Geometry Course Title: Geometry

Transcription

1 Course Title: Geometry Geometry Duration: one year Frequency: one class period daily Year: Text: Geometry(Prentice Hall Mathematics) Other materials: Teacher prepared worksheets Areas to be evaluated: Student s understanding of Geometric concepts Additional activities: Course objectives: The students will: --value mathematics --reason mathematically --develop thinking skills --solve geometric type problems --practice algebraic skills in reference to geometric problems Unit 1: Pre-chapter Time frame:5 days Unit 2:Tools of Geometry Time frame: 11 days Unit 3:Reasoning and Proof Time frame: 11 days Recall Algebra I skills useful for Geometry --solve several types of equations --combine like terms by adding and subtracting --solve using FOIL --factor and solve quadratic equations --converting measurements --simplifying ratios --solving simple absolute value Students will: --Understand basic terms of geometry --Understand basic postulates of geometry --Identify segments and rays --Recognize parallel lines --Find the lengths of segments --Find the measures of angles --Identify special angle pairs --Find the distance between two points in the coordinate plane --Find the coordinates of the midpoint of a segment in the coordinate plane --Find perimeters of rectangles and squares, and circumference of circles Students will: --Recognize conditional statements --Write converses of conditional statements

2 --Write biconditionals --Recognize good definitions --Use the Law of Detachment --Use the Law of Syllogism --Connect reasoning in algebra and geometry --Prove and apply theorems about angles Unit 4: Parallel and Perpendicular Lines Time frame: 17 dats Unit 5: Congruent Triangles Time frame: 17 days Unit 6: Relationships Within Triangles and Quadrilaterals Time frame: 18 days - To identify angles formed by two lines and a transversal - To prove and use properties of parallel lines - To use a transversal in proving lines parallel - To relate parallel and perpendicular lines - To classify triangles and find the measures of their angles - To classify polygons - To find the sums of the measures of the interior and exterior angles of polygons - To graph lines given their equations - To write equations of lines - To relate slope and parallel lines - To relate slope and perpendicular lines - To recognize congruent figures and their corresponding parts - To prove two triangles congruent using the SSS and SAS postulate - To prove two triangles congruent using the ASA and AAS postulates - To use triangle congruence and CPCTC to prove that parts of two triangles are congruent - To use and apply properties of isosceles triangles - To identify congruent overlapping triangles - To prove two triangles congruent by first proving two other triangles congruent - To use properties of midsegments to solve problems - To use properties of perpendicular bisectors and angle bisectors - To identify properties of perpendicular bisectors and angle bisectors - To identify properties of medians and altitudes of a triangle - To define and classify special types of quadrilaterals - To use relationships among sides and among angles of parallelograms - To use relationships involving diagonals of parallelograms or

3 transversals - To determine whether a quadrilateral is a parallelogram - To use properties of diagonals of rhombuses and rectangles - To determine whether a parallelogram is a rhombus or a rectangle - To verify and use properties of trapezoids and kites Unit 7: Similarity and Square Roots Time frame: 18 days - To write ratios and solve proportions - To identify similar polygons - To apply similar polygons - To use AA, SAS, and SSS similarity statements - To apply AA, SAS and SSS similarity statements - Solve by simplifying square roots - Solve by multiplying square roots - Solve by dividing square roots - Solve by adding and subtracting square roots - To find and use relationships in similar right triangles - To use the Side-Splitter Theorem - To use the Triangle-Angle-Bisector Theorem Unit 8: Right Triangles and Trigonometry Time frame: 12 days -- - To use the Pythagorean Theorem - To use the converse of the Pythagorean Theorem - To use the properties of triangles - To use the properties of triangles - To use tangent ratios to determine side lengths in triangles - To use sine and cosine to determine side lengths in triangles - To use angles of elevation and depression to solve problems Unit 9: Area Time frame: 18 days - To find the area of a parallelogram - To find the area of a triangle - To find the area of a trapezoid - To find the area of a rhombus or a kite - To find the area of a regular polygon - To find the area of a regular polygon using trigonometry - To find the area of a triangle using trigonometry - To find the measures of central angles and arcs - To find circumference and arc length - To find the areas of circles, sectors, and segments of circles

4 Unit 10: Surface Area and Volume Time frame: 17 days Unit 11: Circles Time frame: 16 dasys - To find the surface area of a prism - To find the surface area of a cylinder - To find the surface area of a pyramid - To find the surface area of a cone - To find the volume of a prism - To find the volume of a cylinder - To find the volume of a pyramid - To find the volume of a cone - To find the surface area and volume of a sphere - To use the relationship between a radius and a tangent - To use the relationship between two tangents from one point - To use congruent chords, arcs, and central angles - To recognize properties of lines through the center of a circle - To find the measure of an inscribed angle - To find the measure of an angle formed by a tangent and a chord - To find the measures of angles formed by chords, secants, and tangents - To find the lengths of segments associated with circles - To write an equation of a circle - To find the center and radius of a circle COURSE TITLE:Geometry Geometry Unit GRADE LEVEL / DEPT.:ninth through twelfth grade/math UNIT/TITLE: Unit 1: Introduction: Algebra review SEMESTER:first DATE OF REVISION:2013 LENGTH OF UNIT: five days -Recall Algebra I skills useful for Geometry ---solve several types of equations ---combine like terms by adding and subtracting ---solve using FOIL ---factor and solve quadratic equations ---converting measurements ---simplifying ratios ---solving simple absolute value 2 The student uses algebraic concepts in a variety of situations 2.2.A2B quadratic equations with integer solutions

5 2.2.K3A linear equations and inequalities analytically 2.2.K3F equations and inequalities with absolute value quantities containing one variable with a special emphasis on using a number line and the concept of absolute value. Primary means of instruction: Direct teacher instruction using the chalkboard Secondary means of instruction: Student works on a worksheet; self-graded Biblical: God created mathematics for us to understand patterns in nature Integration of other skills: students will apply these Algebra skills with Geometry concepts Evaluations (Formal and informal): homework grades using self-grading; verbal feedback during lectures Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Tools of Geometry SEMESTER: first DATE OF REVISION: 2013 LENGTH OF UNIT: 11 days -To understand basic terms of geometry -To understand basic postulates of geometry -To identify segments and rays -To recognize parallel lines -To find the lengths of segments -To find the measures of angles -To identify special angle pairs -To find the distance between two points in the coordinate plane -To find the coordinates of the midpoint of a segment in the coordinate plane -To find perimeters of rectangles and squares, and circumference of circles - 3 The student uses geometric concepts and procedures in a variety of situations 3.1.K2 angle measures 3.2 The student estimates, measures, and uses geometric formulas in a variety of situations. 3.2.A1B Finding the perimeter and the area of circles, squares, rectangles, triangles, parallelograms, and trapezoids.

6 Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Reasoning and Proof SEMESTER: first DATE OF REVISION: 2013 LENGTH OF UNIT: 11 days - To recognize conditional statements - To write converses of conditional statements - To write biconditionals - To recognize good definitions - To use the Law of Detachment - To use the Law of Syllogism - To connect reasoning in algebra and geometry - To prove and apply theorems about angles State Standard Alignment: Gr.9-12.Geometry 3.1.A3 understands the concepts of and develops a formal or informal proof through understanding of the difference between a statement verified by proof (theorem) and a statement supported by examples (2.4.A1a). 3.1.K2A angle measures

7 Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Parallel and Perpendicular Lines SEMESTER: first DATE OF REVISION: 2013 LENGTH OF UNIT: 17 days - To identify angles formed by two lines and a transversal - To prove and use properties of parallel lines - To use a transversal in proving lines parallel - To relate parallel and perpendicular lines - To classify triangles and find the measures of their angles - To classify polygons - To find the sums of the measures of the interior and exterior angles of polygons - To graph lines given their equations - To write equations of lines - To relate slope and parallel lines - To relate slope and perpendicular lines State Standard Alignment: Gr.9-12.Geometry 3.1.K2 discusses properties of regular polygons related to (2.4.K1g-h): 3.1.K7 recognizes, describes, and compares the relationships of the angles formed when parallel lines are cut by a transversal (2.4.K1h) 3.4.K6 recognizes the equation of a line and transforms the equation into slope-intercept form in order to identify the slope and y-intercept and uses this information to graph the line (2.4.K1f). 3.4.K3 calculates the slope of a line from a list of ordered pairs on the line and explains how the graph of the line is related to its slope (2.4.K1f). 3.4.K4 finds and explains the relationship between the slopes of parallel and perpendicular lines (2.4.K1f), e.g., the equation of a line 2x + 3y = 12. The slope of this line is -2/3. What is the slope of a line perpendicular to this line? 3.1.A3 understands the concepts of and develops a formal or informal proof through understanding of the difference between a statement verified by proof (theorem) and a statement supported by examples (2.4.A1a). COMMUNITY RESOURCES List organizations, guests, field trips, donations, etc.:

8 Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Congruent Triangles SEMESTER: first DATE OF REVISION: 2013 LENGTH OF UNIT: 17 days - To recognize congruent figures and their corresponding parts - To prove two triangles congruent using the SSS and SAS postulate - To prove two triangles congruent using the ASA and AAS postulates - To use triangle congruence and CPCTC to prove that parts of two triangles are congruent - To use and apply properties of isosceles triangles - To identify congruent overlapping triangles - To prove two triangles congruent by first proving two other triangles congruent 3.1.A3 understands the concepts of and develops a formal or informal proof through understanding of the difference between a statement verified by proof (theorem) and a statement supported by examples (2.4.A1a). 3.1.K6A congruence of triangles using: Side-Side-Side (SSS), Angle-Side-Angle (ASA), Side-Angle-Side (SAS), and Angle-Angle-Side (AAS) Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Relationships Within Triangles and Quadrilaterals SEMESTER: first DATE OF REVISION: 2013 LENGTH OF UNIT: 18 days

9 - To use properties of midsegments to solve problems - To use properties of perpendicular bisectors and angle bisectors - To identify properties of perpendicular bisectors and angle bisectors - To identify properties of medians and altitudes of a triangle - To define and classify special types of quadrilaterals - To use relationships among sides and among angles of parallelograms - To use relationships involving diagonals of parallelograms or transversals - To determine whether a quadrilateral is a parallelogram - To use properties of diagonals of rhombuses and rectangles - To determine whether a parallelogram is a rhombus or a rectangle - To verify and use properties of trapezoids and kites 3 The student uses geometric concepts and procedures in a variety of situations. 3.1 The student recognizes geometric figures and compares and justifies their properties of geometric figures in a variety of situations. 3.1.K2B diagonals. 3.1.A3 understands the concepts of and develops a formal or informal proof through understanding of the difference between a statement verified by proof (theorem) and a statement supported by examples (2.4.A1a). 3.1 The student recognizes geometric figures and compares and justifies their properties of geometric figures in a variety of situations. Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Similarity and Square Roots SEMESTER: second DATE OF REVISION: 2013 LENGTH OF UNIT: 18 days

10 - To write ratios and solve proportions - To identify similar polygons - To apply similar polygons - To use AA, SAS, and SSS similarity statements - To apply AA, SAS and SSS similarity statements - Solve by simplifying square roots - Solve by multiplying square roots - Solve by dividing square roots - Solve by adding and subtracting square roots - To find and use relationships in similar right triangles - To use the Side-Splitter Theorem - To use the Triangle-Angle-Bisector Theorem 3.1.K4 recognizes that similar figures have congruent angles, and their corresponding sides are proportional (2.4.K1h). 2.2.K3D radical equations with no more than one inverse operation around the radical expression COMMUNITY RESOURCES List organizations, guests, field trips, donations, etc.: Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Right Triangles and Trigonometry SEMESTER: second DATE OF REVISION: 2013 LENGTH OF UNIT: 12 days - To use the Pythagorean Theorem - To use the converse of the Pythagorean Theorem - To use the properties of triangles - To use the properties of triangles - To use tangent ratios to determine side lengths in triangles

11 - To use sine and cosine to determine side lengths in triangles - To use angles of elevation and depression to solve problems 3.1.K5 uses the Pythagorean Theorem to (2.4.K1h): 3.1.K5A determine if a triangle is a right triangle, 3.1.K5B find a missing side of a right triangle. 3.1.K6B the ratios of the sides in special right triangles: and The student estimates, measures, and uses geometric formulas in a variety of situations Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Area SEMESTER: second DATE OF REVISION: 2013 LENGTH OF UNIT: 18 days - To find the area of a parallelogram - To find the area of a triangle - To find the area of a trapezoid - To find the area of a rhombus or a kite - To find the area of a regular polygon - To find the area of a regular polygon using trigonometry - To find the area of a triangle using trigonometry - To find the measures of central angles and arcs - To find circumference and arc length - To find the areas of circles, sectors, and segments of circles 3.2.K4 states, recognizes, and applies formulas for (2.4.K1h) ($): 3.2.K4A perimeter and area of squares, rectangle, and triangles; 3.2.K4B circumference and area of circles; volume of rectangular solids. 3.2.A1B finding the perimeter and the area of circles, squares, rectangles, triangles, parallelograms, and trapezoids, e.g., a track is made up of a rectangle with dimensions 100 meters by 50 meters with semicircles at each end (having a diameter of 50 meters). What is the distance of one lap around the inside lane of the track?

12 3.1.K8 recognizes and identifies parts of a circle: arcs, chords, sectors of circles, secant and tangent lines, central and inscribed angles (2.4.K1h). Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Surface area and volume SEMESTER: second DATE OF REVISION: 2013 LENGTH OF UNIT: 17 days - To find the surface area of a prism - To find the surface area of a cylinder - To find the surface area of a pyramid - To find the surface area of a cone - To find the volume of a prism - To find the volume of a cylinder - To find the volume of a pyramid - To find the volume of a cone - To find the surface area and volume of a sphere 3.2.A1C finding the volume and the surface area of rectangular solids and cylinders, e.g., a car engine has 6 cylinders. Each cylinder has a height of 8.4 cm and a diameter of 8.8 cm. What is the total volume of the cylinders? 3.2.K5 uses given measurement formulas to find perimeter, area, volume, and surface area of two- and threedimensional figures (regular and irregular) (2.4.K1h).

13 Geometry Unit GRADE LEVEL / DEPT.: ninth through twelfth grade/math UNIT/TITLE Circles SEMESTER: second DATE OF REVISION: 2013 LENGTH OF UNIT: 16 days - To use the relationship between a radius and a tangent - To use the relationship between two tangents from one point - To use congruent chords, arcs, and central angles - To recognize properties of lines through the center of a circle - To find the measure of an inscribed angle - To find the measure of an angle formed by a tangent and a chord - To find the measures of angles formed by chords, secants, and tangents - To find the lengths of segments associated with circles - To write an equation of a circle - To find the center and radius of a circle 3.1.K8 recognizes and identifies parts of a circle: arcs, chords, sectors of circles, secant and tangent lines, central and inscribed angles (2.4.K1h).