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Summit International Preparatory Geometry MYP Course Syllabus School Year: 2014-2015 Instructor: Cristina Niver Room 219 Email: [email protected] Tutoring Hours: Monday, Tuesday, Thursday 4:15-5:15pm, or by appointment I believe all scholars can be successful at math – it takes perfect practice, but it can be done! “I've missed 3000 shots. Twenty-six times the game-winning shot has been trusted to me, and I've missed. I've lost over 300 games. I've failed over and over and over again, and that is why I've succeeded.”- Michael Jordan "A person who never made a mistake never tried anything new." – Albert Einstein The Course: Geometry In this course, scholars will cover the fundamentals of geometry while reviewing algebra principles in preparation for one of the IB Diploma Program math courses. The study of geometry and trigonometry enhances scholars’ spatial awareness and provides them with the tools for analyzing, measuring and transforming geometric quantities in two and three dimensions. Key concepts from other MYP subjects that could be used within the geometry branch include aesthetics (geometric shapes, transformations), change (identities, transformations), communities (angle properties, triangle properties), creativity (transformations, similarity and congruency), identity (unit circle, identities), perspective (coordinate geometry, similarity and congruency), and time, place and space (three-dimensional coordinate geometry, transformations). Geometry is meant to lead students to an understanding that reasoning and proof are fundamental aspects of mathematics and something that sets it apart from the other sciences. Nature of MYP Math “An MYP mathematics programme should be tailored to the needs of students, seeking to intrigue and motivate them to want to learn its principles. Students should see authentic examples of how mathematics is useful and relevant to their lives and be encouraged to apply it to new situations. Mathematics provides the foundation for the study of sciences, engineering and technology. However, it is also evident in the arts and is increasingly important in economics, the social sciences and the structure of language. Students in the MYP are encouraged to use tools to represent information, to explore and model situations, and to find solutions to various problems. These are skills that are useful in a wide range of arenas. MYP mathematics aims to equip all students with the knowledge, understanding and intellectual capabilities to address further courses in mathematics, as well as to prepare those students who will use mathematics in their studies, workplaces and lives in general.” -From MYP Mathematics Subject Guide, 2014 Scope and Sequence: Unit 1: Foundations of Geometry Description Fundamentals of geometry (points, lines, planes, segments, rays, opposite rays, etc.) Use proper written geometric notation to represent segments, line, rays, angles, measure of angles, arrays, etc. Basic angle vocabulary and calculations (supplementary, complementary, straight, right, acute, obtuse, etc.) Segment addition 2: Logic 3: Lines and Angles 4: Triangle Congruence 5: Triangle Similarity 6: Advanced Triangles 7: Quadrilaterals 8: Transformations 9: 2D Geometry Coordinate plane Solving algebraic equations with variables on both sides Solving algebraic equations requiring distribution and combining like terms Inductive reasoning Deductive reasoning Conditionals, converse, inverse and contrapositive Use inductive reasoning to make conjectures and counter examples to disprove conjectures Writing and graphing equations of lines Slopes Distance Formula – using Pythagorean Theorem as well as the distance formula Midpoint Remediate radicals (for connection to Pythagorean Theorem) Identify patterns and solve problems involving parallel lines cut by a transversal. Relate slope to parallel and perpendicular lines Explore line postulates incorporating linear equations (point intercept formula and systems of linear equations) Properties and classifications of triangles Use triangle congruence and corresponding parts of congruent triangles to prove that parts of two triangles are congruent Executing 2 column proofs: SAS, SSS, AAS, ASA, Hypotenuse leg Right triangle similarity Applications with ratios and proportions Dilations Identify and apply properties of similar polygons Justify triangles are similar by applying the AA, SAS, and SSS similarity theorems Find and compare the perimeters and areas of similar polygons Simplify radicals Apply the Pythagorean Theorem and its converse including in problem solving situations Recognize the Pythagorean triples 3-4-5 and 5-12-13 Investigate and apply trigonometric ratios in a right triangle to solve problems with missing sides Apply the trigonometry of right triangles to solve problems including angles of depression and angles of elevation Special right triangles (30-60-90, 45-45-90) SOH CAH TOA Angle of depression Angle of elevation Properties of parallelograms Trapezoids (Right, isosceles, and scalene) Kites Quadrilaterals in the coordinate plane Reflections over either axis as well as the line y=x. Translations – following a rule and/or writing the rule. Rotations – in Multiples of 90 degrees Interior angle sum and exterior angle sum Perimeter and area formulas Composite figures Effect of changing dimensions (on perimeter and area) 10: 3D Geometry 11: Circles 12: Algebra 2 Prep Apothem Nets Isometric and orthographic views Volume of prisms, cylinders, pyramids, cones and spheres Surface area (and lateral surface area) of prisms, cylinders, pyramids, cones and spheres Composite figures Effect of changing dimensions (on surface area and volume) Describe and draw the intersection of a given plane with various threedimensional figures Use orthographic and isometric views of three-dimensional figures to represent and construct three-dimensional figures and solve problems Parts of a circle Including - Radii, diameter, circumference, major/minor arcs, chords, secants, tangents, etc. Calculating circumference and area Proportional reasoning to find arc length and sector area Find measures of central angles, inscribed angles, exterior angles, and arcs Formulate and test conjectures about the properties of tangents to circles Use the properties of congruent chords, arcs, and central angles Use perpendicular bisectors to chords Find the measure of an inscribed angle and an angle formed by a tangent and a chord Find the measures of angles formed by chords, secants, and tangents Fluency with solving equations Fluency with simplifying radicals Graphing and solving systems of equations Quadratics review of solving, graphing, and factoring Prerequisite: Algebra 1 Textbook: Bass, L. and Charles, R., Texas Geometry, Boston, Massachusetts: Pearson Prentice Hall, 2008 Supplies: 1.5’’ -2’’ Binder, binder dividers (5), loose leaf paper, pencils, blue or black ink pens, protractor, compass, Casio calculator Classroom Behavior: Each scholar should attend class with all class materials including their textbook and homework. Each scholar will be expected to abide by all school rules and regulations as outlined in the Code of Conduct. In addition, each student should demonstrate courtesy, respect and consideration to their peers and adults. No food, drink, or gum permitted. Each scholar is expected to be fully engaged in all class activities, to maintain the highest level of integrity and honesty in their work, and to ask for help when needed. Cell Phone Policy: Classroom disruption by cell phones is prohibited. Cell phones may be used for specific lessons, but only at the discretion of the instructor. Assessment: Grades are calculated based on daily exit tickets (quizzes), homework, class projects, and exams. Each grade component will be weighed as follows: homework 10%, exit tickets 10%, quizzes 20%, class projects 20%, and exams 40% Course grades will use the following scale: Letter A Numerical 90 – 100 B 80 – 89 C 70 – 79 F 69 and below Grading Policy: If scholars do not submit assigned homework or projects, they will receive a 10% deduction per class period until the graded assignment is returned. (i.e., once the homework has been graded, the scholar can no longer make up those points). If a scholar misses work due to an excused absence, they may submit their work within two business days of returning to school. Scholars will have the opportunity to redo work in an effort to demonstrate mastery. If a scholar requests a redo opportunity, they will be required to schedule and attend a tutorial with the instructor prior to redoing the assessment (common assessments, homework and exit tickets do not fall under this category). The scholar will have two options to redo an assessment: 1. Retake assessment: scholar may choose to retake an assessment with the understanding that the rigor will be increased to ensure content mastery; scholar will receive a new grade that will replace their previous grade 2. Correct mistakes: scholar may choose to correct their mistakes on a separate sheet on paper showing all their work to receive half of the points missed on their first assessment; for example, if the scholar receives a 70% on a unit test, they may correct their mistakes with the understanding that the new highest grade possible is 85% In order to receive credit for any and all assessments, the scholar must show their work. The instructor may reference scholar work to understand where the scholar needs additional practice to gain mastery. Disabilities: The teachers of scholars requiring accommodations or modifications are notified by the administration when the scholar enters the class; however, parents should feel free to alert their child’s teachers of any such requirements and discuss any concerns they may have. Course Grades: Parents and scholars are encouraged to view grades via POWER SCHOOL on a regular basis. Official grades are provided via report cards and/or transcripts. Important Dates: These are subject to change with adequate notice from the instructor; unit tests may also come in the form of a project dependent upon the topic and testing schedule Unit 1 Exam/Project – August 25th and 26th Unit 2 Exam/Project – September 9th and 10th Unit 3 Exam/Project – September 29th and 30th Math Common Assessment – October 6th Unit 4 Exam/Project – October 28th and 29th Unit 5 Exam/Project – November 13th and 14th Math Common Assessment – December 15th Unit 6 Exam/Project – January 12th and 13th Unit 7 Exam/Project – January 23rd and 26th Unit 8 Exam/Project – February 6th and 9th Unit 9 Exam/Project – February 23rd and 24th Math Common Assessment – March 2nd Unit 10 Exam/Project – April 1st and 2nd Unit 11 Exam/Project – April 22nd and 23rd A paper version of parent and student signatures is required to show that you have read the syllabus and understand the contents therein. If you have any questions, please feel free to contact me. I look forward to working with you and your child as we explore various aspects of Geometry. C.Niver Cut along line and return the bottom. Mrs. Niver, I have read and understand the contents of your syllabus for Geometry. ___________________________________ Parent/Guardian signature Date _______________________________________________ Student signature Date