CURRICULUM CATALOG. GSE Geometry ( ) GA
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1 CURRICULUM CATALOG
2 Table of Contents COURSE OVERVIEW... 1 UNIT 1: TRANSFORMATIONS IN THE COORDINATE PLANE... 2 UNIT 2: SIMILARITY, CONGRUENCE, AND PROOFS PART UNIT 3: SIMILARITY, CONGRUENCE, AND PROOFS PART UNIT 4: SIMILARITY, CONGRUENCE, AND PROOFS PART UNIT 5: RIGHT TRIANGLE TRIGONOMETRY... 3 UNIT 6: SEMESTER EXAM... 3 UNIT 7: CIRCLES AND VOLUME PART UNIT 8: CIRCLES AND VOLUME PART UNIT 9: GEOMETRIC AND ALGEBRAIC CONNECTIONS... 4 UNIT 10: APPLICATIONS OF PROBABILITY... 4 UNIT 11: SEMESTER EXAM... 4 UNIT 12: FINAL EXAM Glynlyon, Inc. i
3 Course Overview is a full year, high school math course for the student who has successfully completed the prerequisite course, Algebra I. The course focuses on the skills and methods of linear, coordinate, and plane geometry. In it, students will gain solid experience with geometric calculations and coordinate plane graphing, methods of formal proof, and techniques of construction. Transformations in the Coordinate Plane: Building on standards from middle school, students will perform transformations in the coordinate plane, describe a sequence of transformations that will map one figure onto another, and describe transformations that will map a figure onto itself. Students will compare transformations that preserve distance and angle to those that do not. Similarity, Congruence, and Proofs Part 1: Building on standards from the previous units and from middle school, students will develop facility with geometric proofs and use the concepts of congruence to prove theorems involving lines, angles, triangles, and other polygons. Similarity, Congruence, and Proofs Part 2: Students will identify criteria for similarity and congruence of triangles and use proportional reasoning to develop a formal understanding of similarity and congruence of triangles. Students will use the concepts of congruence to prove theorems involving triangles and various quadrilaterals. Similarity, Congruence, and Proofs Part 3: Students will use transformation sequences and various types of constructions. Students will investigate circles and spheres. Right Triangle Trigonometry: Students will apply similarity in right triangles to understand right triangle trigonometry. Students will use the Pythagorean Theorem and the relationship between the sine and cosine of complementary angles to solve problems involving right triangles. Circles and Volume Part 1: Students will understand and apply theorems about circles, construct inscribed shapes and tangents to circles, and understand special angles within circles. Students will explore special segments of circles. Circles and Volume Part 2: Students will find the circumference of circles as well as the arc lengths of circles. Students will develop and explain formulas related to circles and the volume of solid figures and use the formulas to solve problems. Building on standards from middle school, students will extend the study of identifying cross-sections of three-dimensional shapes to identifying three-dimensional objects generated by rotations of two-dimensional objects. Geometric and Algebraic Connections: Students will use the concepts of distance, midpoint, and slope to verify algebraically geometric relationships of figures in the coordinate plane (triangles, quadrilaterals, and circles). Students will solve problems involving parallel and perpendicular lines, perimeters and areas of polygons, and the partitioning of a segment in a given ratio. Students will derive the equation of a circle and model real-world objects using geometric shapes and concepts. Applications of Probability: Students will understand independence and conditional probability and use them to interpret data. Building on standards from middle school, students will formalize the rules of probability and use the rules to compute probabilities of compound events in a uniform probability model Glynlyon, Inc. 1
4 Unit 1: TRANSFORMATIONS IN THE COORDINATE PLANE 1. Course Overview 19. Circles: Area of Segments 2. Defined Terms: Definitions 20. Construction: Dividing a Segment 3. Angle Definitions 21. Parallel and Perpendicular Lines 4. Quiz Quiz 4 5. Angle Measurement 23. Introduction: Rigid Motion, or Isometry 6. Angle Relationship Definitions 24. Isometry: Reflection 7. Angle Relationship Theorems (1) 25. Isometry: Translation 8. Angle Relationship Theorems (2) 26. Quiz 5 9. Quiz Similarity Transformation: Dilation 10. Basic Properties of Parallels 28. Product Transformation 11. Transversals and Special Angles 29. Inverse and Identity Transformation 12. More Proofs: Transversals and Special Angles 30. Quiz Continued Proofs: Transversals and Special Angles 31. Performance Task 14. Quiz Alternate Performance Task* 15. More Proofs for Postulates 9 and Special Project* 16. Construction: Perpendiculars 34. Test 17. Construction: Parallels 35. Alternate Test* 18. Circles: Area of Sectors Unit 2: SIMILARITY, CONGRUENCE, AND PROOFS PART 1 1. Geometric Theorems 16. Proving Triangles Congruent (3) 2. Construction: Copying Figures 17. Quiz 3 3. Construction: Bisecting Figures 18. Proving Right Triangles Congruent 4. More Proofs: Transversals and Special Angles 19. Independent Triangles (1) 5. Continued Proofs: Transversals and Special Angles 20. Independent Triangles (2) 6. More Proofs for Postulates 9 and Overlapping Triangles (1) 7. Quiz Overlapping Triangles (2) 8. Construction: Perpendiculars 23. Isosceles Triangles (1) 9. Construction: Tangents to Circles 24. Isosceles Triangles (2) 10. Exterior and Remote Interior Angles of a Triangle 25. Quiz Proofs Involving Triangles 26. Performance Task 12. Quiz Alternate Performance Task* 13. Defining Congruent Triangles 28. Special Project* 14. Proving Triangles Congruent (1) 29. Test 15. Proving Triangles Congruent (2) 30. Alternate Test* 2018 Glynlyon, Inc. 2
5 Unit 3: SIMILARITY, CONGRUENCE, AND PROOFS PART 2 1. Construction of Triangles Meaning of Similarity-Proofs 2. Construction of Triangles Theorems-Similar Polygons 3. Constructing Inscribed Shapes 18. Theorems-Special Segments in Triangles 4. Inequality Theorem in One Triangle Part Similar Right Triangles 5. Inequality Theorem in One Triangle Part Quiz 3 6. Inequality Theorem in Two Triangles 21. Theorem about Right Triangles 7. Quiz Theorem about Right Triangles 8. Quadrilateral Parallelograms Theorems Part Using Similar Triangles in Indirect Measurement 9. Quadrilateral Parallelograms Theorems Part Quiz Triangles that Use Parallelograms in Proofs 25. Performance Task 11. Parallelograms: Rectangles 26. Alternate Performance Task* 12. Parallelograms: Rhombus 27. Special Project* 13. Quiz Test 14. Meaning of Similarity 29. Alternate Test* 15. Meaning of Similarity-Theorems Unit 4: SIMILARITY, CONGRUENCE, AND PROOFS PART 3 1. Characteristics of Circles 15. Construction: Polygons 2. Characteristics of Spheres 16. Construction: Dividing a Segment 3. Tangents 17. Construction: 4th Proportion 4. Arcs 18. Construction: The Geometric Mean 5. Chords 19. Introduction: Rigid Motion, or Isometry 6. Quiz Transformation Sequences 7. Theorems (1) 21. Quiz 4 8. Theorems (2) 22. Performance Task 9. Quiz Alternate Performance Task* 10. Special Angles Type Performance Task 11. Special Angles Type Alternate Performance Task* 12. Special Angles Type Special Project* 13. Quiz Test 14. Special Segments 28. Alternate Test* Unit 5: RIGHT TRIANGLE TRIGONOMETRY 1. Lengths of Sides 9. Using SOH CAH TOA in Trigonometry 2. The Pythagorean Theorem 10. Law of Sines 3. Trigonometry-Sine Ratio 11. Quiz 2 4. Trigonometry-Cosine Ratio 12. Performance Task 5. Trigonometry-Tangent Ratio 13. Alternate Performance Task* 6. Quiz Special Project* 7. Using Trigonometry in Indirect Measure 15. Test 8. Area of Kites 16. Alternate Test* Unit 6: SEMESTER EXAM 1. Exam 2. Alternate Exam* 2018 Glynlyon, Inc. 3
6 Unit 7: CIRCLES AND VOLUME PART 1 1. Construction: Tangents to Circles 10. Special Segments 2. Constructing Inscribed Shapes 11. Quiz 2 3. Tangents 12. Construction: Circles 4. Theorems (1) 13. Performance Task 5. Theorems (2) 14. Alternate Performance Task* 6. Quiz Special Project* 7. Special Angles Type Test 8. Special Angles Type Alternate Test* 9. Special Angles Type 3 Unit 8: CIRCLES AND VOLUME PART 2 1. Circles: Circumference and PI 7. Performance Task 2. Arc Length 8. Alternate Performance Task* 3. Cavalieri's Principle: Volume of Cylinders, 9. Special Project* Pyramids, and Cones 4. Cavalieri's Principle: Volume of Spheres and Other Solids 10. Test 5. Two- and Three-Dimensional Shapes 11. Alternate Test* 6. Quiz 1 Unit 9: GEOMETRIC AND ALGEBRAIC CONNECTIONS 1. Project: Model and Scale Drawing 7. Modeling with Geometric Figures 2. Perimeter and Area 8. Density 3. Equation of a Circle 9. Quiz 2 4. Quiz Special Project* 5. Parallel and Perpendicular Lines 11. Test 6. Proofs with Coordinate Geometry (1) 12. Alternate Test* Unit 10: APPLICATIONS OF PROBABILITY 1. Geometric Probability 7. Two-Way Frequency Tables 2. Addition of Probabilities 8. Quiz 2 3. Multiplication of Probabilities 9. Performance Task 4. Quiz Special Project* 5. Conditional Probability 11. Test 6. Conditional Probability in Real-World Situations 12. Alternate Test* Unit 11: SEMESTER EXAM 1. Exam 2. Alternate Exam* Unit 12: FINAL EXAM 1. Exam 2. Alternate Exam* (*) Indicates alternative assignment 2018 Glynlyon, Inc. 4
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