COURSE DESCRIPTION: This course in plane geometry is designed to acquaint the student with the geometric properties in mathematics necessary for further work in the field. Emphasis is on deductive and inductive reasoning in the solution of proofs. Students work either alone or in collaboration with others to discover geometric properties by experimentation and observation. Technology is used to assist the student in their discoveries.
COURSE OBJECTIVES: The student will apply the concepts of deductive and inductive reasoning to solve problems. He will gain an understanding of the geometry in the world around him and see geometry in many areas - nature, music, art, etc.. He will acquire a vocabulary of geometric terms, organize his thoughts, develop an intuitive approach to mathematics and communicate mathematically, both orally and in writing.
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Chapter |
Competencies |
Assessment |
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Chapter 0 Geometric Art |
The student will see that geometry is not just a college preparatory math class but is a way of thinking and seeing the world. The students will see how geometry appears in nature. He will discover that geometry is alive in cultures and art forms around the world. He will get an informal introduction to the symmetry found in nature and in much geometric art. In addition, he will become familiar with the use of two tools of geometry, the compass and the straightedge. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Project - students create an instructive poster on a topic. |
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Chapter l Inductive Reasoning |
The student is introduced to inductive reasoning, the process of observing patterns, and making generalizations about those patterns. The student will learn that inductive reasoning is basis of the scientific method, that mathematicians use inductive reasoning to make discoveries and then attempt to verify his discoveries logically. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 2 Introducing Geometry |
The student is introduced to the terms and symbols of geometry. In this chapter they will write their own definitions for many geometric figures and terms. He will generate these definitions using inductive reasoning. The geometry class will create their own definitions using an "examples and nonexamples" approach. The student will also practice translating and solving word problems and visualizing geometric figures in and three dimensions. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 3 Using Tools of Geometry |
The student will learn how to use the compass and straightedge and will discover the basic geometric constructions. The student will also discover how to perform many of these constructions using patty papers. The student will also be introduced to Geometer’s Sketchpad. The student will perform his first geometric investigations and make conjectures at the conclusion of those investigations. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Geometer’s Sketchpad explorations Game - Jeopardy-type as review |
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Chapter 4 Line and Angle Properties |
The student explore line and angle relationships. Through explorations he will make some important conjectures, including the Vertical Angles Conjecture conjectures about parallel lines, midpoint and slope conjectures using coordinate geometry, and equations of lines. Although students first apply coordinate geometry in Chapter 1, it is a main focus in Chapter 4. In this chapter, the student will also begin to see simple algebraic and paragraph proofs. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Several projects |
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Chapter 5 Triangle Properties |
The student will discover properties of triangles, including the triangle angle sum, triangle inequalities, properties of isosceles triangles, and what conditions guarantee that two triangles are congruent. Rather than being told that SSS, SAS, ASA, and SAA are shortcuts for congruence, students discover these shortcuts by using tools of geometry. The student will follow the reasoning in flow-chart proofs and create several flow-chart proofs of their own. The student will use a graphing calculator to draw triangles and explore, specifically, the isosceles triangle. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Small projects Graphing Calculator Investigation |
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Chapter 6 Polygon Properties |
Properties of other polygons are explored. The student will make conjectures about angle sums, exterior angles, and properties of special quadrilaterals. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Game - Matho The Geometry Scavenger Hunt |
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Chapter 7 Circles |
The student is introduce to the properties of circles. Using his geometric tools, the student will discover some of the relationships between the angles and line segments in and around circles, including properties of tangents, inscribed angle and central angle relationships, and circumference and diameter relationships. In addition, the student will solve word problems about circles. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Geometer's Sketchpad Project |
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Chapter 8 Transformations and Tessellations |
Symmetry is found in art, architecture, dance, music, poetry, and, of course, mathematics. In this chapter, the student returns to symmetry to explore it more in depth and to discover some basic properties of transformational geometry. Then he will use the properties of transformations to create special tiling patterns, or tessellations. We will look at the works of M. C. Escher. The student will learn a few of Escher's techniques and create his own tessellating designs. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Geometer’s Sketchpad project Graphing Calculator Investigation: |
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Chapter 9 Area |
The student will discover formulas for finding the areas of rectangles, parallelograms, triangles, kites, trapezoids, regular polygons, a circles by cutting apart and rearranging the parts of these figures to determine the formulas for their areas. Then the student will solve word problems using area formulas. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Project: Quilt Making |
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Chapter 10 Pythagorean Theorem |
The student is reintroduced to the Pythagorean Theorem. He will also discover a number of conjectures related to it. The student will then gain experience solving word problems using circle and area conjectures, d = rt relationships, and the Pythagorean Theorem. He will extend the theorem to derive the distance formula in coordinate geometry and the equation of a circle. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Project: Creating a Geometry Flip Book Geometer's Sketchpad Project: A Pythagorean Fractal |
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Chapter 11 Volume |
The student is introduced to the formulas for finding the volumes of prisms, pyramids, cylinders, cones, and spheres. Students will also use the circle conjectures, area conjectures, the Pythagorean Theorem, and density concepts, along with the new volume conjectures, to solve word problems. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Projects Manipulatives used to investigate The Five Platonic Solids and Euler's Formula for Solids |
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Chapter 12 Similarity |
The student will discover some of the basic properties of similarity. He will be asked to find the heights of trees, flagpoles, and buildings by measuring shadows and using similar right triangles. The student will see how important similarity is to industry (particularly in the fields of film, photography, optics, and architecture) and how it is useful in chemistry, physics, and medicine. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Project: Making a Mural Project: Why Elephants Have Big Ears |
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Chapter 13 Trigonometry |
Some of the properties and applications of right triangle trigonometry, including the Law of Sines and Law of Cosines, are introduced. The student will use trigonometry to calculate distances that are difficult or impossible to measure directly.
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Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Geometer's Sketchpad Project |
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Chapter 14 Deductive Reasoning |
The student will learn about the other type of reasoning, deductive reasoning (commonly called logical reasoning). The student will learn logical arguments to symbolic form, and then they will use rules of logic to determine whether their arguments are valid. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 15 Geometric Proof |
Students will use what they learned about deductive reasoning in the previous chapter to prove many of their earlier conjectures. They will use flow-charts to aid them in planning their proofs. They wilt also see how some conjectures are logically related to each other. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test Project: Non-Euclidean Geometries |
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Chapter 16 Sequences of Proofs |
The student will prove some major theorems in Euclidean geometry and learn special proof techniques, such as coordinate proof and indirect proof. Throughout he will perform geometric investigations, make conjectures, and then prove or disprove his conjectures. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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The Geometer's Sketchpad is used for demonstration purposes, as well as a hands-on teaching aid. The students use the software program also to complete some of their projects.