Mathematics Curriculum Document for Geometry

Transcription

1 Unit Title: Essentials of Geometry Time Frame: 12 blocks Grading Period: 1 Unit Number: 1 Curriculum Enduring Understandings (Big Ideas): is a universal language that allows us to communicate in a precise and effective manner. Mathematical statements and arguments require the support of logical reasoning and proof. Geometry and measurement represent real-world objects, properties, and situations. The student will know: Representations and notations of point, line, ray, segment, angle, and plane Definitions of ray, segment, and angle Difference between inductive and deductive reasoning The student will be able to: Identify points, lines, and planes Use segments and congruence to find lengths of line segments Use midpoint and distance formulas (focus skill for PSAT preparedness) Measure and classify angles Describe angle pair relationships (complementary, supplementary, vertical, adjacent, linear) Classify polygons Find perimeter, circumference, and area of polygons and circles Use a compass to construct and recognize constructions of angle bisectors, congruent angles, congruent line segments, perpendicular bisectors Use and apply inductive and deductive reasoning (focus skill for PSAT preparedness) Identify, write, and determine validity of a conditional statement and its converse, inverse, and contrapositive Validate and/or complete proofs about segments and angles Compare and contrast Euclidean vs. Non-Euclidean geometry Unit Title: Essentials of Geometry Unit Number 1 Page 1 of 5

2 Essential Questions: How do we communicate geometric ideas? How do you build a convincing argument to a mathematical statement? What purpose does measurement serve? Student Understanding (student friendly TEKS): Convert measurements between systems (metric and customary) I can distinguish between Euclidean and non-euclidean geometry. (taken from G.1C) I can construct angle bisectors, congruent angles, congruent line segments, and perpendicular bisectors. (taken from G.2A) I can apply the properties of angles and lines and justify their use. (taken from G.2B) I can write a conditional statement its converse, inverse, and contrapositive and determine which are true. (taken from G.3A and G.3C) I can apply deductive and inductive reasoning. (taken from G.3D and G.3E) I can choose the best representation to solve a problem. (taken from G.4A) I can use numeric and geometric patterns to make conclusions. (taken from G.5B) I can draw one and two dimensional figures. (taken from G7.A) I can use formulas involving length, slope and midpoint. (taken from G.7C) I can convert between measurement systems to solve problems. (taken from G. 8F) TEKS: (G.1) Geometric structure. The student understands the structure of, and relationships within, an axiomatic system. The student is expected to: (C) compare and contrast the structures and implications of Euclidean and non-euclidean geometries. (G.2) Geometric structure. The student analyzes geometric relationships in order to make and verify conjectures. The student is expected to: (A) use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships; and (B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic. (G.3) Geometric structure. The student applies logical reasoning to justify and prove mathematical statements. The student is expected to: (A) determine the validity of a conditional statement, its converse, inverse, and contrapositive; (C) use logical reasoning to prove statements are true and find counter examples to disprove statements that are false; (D) use inductive reasoning to formulate a conjecture; and Unit Title: Essentials of Geometry Unit Number 1 Page 2 of 5

3 (E) use deductive reasoning to prove a statement. (G.4) Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. (G.5) Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to: (B) use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles; (G.7) Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly. The student is expected to: (A) use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures; (C) derive and use formulas involving length, slope, and midpoint. (G.8) Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations. The student is expected to: (F) use conversions between measurement systems to solve problems in real-world situations. Targeted College Readiness Standards: IB1, IIA1, IIC1, IIIA1, IIIA2, IIIA3, IIIC1, IIIC3, IIID1, IIID2, IVA1, IVB1, IVB2, VIIIA1, VIIIA2, VIIIA3, VIIIA4, VIIIA5, VIIIB1, VIIIB2, VIIIC1, VIIIC2, VIIIC3, IXA1, IXA2, IXA3, IXB1, IXB2, IXC1,IXC2,IXC3, XA1, XA2,XB1,XB2, XB3 Targeted ELPs: 1C, 1E, 1F, 1H, 2C, 2D, 2E, 2F, 2G, 2H, 2I, 3A, 3B, 3C, 3D, 3E, 3F, 3H, 3J, 4C, 4D, 4F, 4J, 4K, 5B, 5F,5G Academic Vocabulary: (6 steps) Bisect Midpoint Vertical angles Language of Instruction: Content specific vocabulary used to teach the unit. Adjacent Angles Angle (Acute, Right, Obtuse, straight) Angle measure Angles parts (vertex, sides, interior, exterior) Biconditional Collinear Complementary Angles Conclusion Conditional statement Unit Title: Essentials of Geometry Unit Number 1 Page 3 of 5

4 Instruction Congruent (segments and angles Conjecture Contrapositive Converse Coplanar Counterexample Deductive Distance Hypothesis Inductive Inverse Line Linear Pairs Negation Plane Point postulate Ray (including opposite) Segment Supplementary Angles Theorem Instructional Resources: Textbook: Chapter 1 all sections Chapter 2 all sections p. 198, Engaging : TEKS-Based Activities for Geometry (Points, Lines, and Planes Activity 3 p.8-11) Unit Title: Essentials of Geometry Unit Number 1 Page 4 of 5

5 Instructional Suggestions/Examples for PSAT preparedness Technology: Exemplar Lessons: Assessment Student self-assessment & reflection: Career Connections/Real Life Application: Research Based Instructional Strategies: Acceptable evidence or artifacts: Performance Task Unit 1 Unit Title: Essentials of Geometry Unit Number 1 Page 5 of 5