ALGEBRA IIA/GEOMETRY FORM II

Transcription

1 ALGEBRA IIA/GEOMETRY FORM II Textbooks: Geometry, Integrated Mathematics, Second Edition, The University of Chicago School mathematics Project (UCSMP), Prentice Hall, Algebra and Trigonometry, Second Edition by James Stewart, Lothar Redlin, & Saleem Watson 2007, Thompson Brooks / Cole Course Description: The purpose of this course is twofold. The first purpose is to give the students a solid foundation in geometry. Skills developed in Algebra I are integrated throughout this course, although geometry will constitute the main emphasis and subject matter. The students will work on geometry topics for the first three quarters of the year. The second purpose is to reinforce algebra skills and to prepare students, through the introductory two chapters of the Brooks /Cole textbook, for the next mathematics class. This will be done in the last quarter and it will set the stage for following year as students will continue with this text in their junior mathematics course. This course begins with basic geometric concepts and builds on this. Students will be exposed to logic, geometric reflections utilizing congruency, polygons and symmetry, triangle congruency, indirect and coordinate proofs, direct and indirect reasoning, similarity, and work with circles. Additionally, the coordinate geometry follows from the algebra and the transformation geometry introduces the idea of functions in an applied setting. Applications of new mathematical concepts are included in each chapter through the use of word problems. Graphing calculators are required in this course. Additionally, students will be using Geometer s Sketchpad. They will be utilizing this venue for constructions, exploring concepts and applications as well as a means to prove various geometric theorems. Calculator Policy: A TI-84 Silver Edition is required for this course. During the course, students will use the calculator for investigations and to solve problems. Students will be expected to understand how to solve problem both with the calculator and without the calculator. However, students should not expect to be able

2 to use their calculator on every quiz, test, and homework assignment. Course Note: The junior math class, Algebra IIB/Trigonometry, is split into two sections called X and Y. Students assigned to the X class are typically very comfortable with math, master concepts quickly, and need less individual attention. Students assigned to the Y class often need more class time or individual attention to master the concepts. At the end of the sophomore year, students are assigned into either the X or Y junior math class by the sophomore math teacher based upon performance in the sophomore math class.

3 Course Goals: 1. Students will become proficient in the language and vocabulary of geometry. 2. Students will develop the ability to logically prove theorems, utilizing properties, definitions and already proved theorems. 3. Students will develop the ability to visualize, recognize patterns, draw and follow algorithms. 4. Students will become proficient with the Geometer s Sketchpad software. 5. Students will be able to apply geometric ideas in real world situations. 6. Students will be able to represent geometric concepts with coordinates or diagrams. 7. Students will review algebraic concepts from Algebra I and be introduced to equations and inequalities. 8. To enable students to solve problems both with and without a calculator. Course Objectives: At the end of this course students will be able to: 1. Construct, rotate, translate and reflect different figures both manually (using a protractor and compass) and with the Geometer s Sketchpad. 2. Identify and apply the definitions, properties and theorems about segments, lines, rays and angles and use them to prove theorems 3. Identify and apply properties and theorems regarding parallel and perpendicular lines and use them to prove theorems 4. Analyze and apply angle relationships (linear pairs, vertical, complimentary, supplementary, corresponding and alternate interior angles) in real world and mathematical situations. 5. Understand and use the properties, definitions and concerning congruent and similar triangles and other figures to prove additional theorems and solve problems. 6. Use and understand the basic properties of circles (arcs, chords, central angles, inscribed angles) to prove basic theorems and solve problems. 7. Analyze and apply spatial relationships concerning points, lines and planes - betweenness of points, midpoint, segment length, collinear, coplanar, parallel, perpendicular, and skew. 8. Explore geometry to make and test conjectures using geometric tools and the Geometer s Sketchpad. 9. Use transformations (translations, rotations, reflections, glide reflections and dilations) to gain insight, via sketches, coordinates, vectors, function notation, and technology, into other areas of mathematics and to solve real world problems.

4 10. Use similarity of figures and scale factors to analyze and solve problems. 11. Model real world problems using visualization, spatial reasoning and geometric relationships. 12. Understand and express the slope of a line, use two coordinates to find the slope, and use slope to express parallelism and perpendicularity. 13. Find the distance between two points using their coordinates and the Pythagorean Formula or the distance formula. 14. Find the equation of a circle given its center and radius. 15. Find the midpoint of a segment with the midpoint formula and the coordinates of the endpoints. Course Sequence: In Geometry (Quarters 1 through 3) A. Chapter 1: Points and Lines Lesson 1: 1.1 Dots as Points 1.2 Locations as Points 1.3 Ordered Pairs as Points Lesson 2: 1.4 Points in Networks 1.5 Drawing in Perspective Lesson 3: 1.6 The Need for Undefined Terms 1.7 Betweenness and Distance B. Chapter 2: The Language and Logic of Geometry Lesson 1: 2.1 The Need for Definitions 2.2 If-Then Statements 2.3 Converses Lesson 2: 2.4 Good Definitions 2.5 Unions and Intersections of Figures

5 Lesson 3: 2.6 Polygons 2.7 The Triangle Inequality 2.8 Conjectures Test: Chapters 1 and 2 C. Chapter 3: Angles and Lines 3.1 Angles and Their Measures 3.2 Arcs and Rotations 3.3 Properties of Angles 3.4 Algebra Properties used in Geometry 3.5 One-Step Proof Arguments 3.6 Parallel Lines 3.7 Perpendicular Lines Test: Chapter 3 D. Chapter 4: From Reflections to Congruence 4.1 Reflecting Points 4.2 Reflecting Figures 4.3 Miniature Golf and Billiards 4.6 Translations and Vectors 4.8 When are Figures Congruent? Test: Chapter 4 E. Chapter 5: Proofs Using Congruence 5.1 Corresponding Parts of Congruent Figures 5.2 Congruence and Equality 5.3 One- Step Congruence Proofs 5.4 Proofs Using Transitivity 5.5 Proofs Using Reflections 5.6 Auxiliary Figures and Uniqueness 5.7 Sums and Angle Measures in Polygons

6 Test: Chapter 5 F. Chapter 6: Polygons and Symmetry 6.1 Reflections and Symmetric Figures 6.2 Isosceles Triangle 6.3 Types of Quadrilaterals 6.4 Properties of Kites 6.5 Properties of Trapezoids 6.6 Rotation Symmetry 6.7 Regular Polygons Test: Chapter 6 G. Chapter 7: Triangle Congruence 7.1 Drawing Triangles 7.2 Triangle Congruence Theorems 7.3 Proof Using Triangle Congruence Theorems 7.4 Overlapping Triangles 7.5 The SSA Condition and the HL Congruence 7.6 Tessellations (optional) 7.7 Properties of Parallelograms 7.8 Sufficient Conditions for Parallelograms 7.9 Exterior Angles Test: Chapter 7 Approximate Semester Break

7 H. Chapter 8: Perimeters and Areas 8.1 Perimeter Formulas 8.2 Fundamental Properties of Area 8.3 Areas of Irregular Regions 8.4 Areas of Triangles 8.5 Areas of Trapezoids 8.6 The Pythagorean Theorem 8.7 Arc Length and Circumference 8.8 The Area of a Circle Test: Chapter 8 Chapters 9: Three Dimensional Figures Chapter 10: Surface Areas & Volumes 9.1 Points, Lines, Planes in Space 9.3 Prisms and Cylinders 10.1 Surface Areas of Prisms and Cylinders 9.4 Pyramids and Cones 10.2 Surface Areas of Pyramids and Cones 9.5 Spheres and Sections 10.9 The Surface Area of a Sphere 10.5, 10.7 Volumes of Prisms, Cylinders, Pyramids, and Cones Test: Chapters 9 and 10 J. Chapter 12: Similarity (no proofs only the concepts) 12.5 Similar Figures Theorem 13.1 The SSS Similarity Theorem 13.2 The AA and SAS Similarity Theorem K. Chapter 14: Circles Chapter 14 is important for the SAT. These Important concepts will be covered and students will solve problems (no proofs) Identify the parts of the circle 14.2 The Inscribed Angle Theorem

8 14.4 Angles formed by Chords & Secants 14.5 Tangents to Circles are perpendicular to their radius Test: Chapters 12 and 14 Approximate 4 th Quarter Work: In Algebra and Trigonometry Additional sections will be covered if time permits. I. Chapter P: Prerequisite Chapter P.2 Real Numbers (using interval and set notation, definition of absolute value) P.3 Integer Exponents P.4 Rational Exponents and Radicals P.5 Algebraic Expressions P.6 Factoring P.7 Rational Expressions