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Geometry Summer School Instructor: Ms. Seifullah Room: 328 E-mail: [email protected] COURSE GOALS Course Description: Geometry means “earth measurement”. The more formal study of geometry today is based on interest and logical reasoning and relationships rather than in measurement alone. In this course we will use technology and relevant projects to develop an understanding of geometry, how it relates to our environment and is used in our world. An understanding of geometry is beneficial for everyone, not just those interested in careers in math. Big Ideas: To progress from observers of mathematics to developing rigorous and deductive reasoning as players in the game of math. Essential Questions: 1. 2. 3. 4. How will I be able to use geometry in everyday life? How are mathematical formulas derived? How do I prove mathematical concepts? What are the relationships between geometric figures? Knowledge Outcomes: 1. 2. Scholars will increase mathematical language. Scholars will learn various problem solving methods. Performance Outcomes & Skills: Scholars will be able to construct formal and informal proofs. Scholars will be able to construct geometric objects. Scholars will be able to show correlation between geometric figures. Recommended Internet Resources: 1. 2. 3. http://mathopenref.com/ links to all topics with definitions and animated examples desmos.com - online graphing tool geogebra - graphing, constructing tool http://www.khanacademy.com – video tutorial, good for review http://www.mathisfun.com – detailed notes with examples and embedded graphing tool http://www.regentsprep.org – fun to look at, covers Regents topics http://purplemath.com – detailed notes and examples http://www.jmap.org – has every regents question ever given and answers by topic or test Topics to be covered: *What students should already know or will be covered is indicated by 8th grade, Algebra 1 (A1) 8/A1 Graphing Linear 8/A1 Writing Linear (slope-intercept and point slope) 8/A1 Identifying Points on a Line A1 Parallel and Perpendicular Lines A1 Systems of Equations 8 Measuring Angles 8 Complementary, Supplementary 8 Vertical Angles 8/A1 Pythagorean Theorem 8 Classifying Polygons 8/A1 Perimeter 8/A1 Circumference A1 Area of Circles A1 Surface Area Geometry Topics in order Tools of Geometry Lines, rays, line segments Planes Angles and Triangle Relationships Parallel Lines and Transversals Interior and Exterior Angles Angle and Segment Addition Postulate Coordinate Geometry The Coordinate Plane Midpoint/ Mid-segments/ Side Splitter Theorem Distance Formula (through Pythagorean Theorem) Slope Equation and graphing of a Line Graphing a system of equations Parallel and Perpendicular lines Equation and graphing of a circle Locus Constructions (mathopenref.com) 30-60-90 Triangle; Angle bisector; Perpendicular bisector; Equilateral Triangle… Solid Geometry Area and Surface Area Volume Logic Conditional, Inverse, Converse, Biconditional, Contrapositive Statements; Truth Value Triangles Altitudes and Medians (orthocenter, incenter, circumcenter) Isosceles Triangle Theorem Exterior Angle Theorem Triangle Inequality Theorem Angle Side Relationship Triangle Congruency Similarity Proofs Triangle Proofs Polygons Classifying, Interior and Exterior Angles Quadrilaterals Properties of Rhombus, Kite, Square, Rectangle, Parellelograms, Trapezoids Quadrilateral Proofs Circles Segments Intercepted by Circle (Arcs, Chords, Tangents, Secants) Circle Proofs Transformations (Symmetry, Rotations, Reflections, Translations, Dilations, Composition) COURSE REQUIREMENTS You are required to complete a number of assignments… The assignments described below are those that earn points toward your final grade. ASSIGNMENT Tests/Quiz* PERCENT 25% GRADING SCALE A+ 97 - 100 A 93 - 96 A- 90 - 92 B+ 87 - 89 B 83 - 86 B- 80 - 82 C+ 77 - 79 Projects 25% Class Learning 25% Homework 10% Journaling 10% Portfolio 5% C 75 - 76 C- 70 - 74 D 69 - 60 F Below 60 ASSESSMENT The following are the grade percentage distribution and the rubric used to grade your in class performance: 1. Attendance, Preparation, Participation, and Disposition (100 points = 20%) EXCELLENT GOOD FAIR You always actively participate You miss one class and make You miss two classes and in group and class it up with a paper. make them up with two discussions. papers. UNACCEPTABLE You miss more than three classes. You seldom or never participate in You often participate in group class and group discussions. You demonstrate great effort and class discussions. You sometimes participate in and enthusiasm in the course. group and class discussions. You demonstrate adequate effort and enthusiasm in the course. You demonstrate little or no effort and enthusiasm in the course. You demonstrate some effort and enthusiasm in the course. * The lowest Quiz grade will be dropped Tools: TI-84 calculator compass protractor ruler pencils black pens eraser one subject notebook for class work and homework one pack of graph paper folder