GEOMETRY Teacher: LAIRD JONAS EMAIL ADDRESS: ljonas@erhsnyc.net EMILY MELNICK emelnick@erhsnyc.net Year: 2015-2016 Course Description In Geometry, we will explore the relationships between points, lines, angles, shapes, planes and objects. Our study will incorporate our knowledge of algebra and logical reasoning to present formal proofs, to develop geometric theorems and to derive formulas to determine slopes, distances, midpoints, areas, perimeters and volumes. My goal is to provide you with the guidance and support that will help you to develop a deeper understanding of how mathematics works. We will develop problem-solving strategies that will allow us to analyze and interpret information given to draw conclusions based on and beyond what was provided. Essential Questions: 1. What makes a logical argument? 2. Why is the notion of equivalence important? 3. How do we view the world in relation to lines, angles and shapes? Regents Exam Students will take the Geometry Regents exam at the end of this course. Class and Extra Help Schedule Class Time: Section 1: Monday-Friday period 8 (1:12-2:00) Section 2: Monday-Friday period 1 (8:20-9:02) Extra Help Time: Tuesday 7:30-8:15
Course Requirements A notebook and a homework folder Pens, pencils, a ruler, and a compass TI-83+ or TI-84+ graphing calculator You are expected to come to class prepared with your notebook, homework book, pens, pencils, ruler and graphing calculator. Failure to do so will affect your grade. Criteria for Success i. Homework Homework serves two main purposes. It allows you to practice what was taught in class and to determine whether you understand the material. You will be selected to present homework assignments in class. I will check that you did the homework every day. A point will be taken from your homework grade for missing homework. If you do not understand a homework questions you are encouraged to send me an email with questions about the assignment. You can also see me in the mornings Tuesday 7:30 8:15 for extra help. ii. regular iii. Homework of the Week (HOW) You will be given a weekly homework assignment (HOW) in addition to your homework assignment. These assignments will be based on past Regents exams. Tests/Quizzes Tests and quizzes are given on a regular basis. v. Participation/Presentation Participation and presentations in class are also critical to your success. You are expected to share your ideas and pay attention when others are speaking. This is an integral part of class discussions and group work. You are also expected to present problems on the board. Your grades for presentation and participation reflect your contribution to the learning process.
Grading Policy Homework Test/Quizzes Participation/Presentation 15 pts 70 pts 15pts 100 pts
Course Outline Textbook: Charles, Randall I., Hall, Basia, Kennedy Dan, Bass, Laurie E., Johnson, Art, Murphy, Stuart J., Wiggins, Grant, Geometry Common Core, New Jersey, Pearson Education 2010. Unit Time Topics 1 2 weeks Tools of Geometry i. Points, Lines and Planes ii. Measuring Segments and Angles iv. Exploring angle Pairs v. Basic Constructions vi. Midpoint and Distance 2 2 weeks Reasoning and Proofs i. Patterns and Induction Reasoning ii. Conditional Statements iii. Biconditionals and Definitions iv. Deductive Reasoning v. Reasoning in Algebra and Geometry vi. Proving Angles Congruent 3 2 weeks Parrallel Lines and Perpendicular Lines 4 3 weeks Congruence Triangles i. Lines and Angles ii. Parallel and Perpendicular Lines iii. Triangles iv. Equation of Lines in the Coordinate Plane v. Slopes of Parallel and Perpendicular Lines i. Triangle Congruence ii. Congruence in Corresponding Parts iii. Congruence Isosceles, Equilateral Triangles and Right Triangles iv. Congruence in Overlapping Triangles 5 2 weeks Relationships Within Triangles i. Midsegments of a Triangle ii. Perpendicular and Angle Bisectors iii. Bisectors in Triangles iv. Medians and Altitudes
v. Indirect Proofs vi. Inequalities in Triangles 6 2 weeks Polygons and Quadrilaterals 7 2 weeks Similarity i. The Polygon-Angle Sum Theorem ii. Properties of a Parallelogram iii. Proving That a Quadrilateral is a Parallelogram iv. Properties of a Rhombuses, Rectangles, and Squares v. Trapezoids and Kites vi. Polygons in the Coordinate Plane vii. Proofs Using Coordinate Geometry i. Ratios and Proportions ii. Similar Polygons and Triangles iii. Proving Triangles Similar iv. Proportions in Triangles 8 2 weeks Right Triangles and Trigonometry i. The Pythagorean Theorem and Its Converse ii. Special Right Triangles iii. Trigonometry iv. Angle of Elevation and Depression v. Laws of Sine and Cosine 9 2 weeks Transformation 10 2 weeks Area i. Translation ii. Reflection and Rotation iii. Compositions of Isometry iv. Triangle Congruence v. Dilations vi. Similarity Transformations i. Areas of Triangles and Parallelograms ii. Areas of Trapezoids and Kites
iii. Areas of Regular Polygons iv. Perimeters and Areas of Regular Figures v. Trigonometry and Areas vi. Areas of Circles and Sectors vii. Geometric Probability 11 2 weeks Surface Area and Volume 12 3 weeks Circles 13 2 weeks Probability i. Surface Areas of Prisms and Cylinders ii. Surface Areas of Pryamids and Cones iii. Volumes of Prisms, Cylinders, Pyramids and Cones iv. Surface Areas and Volumes of Spheres and Similar Solids i. Tangent Lines ii. Chords and Arcs iii. Inscribed Angles iv. Angle Measures and Segment Lengths v. Circles in the Coordinate Plane vi. Locus i. Probability Distribution ii. Permutations and Combinations iii. Probability of Multiple Events