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Course Title: Geometry Instructional/Pacing Guide Not Aligned to the 2011-2012 Benchmarks Unit 1 Basics of Geometry and Reasoning Time Frame: Weeks 1-5 Benchmark Week: 5 Week # Dates Standard(s) 2-5 8/29 – 9/23 1.0 Students demonstrate understanding by identifying & giving examples of undefined terms, axioms, theorems, & inductive & deductive reasoning. 3.0 Students construct & judge the validity of a logical argument & give counterexamples to disprove a statement. 16.0 Students perform basic constructions with a straightedge & compass, such as angle bisectors, perpendicular bisectors, & the line parallel to a given line through a point off the line. 22.0 Students know the effect of rigid motions on figures in the coordinate plane & space, including rotations, translations, & reflections. Total number of questions on Benchmark: 14 Topic Know the difference between inductive and deductive reasoning, and can identify each. Textbook Connections Number of Questions on CST 2 4 Know the definition of and can provide a counterexample to an argument. Construct perpendicular bisectors, and angle bisectors with a compass. Translations, reflections, and rotations 4 3 Page 1 of 8 Last Revised: January 20, 2012 Course Title: Geometry Instructional/Pacing Guide Not Aligned to the 2011-2012 Benchmarks Unit 2 Angle properties of Polygons Time Frame: Weeks 6-8 Benchmark Week: 8 Week # 6-8 Dates 9/26 – 10/14 Standard(s) 2.0 Students write geometric proofs, including proofs by contradiction. 6.0 Students know and are able to use the triangle inequality theorem. 12.0 Students find & use measures of sides & of interior & exterior angles of triangles & polygons to classify figures & solve problems. Topic Geometric Proofs Textbook Connections Number of Questions on CST 3 Proofs by Contradiction Triangle Inequality Theorem 1 5 Measures of Sides and Interior and Exterior Angles Total Number of Questions on Benchmark: 14 Page 2 of 8 Last Revised: January 20, 2012 Course Title: Geometry Instructional/Pacing Guide Not Aligned to the 2011-2012 Benchmarks Unit 3: Parallel, Perpendicular and Properties of Quadrilaterals Time Frame: Weeks 9-12 Benchmark Week: 12 Week # 9-12 Dates 10/17 – 11/11 Standard(s) 7.0 Students prove & use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, & the properties of circles. 4.0 Students prove basic theorems involving congruence & similarity. 13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, & exterior angles. Topic Textbook Connections Number of Questions on CST Prove Parallelism theorems. 5 2/3 Solve for angles involving parallel lines cut by a transversal. 5 Know various properties of quadrilaterals such as sum of interior angles and diagonals. 2 Students know linear pair, vertical, supplementary, and complementary angles, and use this knowledge to solve problems in various contexts. Construct a line parallel to a given line through a point off the line with a compass. Number of questions on the Benchmark: 20 Page 3 of 8 Last Revised: January 20, 2012 Course Title: Geometry Instructional/Pacing Guide Not Aligned to the 2011-2012 Benchmarks Unit 4: Area and Volume Time Frame: Weeks 13-17 Benchmark Week: 17 Week # 13-17 Dates 11/14 – 12/09 Standard(s) 8.0 Students know, derive, & solve problems involving the perimeter, circumference, area, volume, lateral area, & surface area of common geometric figures. 9.0 Students compute the volumes & surface areas of prisms, pyramids, cylinders, cones, & spheres; & students commit to memory the formulas for prisms, pyramids, & cylinders. 10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, & trapezoids Number of Questions on the Benchmark: 20 Topic Solving for area and perimeter of various polygons Finding the surface area and volume of three-dimensional figures Textbook Connections Number of Questions on CST 4 2 4 Page 4 of 8 Last Revised: January 20, 2012 Course Title: Geometry Instructional/Pacing Guide Not Aligned to the 2011-2012 Benchmarks Unit 5: Similarity and Congruence Time Frame: Weeks 18-21 Benchmark Week: 21 Week # 18- 21 Dates 12/12– 01/13 Standard(s) Topic 4.0 Students prove basic theorems involving congruence & similarity. 5.0 Students prove that triangles are congruent or similar, & they are able to use the concept of corresponding parts of congruent triangles. 11.0 Students determine how changes in dimensions affect the perimeter, area, & volume of common geometric figures & solids. Know properties of congruent triangles. Textbook Connections Number of Questions on CST 5 Know properties of similar polygons including perimeters and volume. 2 Know how to prove triangles are congruent. 1 Know the effect on perimeter, area, and volume when changing the dimensions of a polygon. Number of Questions on the Benchmark: 20 Page 5 of 8 Last Revised: January 20, 2012 Course Title: Geometry Instructional/Pacing Guide Not Aligned to the 2011-2012 Benchmarks Unit 6 : Pythagorean Theorem Time Frame: Weeks 21-22 Benchmark Week: 22 Week # 21-22 Dates 01/23-02/03 Standard(s) 14.0 Students prove the Pythagorean theorem. 15.0 Students use the Pythagorean theorem to determine distance & find missing lengths of sides of right triangles. 17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, & various forms of equations of lines & circles. Number of Questions on the Benchmark: 20 Topic Pythagorean Theorem Proving the Pythagorean Theorem Distance and Midpoint Formulas Textbook Connections Number of Questions on CST 1/3 2 3 Page 6 of 8 Last Revised: January 20, 2012 Course Title: Geometry Instructional/Pacing Guide Not Aligned to the 2011-2012 Benchmarks Unit 7 Trigonometry Time Frame: Weeks 23-24 Benchmark Week: 24 Week # 23-24 Dates 02/06 – 02/17 Standard(s) 18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know & are able to use elementary relationships between them. For example, tan( x ) = sin( x )/cos( x ), (sin( x )) 2 + (cos( x )) 2 = 1. 19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle & a length of a side. 20.0 Students know & are able to use angle & side relationships in problems with special right triangles, such as 30°, 60°, & 90° triangles & 45°, 45°, & 90° triangles. Number of Questions on the Benchmark: 20 Topic Vocabulary relating to trig functions. Write trigonometric ratios. Use elementary relationships between trigonometric ratios. Use trigonometric trig functions to solve for an unknown side length of a side of a right triangle, given an angle and a length of a side. Use special right triangle relationships to find missing side lengths of 30-60-90 and 45-45-90 triangles. Textbook Connections Number of Questions on CST 3 3 1 Page 7 of 8 Last Revised: January 20, 2012 Course Title: Geometry Instructional/Pacing Guide Not Aligned to the 2011-2012 Benchmarks Unit 8 Circles Time Frame: Weeks 25-28 Benchmark Week: 28 Week # Dates 25-28 02/20 – 03/09 03/12 – 03/16 (CAHSEE) Resume Unit 8 03/19 – 03/23 Standard(s) Topic 21.0 Students prove & solve problems regarding relationships among chords, secants, tangents, inscribed angles, & inscribed & circumscribed polygons of circles. Learn vocabulary relating to circles Use properties and theorems about tangents. Use arc addition postulate Use Theorems about chords of circles. Use theorems about the inscribed angles of a circle. Use theorems about inscribed polygons. Use theorem about tangents and chords. Use theorems about lines intersecting inside or outside a circle. Use theorems about intersecting chords. Use theorems about segments of tangents and secants. Identify the equation of a circle given the center and radius of the circle. Identify the graph of a circle when its equation is given. Textbook Connections Number of Questions on CST 5 Number of Questions on the Benchmark: 20 Page 8 of 8 Last Revised: January 20, 2012