Geometry Syllabus Certificated Teacher: Date: 2012-13 Course Title: Geometry A and B Desired Results Credit: one semester (.5) X two semesters (1) Prerequisites and/or recommended preparation: Completion of Algebra 1 Estimate of hours per week engaged in learning activities: 5 hours of class work per week Instructional Materials: All learning activity resources and folders are contained within the student online course. Online course is accessed via login and password assigned by student s school (web account) or emailed directly to student upon enrollment, with the login website. This course requires a MathXL account which will be provided by your course instructor. Holt McDougal Geometry 2011 online videos, examples, and activities. Course Overview: This course is designed to develop students ability to make conjectures and to logically verify them if possible. Students will continue to develop skills learned in Algebra with an emphasis on the physical world around them. Enduring Understandings for Course: We can use a variety of mathematical tools to describe our world and help solve daily problems. We can use logic to reason out solutions to problems and prove or disprove conjectures about the world around us. Establish Goals: WA State EALRS. Big Idea Target 1A G.7.C G.7.E Target 1B G.3.D, G.4.A, G.4.B, G.4.C Target 1C G.2.C, G.7.E Unit 1 Language of Geometry Language of Geometry We can distinguish between the types of quadrilaterals and triangles and sketch them. We can solve problems about line segments on the coordinate plane. We can construct, label and use vocabulary about geometric shapes. Understanding Quadrilaterals and Triangles 1. I can distinguish between types of quadrilaterals (rectangle, square, rhombus, parallelogram, trapezoid, and kite). 2. I can distinguish between the types of triangles (acute, right, obtuse, scalene, isosceles, or equilateral). 3. I can use the definition of a shape to justify its type. 4. I can sketch and identify geometric shapes with reasonable accuracy. Understanding the Coordinate Plane in Geometry 1. I can use slope to determine if lines are perpendicular or parallel. 2. I can use the distance formula to determine lengths of line segments. 3. I can find the midpoint of a line segment. 4. I can determine the equation of a line given 2 points. 5. I can determine the equation of a line through a point & parallel to a line. 6. I can determine the equation of a line through a point & perpendicular to a line. Understanding Tools in Geometry 1. I can use tools to make accurate measurements. 2. I can perform basic constructions with a compass and straight edge.
Connections G.4.A, G.4.B,C, G.7.B Big Idea Target 2A G.1.A, G.1.B, G.1.E G.7.G, G.7.H Target 2B G.1.D, G.1.E, G.1.F Target 2C G.1.A, G.1.C, G.5.B, G.5.D G.7.H Target 2D G.2.B G.7.G Connections G.1.A, G.1.C, G.1.F, G.2.B G.7.B, G.7.H G.1 BIG IDEA Target 3A G.1.D, G.1.E, G.5.B, G.5.C Target 3B G.2. A, G.2.B, G.2.C 1. I can solve problems by reasoning with geometry and algebra. Understanding in Mathematics 1. I can use geometric notation to name shapes and describe relationships. 2. I can use geometric vocabulary to explain my thinking. Unit 2 Reasoning Reasoning Reasoning can be used to make decisions and draw conclusions. Recognizing different forms of reasoning helps us validate our arguments. We understand the role of assumptions, definitions, and theorems in geometric Reasoning is similar to reasoning in life situations. Understanding Inductive Reasoning 1. I can identify inductive reasoning. 2. I can make conjectures based on observations. 3. I can use a counter-example to show a conjecture is false. Understanding Conditional Statements 1. I can write a statement in if-then form. 2. I can identify the hypothesis and conclusion of a conditional statement. 3. I can write the converse, inverse, and contrapositive of a conditional statement, and use a counter-example to show a statement is false. 4. I can use a bi-conditional statement when writing definitions. Understanding Deductive Reasoning 1. I can identify deductive reasoning. 2. I can draw conclusions using the Law of Detachment, the Law of Syllogism, and the Law of Contrapositive. 3. I can use algebra to justify the truth of a conjecture. 4. I can use properties of rigid transformations to justify the truth of a conjecture. 5. I can use deductive arguments to justify the truth of a conjecture. Understanding angle and segment relationships 1. I can identify angle pairs (Complementary, supplementary, vertical, adjacent, linear pairs). 2. I can solve problems using angle pairs and segment relationships. 1. I can find examples of using inductive and deductive reasoning in my life. 2. I can solve problems by reasoning with geometry and algebra. 3. I can describe the consequences of changing assumptions or using different definitions for a situation. Understanding in Mathematics 1. I can use geometric notation and symbols with deductive reasoning. 2. I can use geometric vocabulary to explain my thinking. 3. I can organize and present my thinking for a given audience. Unit 3 Reasoning with Lines and Angles Reasoning with Lines and Angles Euclidian Geometry is a system that helps us understand our world. We can make and test conjectures about angles formed by parallel and perpendicular lines. We can verify and explain conjectures and theorems, using definitions, postulates, and theorems as justification. Understanding Deductive Reasoning 1. I can use deductive reasoning to verify and explain theorems. (Not tested) 2. I can use deductive reasoning to verify and explain conjectures or geometric statements. 3. I can use transformations to justify the truth of a conjecture. 4. I can explain the role of definitions, undefined terms, postulates (axioms), and theorems. Understanding Angle Relationships with Lines 1. I can identify angle pairs (corresponding, alternate interior, alternate exterior, and same-side interior) 2. I can draw conclusions about angle pairs formed by parallel lines and a transversal. 3. I can use angle relationships to determine when lines are parallel. 4. I can apply theorems about parallel and perpendicular lines.
5. I can solve problems involving angles and parallel lines. 6. I can use and explain constructions related to parallel and perpendicular lines. Target 3C G.3.A, G.3.G Connections G.4.A, G.4.B,C, G.7.B BIG IDEA Target 4A G.3.B, G.6.D Target 4B G.2.A, G.2.B, G.3.B, G.5.C Target 4C G.2.B, G.2.C, G.3.A, G.3.B, G.4.C Target 4D G.1.D, G.1.E, G.1.F, G.7.H Connections G.4.A, G.4.B, G.4.C, G.4.D, G.7.B Big Idea Target 5A G.2.A, G.2.B, G.3.F, G.3.G, G.4.A, Understanding Angles and Segments in a Triangle 1. I can use the exterior angle theorem for triangles to solve problems. 2. I can use the sums of the interior and exterior angles of a convex polygon to solve problems. 1. I can solve problems by reasoning with geometry and algebra, including systems of equations. 2. I can use transformations to solve problems. 3. I can use coordinate geometry to solve problems. Understanding in Mathematics 1. I can use geometric notation and vocabulary to describe relationships and explain my thinking. 2. I can present my thinking in an organized, logical way. 3. I can use accepted reasons to justify my thinking. Unit 4 Triangle Congruence and Similarity and Proof Triangle Congruence and Similarity and Proof Similar and congruent have many real world applications. We understand necessary and sufficient conditions to determine if triangles are similar or congruent. We use similar or congruent triangles to prove theorems and conjectures. Understanding and Applying Triangle Similarity 1. I can use AA, SAS, and SSS to determine if triangles are similar. 2. I can use similar triangles to solve problems. 3. I can find the area and perimeter of similar triangles. Understanding Triangle Congruence 1. I can identify the corresponding congruent parts given congruent triangles. 2. I can use SSS, SAS, ASA, AAS to determine if triangles are congruent. 3. I can demonstrate by counter-example that not all SSA triangles are congruent. Applying Triangle Congruence 1. I can use corresponding parts of congruent triangles to solve problems. 2. I understand the characteristics of the angle bisectors and perpendicular bisectors of a triangle. Understanding Deductive Reasoning 1. I can use similar triangles to prove conjectures or theorems. 2. I can use congruent triangles to prove conjectures or theorems. 3. I can use deductive reasoning to prove conjectures or theorems. 1. I can solve problems by reasoning with geometry and algebra. 2. I can use properties of triangles to solve real world problems. 3. I can use coordinate geometry to solve problems. Understanding in Mathematics 1. I can use geometric notation to name shapes and describe relationships. 2. I can use geometric vocabulary to explain my thinking. 3. I can organize my proofs using two-column, flow-chart, and paragraph forms. 4. I can use accepted reasons to justify my thinking. Unit 5 Quadrilaterals Quadrilaterals Understand properties of special quadrilaterals, including parallelograms, squares, rectangles, rhombuses, and trapezoids. Understand properties that define special quadrilaterals. Understanding Quadrilaterals 1. I can identify properties of special quadrilaterals. 2. I can define special quadrilaterals using necessary and sufficient conditions. 3. I can use and apply properties of special quadrilaterals in the coordinate plane.
G.4.B, G.4.C Target 5B G.1.D, G.1.E, G.1.F, Connections G.4.A, G.4.B,C, G.7.A- C Big Idea Target 6A G.3.D, G.3.E Target 6B G.3.C Connections G.4.B,C, G.7.A,B,C Big Idea Target 7A G.6.A, G.6.C, G.6.F Target 7B G.6.C, G.6.F Connections G.6.F Understanding Deductive Reasoning 1. I can use deductive reasoning to prove theorems about quadrilaterals. (Not tested) 2. I can use deductive reasoning to prove conjectures about quadrilaterals. 4. I can solve problems by reasoning with geometry and algebra. 5. I can use properties of quadrilaterals to solve problems. 6. I can use coordinate geometry to solve problems. 7. I can use properties of quadrilaterals to find areas. Understanding in Mathematics 5. I can use geometric notation to name shapes and describe relationships. 6. I can use geometric vocabulary to explain my thinking. 7. I can organize my proofs using two-column, flow-chart, and paragraph forms. 8. I can use accepted reasons to justify my thinking. Unit 6 Right Triangles Right Triangles The properties of right triangles are used in many ways in the real world. We can choose from a variety of strategies to solve problems. Understanding Right Triangles 1. I can use the Pythagorean Theorem and its converse. 2. I can use sine, cosine, tangent ratios to find missing sides and angles. 3. I can solve problems involving right triangles. Understanding Special Right Triangles 1. I can find missing sides and angles of 30-60-90 triangles. 2. I can find missing sides and angles of 45-45-90 triangles. 3. I can solve problems involving special right triangles. 8. I can solve problems by reasoning with geometry and algebra. 9. I can use coordinate geometry to solve problems. 10. I can use properties of right triangles to find areas. Understanding in Mathematics 3. I can use correct notation and vocabulary to explain my thinking. 4. I can use an appropriate level of precision in my work, for a given audience. Unit 7 Area and Volume Area and Volume Determine area of two dimensional figures Determine surface area of three dimensional figures Determine volume of three dimensional figures Understanding Area of Two and Three - Dimensional Figures 4. I can determine area of a regular polygon. 5. I can determine area of a circle. 6. I can determine arc length along a circle. 7. I can determine surface area of right regular prisms 8. I can determine surface area of right cylinders 9. I can solve problems involving area. Understanding Volume of Three Dimensional Figures 4. I can determine volume of regular rectangular prisms. 5. I can determine volume of right cylinders. 6. I can solve problems involving volume. 11. I can solve problems by reasoning with area and volume. Understanding in Mathematics 5. I can use correct notation and vocabulary to explain my thinking. 6. I can use an appropriate level of precision in my work, for a given audience.
Understandings: Unit 1 Students will: Understand the shapes of Geometry Understand the coordinate plane in Geometry (linear functions, distance, midpoint) Understand how to communicate and use proper terminology for describing geometric figures Unit 2 Students will: Understand how to use inductive reasoning to verify conjectures Understand how to use deductive reasoning to prove or disprove statements Understand how to organize logical reasoning into various forms of proof Understand angle relationships between parallel lines and transversals Unit 3 Students will: Understand deductive reasoning Understand angle relationships with lines Understand angles and segments in a triangle Unit 4 Students will: Understand and apply triangle similarity Understand and apply triangle congruence Use deductive reasoning Unit 5 Students will: understand quadrilaterals Deductive reasoning involving quadrilaterals Unit 6 Students will: Understand right triangle trigonometry Special right triangles Solve problems using right triangle properties Unit 7 Students will: Understand the area of two and three dimensional shapes Understand volume of three dimensional shapes Essential Questions: How can you use your knowledge of algebra to develop your understanding of geometric properties? How can rigid transformations be used to verify properties of geometric figures? How does understanding properties of geometric figures relate to my life? How do I know if I have proven something? Students will know: How to make conjectures about the physical world around them using logical reasoning and properties of many kinds of geometric figures. Students will be able to: Apply and use theorems, postulates, and definitions about geometric figures Apply and use rules of similarity Formulate proofs of varying form Use transformations to prove geometric properties Write and solve algebraic equations based on their understanding of geometric properties Communicate using the formal language and notation for Geometry Evidence of Assessment Performance Tasks: Units are arranged so that students work through MathXL to master many of the objectives. Additional exercises are provided to develop application of newly learned concepts. Each unit concludes with both a skills-based assessment and one with applications.
Oher Evidence (self-assessments, observations, work samples, quizzes, tests and so on): Work in Math XL Quizzes and Unit tests in Math XL Activity Completion in Blackboard Weekly blogging on unit-specific topics Unit Assessment on Blackboard Types of Learning Activities Each unit follows the same basic pattern: 1. Work in MathXL 2. Weekly Blog Entries 3. Target Activities (including additional work if needed to meet standard) 4. Unit Assessments Online office hours are available for students to get real-time help with their learning. Direct Instruction Indirect Instruction Experiential Learning x Structured Overview x Mini Presentation x Drill & amp; Practice x Demonstrations Other (List) x Problem-based Case Studies x Inquiry x Reflective Practice Project Paper Concept Mapping Other (List) Learning Activities: 1 st Semester Geometry A Learning Activities Week 1 Getting Started Get Logged into Blackboard Check Announcements Go Through Start Here Set up MathXL account Find a Proctor Virt Field Trip Experiments x Simulations Games Field Observ, Role-playing x Model Bld, Surveys Other (List) Week 2 Start Unit 1 Foundations of Geometry Unit 1 Target 1A Task #1 Understanding Points Lines and Planes Task #2 Understanding Quadrilaterals Task #3 Understanding Triangles Week 3 Continue Unit 1 Foundations of Geometry Unit 1 Target 1A Independent Study Essays x Self-paced Computer Journals Learning Logs Reports Directed Study Research Projects Other (List) Interactive Instruction x Discussion Debates Role Playing Panels Peer Partner Learning Project team Laboratory groups x Think, Pair, Share Cooperative Learning Tutorial Groups Interviewing Conferencing Other (List)
Task #4 Target 1A Quiz Unit 1 Target 1B Task #1 Parallel and Perpendicular Lines Task #2 Midpoint and Distance Week 4 Continue Unit 1 Foundations of Geometry Unit 1 Target 1B Task #3 Point Slope Form Task #4 Writing Equations of Parallel and Perpendicular Lines Task #5 Target 1B Quiz Week 5 Continue Unit 1 Foundations of Geometry Unit 1 Target 1C Task #1 Measuring Segments Task #2 Measuring Angles Task #3 Constructions Task #4 Target 1B Quiz Week 6 Complete Unit 1 Foundations of Geometry Start Unit 2 Reasoning Unit 1 Assessment Unit 2 Target 2A Task #1 Understanding Inductive Reasoning Target 2A Quiz Week 7 Continue Unit 2 Reasoning Unit 2 Target 2B Task #1 Conditional Statements Task #2 Bi-Conditional Statements Task #3 Target 2B Quiz Week 8 Continue Unit 2 Reasoning Unit 2 Target 2C Task #1 Deductive Reasoning Task #2 Algebraic Proof Task #3 Target 2C Quiz Week 9 Continue Unit 2 Reasoning Unit 2 Target 2D Task #1 Angle Relationships Task #2 Geometric Proof Task #3 Flowchart and Paragraph Proof Task #4 Target 2D Quiz Week 10 Complete Unit 2 Reasoning Start Unit 3 Reasoning with Lines and Angles
Unit 2 Assessment Unit 3 Target 3A Task #1 Lines and Angles Task #2 Proving Lines Parallel Task #3 Perpendicular Lines Week 11 Continue Unit 3 Reasoning with Lines and Angles Unit 3 Target 3A Task #4 Target 3A Quiz Unit 3 Target 3B Task #1 Angle Relationships in Triangles Task #2 Exterior Angle Theorem Task #3 Medians and Altitudes of Triangles Week 12 Complete Unit 3 Reasoning with Lines and Angles Unit 3 Target 3B Task #4 Triangle Mid-Segment Task #5 Target 3B Quiz Unit 3 Assessment Week 13 Start Unit 4 Triangle Congruence and Similarity and Proof Benchmark #1 Benchmark #1 Unit 4 Target 4A Task #1 Similarity Task #2 Triangle Similarity Week 14 Continue Unit 4 Triangle Congruence and Similarity and Proof Unit 4 Target 4A Task #3 Applying Triangle Similarity Task #4 Proportional Reasoning Task #5 Target 4A Quiz Week 15 Continue Unit 4 Linear Systems Unit 4 Target 4B Task #1 Congruent Triangles Task #2 Triangle Congruence SSS and SAS Task #3 Triangle Congruence ASA and AAS Task #4 Target 4B Quiz Week 16 Complete Unit 4 Triangle Congruence and Similarity and Proof Unit 4 Target 4C Task #1 Triangle Congruence CPCTC Task #2 Perpendicular and Angle Bisector Task #3 Target 4C QUiz Unit 4 Assessment Week 17 Notebook Check
Notebook Check Finish up any needed work 2 nd Semester Geometry B Learning Activities Week 1 Getting Started Get Logged into Blackboard Check Announcements Go Through Start Here Set up MathXL account Find a Proctor Week 2 Start Unit 5 Quadrilaterals Unit 5 Target 5A Task #1 Properties and Attributes of Polygons Task #2 Properties of Parallelograms Task #3 Conditions of Parallelograms Week 3 Continue Unit 5 Quadrilaterals Unit 5 Target 5A Task #4 Conditions of Special Parallelograms Task #5 Properties of Kites and Trapezoids Task #6 Target 5A Quiz Week 4 Complete Unit 5 Quadrilaterals Unit 5 Target 5B Task #1 Proof with Quadrilaterals Task #2 Target 5B Quiz Unit 5 Assessment Week 5 Start Unit 6 Right Triangles Benchmark #2 Benchmark #2 Unit 6 Target 6A Task #1 Pythagorean Theorem Task #2 Trigonometric Ratios Week 6 Continue Unit 6 Right Triangles Unit 6 Target 6A Task #3 Solving RIght Triangles Task #4 Angles of Elevation and Depression Task #5 Target 6A Quiz Week 7 Complete Unit 6 Right Triangles Unit 6 Target 6B
Task #1Applying Special Right Triangles Task #2 Target 6B Quiz Unit 6 Assessment Week 8 Start Unit 7 Area and Volume Unit 7 Target 7A Task #1Solid Geometry Task #2 Surface Area of Prisms and Cylinders Task #3 Surface Area of Cones and Pyramids Week 9 Continue Unit 7 Area and Volume Unit 7 Target 7A Task #4 Target 7A Quiz Unit 7 Target 7B Task #1 Volume of Prisms and Cylinders Task #2 Volume of Pyramids and Cones Week 10 Complete Unit 7 Area and Volume Unit 7 Target 7B Task #3 Spheres Task #4 Target 7B Quiz Unit 7 Assessment Week 11 Start Unit 8 Circles Benchmark #3 Benchmark #3 Unit 8 Target 8A Task #1 Lines that Intersect Circles Task #2 Arcs and Chords Week 12 Continue Unit 8 Circles Unit 8 Target 8A Task #3 Sector Area and Arc Length Task #4 Circles in the Coordinate Plane Task #5 Target 8A Quiz Week 13 Continue Unit 8 Circles Unit 8 Target 8B Task #1 Inscribed Angles Task #2 Angle Relationships in Circles Task #3 Target 8B Quiz Week 14 Continue Unit 8 Circles
Unit 8 Target 8C Task #1 Segment Relationships in Circles Task #2 Target 8C Quiz Week 15 Complete Unit 8 Circles Notebook Check Unit 8 Target 8C Unit 8 Assessment Notebook Check Week 16 EOC Review EOC Review Assignment in Math XL Week 17 Finish up any needed work