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GEOMETRY Mathematics Prince George’s County Public Schools SY 2009-2010 Prerequisites: Algebra 1 Credits: 1.0 Math, Merit Geometry provides students with the skills outlined in the Maryland Core Learning Goals for Geometry. These skills include using logic to develop arguments, working with the postulates and theorems of Euclidian geometry, applying rules for parallel and perpendicular lines, identifying congruent and similar figures, classifying polygons, measuring angles and segments, writing proofs of triangle congruence, drawing, constructing, and performing plane transformations . INTRODUCTION: Typically in a Math class, to understand the majority of the information it is necessary to continuously practice your skills. This requires a tremendous amount of effort on the student’s part. Each student should expect to dedicate 2 - 3 hours of studying for every hour in class. Some hints for success in a Math class include: attending class daily, asking questions in class, and thoroughly completing all the homework problems with detailed solutions as soon as possible after each class session. INSTRUCTOR INFORMATION: Name: Dr. Eulalia N. Bentillo E-Mail: [email protected] Planning: Phone: CLASS INFORMATION: COURSE NUMBER: CLASS MEETS: Every other day for 90 minutes ROOM: C4110 TEXT: Geometry, Prentice Hall WEB SITE: www.phsuccessnet.com CALCULATORS The use of a graphing calculator is required. While participants may use any graphing calculator, the instruction in the course requires the TI-83. The TI-84 is very similar and can be used as well. Knowledge and competence for use of other graphing calculators will be the sole responsibility of the student. GRADING Grade Percentage Category Brief Description Class Work This includes all work completed in the classroom setting. This includes but is not limited to: Notebooks, Warm-ups, Vocabulary, and Written Responses to Constructed Responses (BCR/ECR), Active Participation in Math projects, Completion of Assignments This includes all work completed outside the classroom to be graded on its completion and student’s preparation for class (materials, supplies, etc.). Assignments can include, but are not limited to: Problem of the Week, Daily Class Homework Assignments, and Friday Night Homework. This category entails both the traditional (exams & quizzes) and alternative (presentations, projects, portfolios) methods of assessing student learning. Suggested criteria for grading presentations projects, portfolios, include a) Concepts/objectives have been met, b) Completion of project and c) Creativity, originality. This category may include but is not limited to: Exams, Quizzes, Portfolios, Research/Unit Projects, and Oral Presentations. Homework Assessment 30% 20% 50% Your grade will be determined using the following scale: 90% - 100% A 80% - 89% B 70% - 79% C 60% - 69% D 59% and below E SAT: SAT preparation is infused into daily instruction. The curriculum is embedded with standardized test preparation activities and test-taking strategies that will help students be successful on high-stakes tests like the SAT, ACT or college entrance exams. The practice in each lesson will prepare the students for the format as well as for the content. IMPORTANT DATES First Quarter Progress Report End of First Quarter: First Quarter Report Cards Released Parent/Teacher Conferences Thanksgiving Second Quarter Progress Report Winter Break End of Second Quarter Second Quarter Report Card Released Third Quarter Progress Report Spring Break End of Third Quarter Third Quarter Report Card Released Fourth Quarter Progress Report End of Fourth Quarter Tuesday, October 6, 2009 Thursday, October 29, 2009 Tuesday, November 10, 2009 Wednesday, November 11, 2009 November 25 – November 27, 2009 Friday, December 18, 2009 December 24, 2009 – January 3, 2010 Friday, January 22, 2010 Wednesday, February 3, 2010 Thursday, March 4, 2010 March 29 – April 5, 2010 Thursday, March 25, 2010 Wednesday, April 14, 2010 Monday, May 10, 2010 Thursday, June 10, 2010 First Quarter at a Glance Throughout first quarter reasoning and proof, communication, and connections in mathematics should be emphasized. As students learn the theorems, axioms, and postulates, they should be guided through deductive reasoning procedures in order to learn logical thinking processes. By the end of First Quarter Geometry students should be able to: Tools of Geometry Use inductive reasoning Make conjectures Understand basic terms and postulates Identify segments, rays, and parallel lines Find the length of segments and the measures of angles Perform basic constructions Find the distance between two points on the coordinate plane Find perimeter, circumference, and area Reasoning and Proof Recognize conditional statements and write converses Write bi-conditionals and definitions Use the law of detachment and syllogism Justify steps of a logical argument Prove and apply theorems about angles Parallel and Perpendicular Lines Identify angles formed by parallel lines and a transversal Use a transversal in order to prove that lines are parallel Classify triangles and find the measures of their angles Graph lines given their equations Relate slope and parallel and perpendicular lines Congruent Triangles Recognize congruent figures and their corresponding parts Prove two triangles congruent Second Quarter at a Glance Throughout second quarter reasoning and proof, communication, and connections in mathematics should be emphasized. As students learn the theorems, axioms, and postulates, they should be guided through deductive reasoning procedures in order to learn logical thinking processes. By the end of Second Quarter Geometry students should be able to: Congruent Triangles Prove that triangles are congruent Use and apply properties of isosceles triangles Use congruent triangles in proofs Relationships within Triangles Apply midsegments in problem solving Use perpendicular and angle bisectors Identify properties of perpendicular and angle bisectors, medians and altitutes Write the negation, contrapositive, and inverse of a conditional statement Use inequalities involving sides and angles Quadrilaterals Define and classify special types of quadrilaterals Use relationships of diagonals, sides, and angles that are present in special quadrilaterals Prove that a quadrilateral is a parallelogram, rectangle, rhombus, and kites Use coordinate geometry in proofs of quadrilaterals Area Find the Area of parallelograms Use the Pythagorean Theorem Use properties of special right triangles Find the area of trapezoids, rhombuses, and kites Third Quarter at a Glance Throughout third quarter measurement and connections should be emphasized. As students learn discover different geometric figures, the relationship of the properties of area, surface area, circumference and individual measurements should be highlighted. By the end of Third Quarter Geometry students should be able to: Area Find the area of regular polygons Find the measure of central angles and arcs Find the area of circles, sectors, and segments Use geometry to find probabilities Similarity Write ratios and solve proportions Identify and apply similar polygons Prove triangles similar Find and use relationships in similar right triangles Use the side splitter and angle bisector theorem Right Angle Trigonometry Use tangent, sine, and cosine ratios Describe and add vectors Use trigonometry to find area of triangles Surface Area and Volume Find the number of faces, edges, and vertices of a three dimensional figure Use nets Find the surface area of prisms, cylinders, pyramids and cones Find the volume of prisms, cylinders Fourth Quarter at a Glance Throughout fourth quarter measurement and connections should be emphasized. As students learn the equations of different types of figures, the relationships to prior knowledge should highlighted in order to assist the student’s construction of knowledge. By the end of fourth Quarter Geometry students should be able to: Surface Area and Volume Find the volume prisms, cylinders, pyramids, and cubes Find the surface area and volume of a sphere Find the ratios between area and volumes of similar figures Circles Use the radius and tangent relationship to investigate circles Use congruent chords, arcs, and central angles Recognize properties of lines through the center of a circle Find the measure of an inscribed angle Find the measure of an angle formed by a tangent and a chord Find angle measures and segment lengths of a circle Write an equation of a circle Find the center and radius of a circle Draw and describe a locus Identify isometries Find reflection images Describe translations using vectors Find translation images using matrix and vector sums