COURSE DESCRIPTION: A beginning course where students use an intuitive approach to geometry. Formal proofs and informal proofs are part of this course. An informal approach used to "discover" certain properties, theorems and postulates in the first semester of the course. Students draw, measure, and make assumptions about theorems and topics. The student is lead to many of his conclusions by repetition of the same process on each topic. The Geometer's Sketchpad is used throughout the course.
COURSE GOALS: To provide the student with the foundation for future courses in math, science or business, and provide the student with the skills necessary to solve many everyday problems where critical thinking plays a part.
COURSE OBJECTIVES:
To help the student develop skills in logical reasoning and spatial visualization; to enable the student to express mathematical ideas orally and in writing; to help the student apply geometric concepts and skills; to help the student appreciate the need for precision of the language of mathematics; to teach the student greater responsibility for his own learning; to provide the student with hands on activities to encourage visual thinking; to provide the student with the tools to solve problems better, not just in mathematics but in other subjects, by teaching skills for critical thinking, analyzing and drawing logical conclusions.
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Unit |
Competencies |
Assessment |
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Unit 1 Terminology and Notation |
The student will know the basic geometric terms and symbols. The student will be able to classify triangles, determine the size of angles, use a protractor to measure angles, and make accurate drawings of triangles and quadrilaterals. The student will also learn the different types of angles and the angles of a triangle. The student will also classify polygons and derive the formula for calculating the number of diagonals in a convex polygon. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 2 Geometric Construction |
The student will use a compass, pencil and straightedge to make geometric constructions of angle bisectors, angles, segments, and triangles. The student will learn the definition of regular, and construct triangles, hexagons, dodecagons, quadrilaterals, octagons, and pentagons inscribed in circles. The student will also learn the meaning of perpendicular and how to construct perpendicular bisectors and lines. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 3 Parallel & Perpendicular Lines |
The student will learn about the different angles formed when lines intersect at different points. The student will be able to identify transversals, types of angles along a transversal, and parallel lines. The student will learn about the relations of angles formed when parallel lines are cut by a transversal, and find measures of angles of more complex figures involving parallel lines and triangles. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 4 Quadrilaterals |
The student will learn properties of certain special quadrilaterals such as parallelogram, rectangle, rhombus, square, trapezoid, and isosceles trapezoid. The student will also identify the properties of a quadrilateral and identify the specific quadrilaterals based on its properties |
Homework Class Discussions Presentations Quizzes Unit Test |
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Unit 5 Perimeter and Circumference |
The student will determine the circumference of a circle and use the formula to solve application problems dealing with circles. The student will also determine the perimeter of a variety of figures. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 6 Area |
The student will find the area of squares, rectangles, circles, parallelograms, triangles, and trapezoids. The student will also find the surface area of spheres and a variety of nonconventional figures. The student will be able to find the lengths of the base and altitude of triangles, parallelograms and trapezoids given the area and other pertinent information. The student will use the area formulas in application problems. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 7 Right Triangles |
The student will learn how and when to use the Pythagorean Theorem. The student will find the lengths of sides of triangles and will be able to recognize "special triangles". The student will use the three basic trigonometric ratios to find missing lengths or angles of a right triangle. The student will be able to determine which of the trigonometric ratios to use in application problems. The student will also be introduced to Pythagorean Triples. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 8 Solids |
The student will find the volume of prisms, right prisms, right cylinders, solids, spheres, pyramids, and cones. The student will use the volume formulas and the appropriate values for pi to solve application problems. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 9 Coordinate Geometry |
The student will know coordinate geometry terminology and be able to find the distance between points, classify polygons, and find the area of a polygon by using the distance formula. The student will also be able to find the midpoint of a segment using the midpoint formula, and be able to find the slope of a line. The student will be able to recognize linear equations in standard form, slope-intercept form, and point-slope form. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 10 Congruent Triangles |
The student will determine if two triangles are congruent using the SSS, SAS, ASA, AAS Postulates, and the HL Theorem. The student will use flowchart proofs, and two-column proofs to prove the congruency of 2 triangles and multiple congruencies, |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 11 Similarity |
The student will determine if polygons are similar. The student will use ratios and proportions to find lengths of sides, perimeter, area, and volume of polygons. The student will also use AA, SSS, and SAS Postulates and Theorems to prove similarity in triangles. The student will use ratio and proportions to solve application problems and determine lengths of sides of similar triangles. The student will use a compass to construct proportional segments. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 12 Angles of Polygons |
The student will derive formulas for the sum of the measures of interior angles, the measure of interior angles, the sum of exterior angles, and the exterior angles. The student will find lengths and angle measures of polygons using the formulas. The student will use formulas to determine the area of regular polygons and solve application problems. The student will also use a compass to locate the center of a polygon. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 13 Circles |
The student will learn terminology, notation, angle formulas, and segment formulas involving circles. The student be able to recognize angle relationships, find measures of arcs, central angles, inscribed angles, angles formed by tangents, angles formed by chords, and angles formed by secants. The student will also determine segment lengths and solve application problems. |
Homework Class Discussion Presentations Quizzes Unit Test |
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Unit 14 Transformations and Tessellations |
The student will know the basic motions (translation, rotation, and reflection) of transformation and tessellation. The student will recognize symmetry in letters, numbers, flags, nature, pictures, and designs. The student will create tessellation drawings by hand, and also create tessellation designs on the computer using the Geometer’s Sketchpad © program. |
Homework Class Discussion Presentations Quizzes Unit Test |
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