Honors Geometry Syllabus CHS Mathematics Department

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1 Honors Geometry Syllabus CHS Mathematics Department Contact Information: Parents may contact me by phone, email or visiting the school. Teacher: Mr. Seth Moore Email Address: seth.moore@ccsd.

CHS Mission Statement: Our mission is to prepare our students to serve their communities and to commit to life-long learning Course Description and Prerequisite(s) from Course Handbook: Geometry -

1 1 Honors Geometry Syllabus CHS Mathematics Department Contact Information: Parents may contact me by phone, or visiting the school. Teacher: Mr. Seth Moore Address: or Phone Number: (740) ext Online: CHS Vision Statement: Our vision is to be a caring learning center respected for its comprehensive excellence. CHS Mission Statement: Our mission is to prepare our students to serve their communities and to commit to life-long learning Course Description and Prerequisite(s) from Course Handbook: Geometry State Course # Prerequisite: Algebra I Required Option Grade: 9-10 Graded Conventionally Credit: 1 In depth study of two and three-dimensional geometry including representing problem situations using geometric models, deductive reasoning, and geometry from an algebraic perspective. The fundamental purpose of the course in Geometry is to formalize and extend students geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized dearly in this course. Close attention should be paid to the introductory content for the Geometry conceptual category found in the high school CCSS. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Learning Targets per Unit: Defined below for clarity are the Unit Titles, Big Ideas of every Unit taught during this course, and the Essential Questions to be answered to better understand the Big Ideas. A student s ability to grasp and answer the Essential Questions will define whether or not he or she adequately learns and can

2 2 apply the skills found in Big Ideas. This will ultimately define whether or not a student scores well on assessments given for this course. The Common Core Standards can be found at 1 st or 3 rd Quarter o Unit I Title: Constructions Big Idea #1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO. 1 Essential Question #1: What distinguishes a line segment, ray, and line from one another? Essential Question #2: What discerns a set of parallel lines from a set of perpendicular lines? Essential Question #3: How are line segments and points used to create angles and circles? Big Idea #2: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.CO.12 and G.CO.13 Essential Question #1: How can a variety of tools be used to copy a segment or angle and bisect a segment or angle? Essential Question #2: How can a variety of tools be used to construct perpendicular lines, including the perpendicular bisector of a line segment; and construct a line parallel to a given line through a point not on the line? Essential Question #3: How are equilateral triangles, squares, and regular hexagons inscribed in a circle? o Unit II Title: Congruence and Proof Big Idea #1: Understanding congruence in terms of rigid motions. G.CO.2, G.CO.3, G.CO.4, G.CO.5, G.CO.6, G.CO.7, and G.CO.8 Essential Question #1: How are transformations represented in the plane using, transparencies and geometry software? Essential Question #2: Given two figures, how can the definition of congruence in terms of rigid motion be used to decide if they are congruent? Essential Question #3: How can the definition of congruence in terms of rigid motion be used to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent? Essential Question #4: How do the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions? Big Idea #2: Prove geometric theorems about lines and angles. G.CO.9

3 3 Essential Question #1: How are vertical angles proven congruent? Essential Question #2: What can be proven congruent when parallel lines are cut by a transversal? Essential Question #3: What effect does a perpendicular bisector have on a line segment? Big Idea #3: Prove geometric theorems about triangles. G.CO.10 and G.C.3 Essential Question #1: How are the interior angles of a triangle proven to measure 180? Essential Question #2: How are the base angles of an isosceles triangle proven to be congruent? Essential Question #3: How can midsegments, perpendicular bisectors, and angle bisectors be used to solve problems? Essential Question #4: What are the similarities and differences of a circumcenter, incenter, orthocenter, and centroid? Essential Question #5: How are the inscribed and circumscribed circles of a triangle constructed? Big Idea #4: Prove geometric theorems about parallelograms. G.CO.11 Essential Question #1: What characteristics of a quadrilateral are used to prove it to be a parallelogram? Essential Question #2: How are parallelograms proved to be rectangles? o Unit III Title: Similarity and Proof Big Idea #1: Understand similarity in terms of similarity transformations. G.SRT.1a, G.SRT.1b, G.SRT.2, and G.SRT.3 Essential Question #1: What happens to a pair of parallel lines when they are dilated, if one of the lines lies on the center of dilatation? Essential Question #2: What determines the new length of a line segment that is dilated? Essential Question #3: Given two figures, how can the definition of similarity in terms of similarity transformations decide if geometric figures are similar? Essential Question #4: How are the properties of similarity transformations used to establish the AA criterion for two triangles to be similar? Big Idea #2: Prove theorems involving similarity. G.SRT.4 and G.SRT.5

4 4 Essential Question #1: How can the theorem a line parallel to one side of a triangle divides the other two proportionally be proven? Essential Question #2: How is the Pythagorean Theorem derived in terms of similarity? Essential Question #3: How can congruence and similarity criteria for triangles be used to solve problems? 2 nd or 4 th Quarter o Unit IV Title: Trigonometry and Circle Big Idea #1: Define trigonometric ratios and solve problems involving right triangles. G.SRT.6, G.SRT.7, and G.SRT.8 Essential Question #1: How are the trigonometric ratios determined for acute angles? Essential Question #2: What relationship is derived from the sine and cosine of complementary angles? Essential Question #3: How can trigonometric ratios and the Pythagorean Theorem be used to solve right triangles in applied problems? Big Idea #2: Translate between the geometric description and the equation of a circle. G.GPE.1 Essential Question #1: Given the center of a circle and its radius, how can the equation of the circle be derived? Essential Question #2: Given a circle in the coordinate plane, how is its equation derived? Essential Question #3: When can completing the square be used to find the center and radius of a circle given by an equation? Big Idea #3: Understand and apply theorems about circles. G.C.1, G.C.2, and G.C.3 Essential Question #1: Why are all circles similar? Essential Question #2: When lines intersect a circle or within a circle, how can the measures of the resulting arcs, angles, and segments be found? Essential Question #4: What can be proven about quadrilaterals inscribed in a circle? Big Idea #4: Find arc lengths and areas of sectors of circles. G.C.5 Essential Question #1: What is radian measure of an angle? Essential Question #2: How is the arc length of the arc intercepted by an angle derived? Essential Question #3: How is the area sector derived? o Unit V Title: Connecting Algebra and Geometry through Coordinates Big Idea #1: Use coordinates to prove simple geometric theorems about lines algebraically. G.GPE.5 and G.GPE.6

5 5 Essential Question #1: Find the slope and segment length of the given segment in the coordinate plane. Essential Question #2: Use the distance formula to find the distance between the two given points. Essential Question #3: How is a point on a directed line segment between two given points that partition the segment in a given ration found? Essential Question #4: How can the equation of a line parallel or perpendicular to a given line that passes through a given point be determined? Big Idea #2: Use coordinates to prove simple geometric theorems about figures algebraically. G.GPE.4 and G.GPE.7 Essential Question #1: When given a quadrilateral in the coordinate plane, how can the properties of parallel and perpendicular lines be used to classify it? Essential Question #2: How can the formulas for slope, distance, and midpoint be used to classify given quadrilaterals in the coordinate plane? Essential Question #3: How can coordinates be used to compute perimeters and areas of polygons? o Unit VI Title: Extending to Three Dimensions Big Idea #1: Understanding measurement in three dimensions. G.GMD.1, G.GMD.3, and G.GMD.4 Essential Question #1: What problems can be solved using the volume formulas for cylinders, pyramids, cones, and spheres? Essential Question #2: What determines the shapes of twodimensional cross-sections of three-dimensional objects? Essential Question #3: What three-dimensional objects are generated by rotations of two-dimensional objects? Big Idea #2: Apply geometric concepts in modeling situations. G.GM.1, G.GM.2, and G.GM.3 Essential Question #1: How are geometric shapes, their measures, and their properties used to describe everyday objects? Essential Question #2: How are concepts of density based on area and volume in modeling situations applied to real world situations? Essential Question #3: How are geometric methods applied to solve real world area design problems? END OF COURSE EXAM Course Material: Google Chromebook

6 6 Textbook: Supplemental Textbook(s): None Electronic Resources: ConnectED ALEKS Blackboard Grading: Unit Exams 50% Assessments (Including: Quizzes, Essays, Labs, and Projects) 30% Class work/homework 20% End of Course Exam is 20% of a student s final grade. Grading Scale: The grading scale for Chillicothe High School can be found in the student handbook or online at Late Work: Late work will be subject to the board adopted policy on assignments that are turned in late (to be reviewed in class). Information can be viewed on-line at CHS TENTATIVE Honors Geometry Course Schedule This is an overview of what will be covered in this course at CHS for this school year. Although, I would like to follow this plan verbatim this years tentative schedule is subject to change (at the teachers discretion). 1st or 3rd 9 Weeks: Week 1: Beginning of the Year Pre-Assessment Exam Unit I Title: Constructions Week 1: Chapter 1: 1, 2, 3, and 4 Chapter 3: 1 and 2 Week 2: Chapter 1 Extensions: 5 and 6 Chapter 3: 2 and 5 Chapter 4: Extension 4 Chapter 5: Extensions 1, 2, Unit I Summative Assessment Unit II Title: Congruence and Proof Week 3-4: Chapter 2: 7 and 8 Chapter 4: 1, 3 Chapter 9: 1,2,3, 4, and 5 Weeks 5-6: Chapter 4: 2, 4, 5, and 6

7 Chapter 5: 1, 2, 3, 5, and 6 Chapter 6: 3 and 4 Unit II Summative Assessment Unit III Title: Similarity and Proof Week 7-8: Chapter 7: 2, 6, 7 Chapter 9: 6 and Extension 6 Weeks 9: Chapter 4: 3, 4, 5 Chapter 7: 3, 4, 5 Chapter 8: 1 2nd or 4th 9 Weeks: Week 1: Chapter 4: 3, 4, 5 Chapter 7: 3, 4, 5 Chapter 8: 1 Unit III Summative Assessment Unit IV Title: Trigonometry and Circles Week 2: Chapter 8: 2, 3, 4, and 5 Week 3-4: Chapter 10: 1, 2, 3, 4, 5, and 8 Week 5: Chapter 10: 2 Unit IV Summative Assessment Unit V Title: Connecting Algebra and Geometry through Coordinates Week 6: Chapter 3: 3 and 4 Chapter 11: 1, 3 Week 7: Chapter 1: 6 Chapter 6: 2, 3, 4, 5, 6 Unit V Summative Assessment Unit VI Title: Week 8: Chapter 1: 7 Chapter 11: 3 Chapter 12: 1, 4, 5, and 6 Week 9: Chapter 2: 5 Chapter 3: 6 Chapter 6: 1 Chapter 7: 1 Chapter 11: 2, 4, and 5 Chapter 12: 2, 3 7

8 8 Unit VI Summative Assessment END OF COURSE EXAM Performance Based Section: Writing Assignments/Exams/Presentations/Technology One or more of the End of Unit Exams may be Performance Based. According to the Ohio Department of Education, Performance Based Assessments (PBA) provides authentic ways for students to demonstrate and apply their understanding of the content and skills within the standards. The performance based assessments will provide formative and summative information to inform instructional decisionmaking and help students move forward on their trajectory of learning. Some examples of Performance Based Assessments include but are not limited to portfolios, experiments, group projects, demonstrations, essays, and presentations.

9 9 CHS Honors Geometry Course Syllabus After you have reviewed the preceding packet of information with your parent(s) or guardian(s), please sign this sheet and return it to me so that I can verify you understand what I expect out of each and every one of my students. Student Name (please print): Student Signature: Parent/Guardian Name (please print): Parent/Guardian Signature: Date:

Honors Geometry Syllabus CHS Mathematics Department

1 Honors Geometry Syllabus CHS Mathematics Department Contact Information: Parents may contact me by phone, email or visiting the school. Teacher: Mr. Seth Moore Email Address: seth.moore@ccsd.us Phone