHATHAMS CURRICULUM PROFILE V. Instructional Materials McDougal Little Geometry Geometer’s Sketchpad Scientific Calculator Manipulatives Math Games Teacher Generated Materials Math Literature Challenge Materials VI. Key Performance and Benchmark Tasks Unit Tests, Formative and Summative Assessment and Final Exam Content knowledge demonstrated on homework, unit quizzes and tests that include elements of traditional assessment tools such as short answer, definitions and problem solving. Content knowledge and understanding demonstrated by application of mathematical concepts to real world situations. Performance Tasks Content knowledge and mathematical skills demonstrated through the construction of various projects including labs using Geometer’s Sketchpad. Class participation and graded discussion Content knowledge and mathematical skills demonstrated by in class dialogue and collaboration in addition to guided discussions.
