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GEOMETRY (SECONDARY) ESSENTIAL UNIT (E10) (Circles) (July 2013) Unit Statement: The properties of circles, including their tangents and secants, arcs and their angles, segments and sectors, are identified and employed to solve problems. The equation of the circle in coordinate geometry is also presented and employed. Essential Outcomes: (must be assessed for mastery) Problem solving and higher order thinking components are essential for ‘A’ level mastery. Each outcome can contain problem solving and higher order thinking components (as found in suggested text). 1. The Student Will identify tangents, secants, and chords and use properties of tangents to solve problems (12.1 pp 792 - 800). 2. TSW apply properties of arcs and chords to solve problems (12.2 pp.802 - 809). 3. TSW find arc lengths and areas of sectors (12.3 pp. 810 - 815). 4. TSW find the measures of inscribed angles and use their properties to solve problems (12.4 pp. 820 - 827). 5. TSW find the measures of angles formed by lines that intersect circles and use the angle measures to solve problems (12.5 pp. 830 - 837). 6. TSW find the lengths of segments formed by lines that intersect circles and use the lengths to solve problems (12.6 pp. 840 - 846). 7. TSW write equations and graph circles in the coordinate plane and use the equations to solve problems (12.7 pp. 847 - 853). Introduced and Practiced Outcomes: (taught not assessed) 1. The Student Will use proportions to convert angle measures from degrees to radians (12.3 pp. 816-817). Key Terms and Concepts: adjacent arcs chord congruent circles interior of circle secant semicircle arc common tangent exterior of circle major arc secant segment subtend arc length central angle concentric circles congruent arcs inscribed angle intercepted arc minor arc point of tangency sector of circle segment of circle tangent of circle tangent segment 33 QSI GEOMETRY SEC E10 Copyright © 1988-2013 Suggested Assessment Tools and Strategies: Attached Rubric or teacher generated rubric that assesses ALL essential outcomes (TSWs). Suggested Resources: Holt McDougal Geometry, Chapter 12, Sections 1 - 7. Holt McDougal Geometry, Problem Solving Workbook Holt McDougal Geometry, Practice Worksheets Holt McDougal Geometry, Reading Strategies Holt McDougal Geometry, Reteach Worksheets Holt McDougal Geometry, Challenge Worksheets Holt McDougal Geometry, Assessment Resources Technology Links: Holt McDougal Geometry, Online Edition, 6-year subscription Holt McDougal Geometry, Interactive Answers and Solutions CD-ROM Holt McDougal Geometry, Lesson Tutorial Videos DVD-ROM Holt McDougal Geometry, Teacher One-Stop DVD On Core Mathematics Deluxe Eamview Grades 6-12 CD-ROM On Core Mathematics High School Activity Generator CD-ROM Follett Destiny WebPath Express (found on school’s automated library system) Tenmarks www.tenmarks.com/ Khan Academy https://www.khanacademy.org/ PhET Simulations http://phet.colorado.edu/en/simulations/category/math EVALUATION RUBRIC FOUND ON FOLLOWING PAGE…………….. 34 QSI GEOMETRY SEC E10 Copyright © 1988-2013 UNIT EVALUATION RUBRIC Geometry Essential Unit 10 (E10) To receive a ‘B’, the student must show ‘B’ level mastery on all seven TSW’s. To receive an ‘A’, the student must show ‘A’ level mastery in at least 4 of the 7 available TSW’s and ‘B’ level mastery on all of the remaining TSW’s. ‘A’ LEVEL ‘B’ LEVEL 1- identify tangents, secants, and chords and use properties of tangents to solve problems. The student is able to state if it is possible to draw tangents to circles given various information about the circles. The student can identify tangents, secants, and chords and use properties of tangents to solve problems. 2- apply properties of arcs and chords to solve problems. The student is able to construct a circle through three noncollinear points. The student is able to apply properties of arcs and chords to solve problems. 3- find arc lengths and areas of sectors. The student can find arc lengths of circles with different radii which would yield equal sector areas. The student can find arc lengths and areas of sectors. 4- find the measures of inscribed angles and use their properties to solve problems. The student is able to use angle measures of inscribed polygons to justify that the sum of the interior angles of a triangle is 180. The student can find the measures of inscribed angles and use their properties to solve problems. 5- find the measures of angles formed by lines that intersect circles and use the angle measures to solve problems. The student can design a multi-step proof using angles formed by lines that intersect circles. The student is able to find the measures of angles formed by lines that intersect circles and use the angle measures to solve problems. 6. find the lengths of segments formed by lines that intersect circles and use the lengths to solve problems. The student is able to extend the Chord-Chord Product Theorem to prove the Pythagorean Theorem. The student can find the lengths of segments formed by lines that intersect circles and use the lengths to solve problems. 7. write equations and graph circles in the coordinate plane and use the equations to solve problems. The student can solve complex, multi-step story problems involving circular areas on a map. The student can write equations and graph circles in the coordinate plane and use the equations to solve problems. TSW 35 QSI GEOMETRY SEC E10 Copyright © 1988-2013 Notes