Curriculum Guide: Geometry Term 2, RMS 3rd Quarter GRADE 8-12 Unit of Study: Similarity Resources: Textbook Geometry (Holt, Rinehart & Winston) Ch. 7, pp. 451-508, sketchpad software Length of Study: Block 8 days RMS 16 days Unit of Study: Right Triangles & Trigonometry Resources: Textbook Geometry (Holt, Rinehart & Winston) Ch. 8, pp. 515-576, sketchpad software Length of Study: Block 7 days RMS 14 days Unit of Study: Extending Perimeter, Circumference, and Area Resources: Textbook Geometry (Holt, Rinehart & Winston) Ch. 9, pp. 585-644, sketchpad software Length of Study: Block 6 days RMS 12 days Geometry/Spatial Concept Geometry/Spatial Concept Geometry/Spatial Concept Writing Benchmarks MA 12.4.3 The student will evaluate characteristics and properties of 2- & 3- dimensional geometric shapes. Benchmarks MA 12.4.5 The student will apply right triangle trigonometry to find length and angle measures. Benchmarks MA 12.4.6 The student will apply geometric properties to solve problems. Benchmarks Proof Writing 1
ASSESSMENT RECOMMENDATIONS Standard: Benchmark MA 12.4.3 The student will evaluate characteristics and properties of 2- & 3- dimensional geometric shapes Skills Skills Skills Skills Classify shapes in terms of similarity Prove triangles are similar Explanation Possible Assessments FOR Learning Use proportions to find measures in similar figures. Use similar triangle theorems to prove triangles similar. Required Assessments OF Learning Selected Response Multiple choice (Choose the similar figures) Essay Assessment Find missing measures using proportions. Personal Communication Write proofs for similar triangles 2
SUGGESTED INSTRUCTIONAL STRATEGIES Standard: WHOLE GROUP Activities: Benchmark: Use sketchpad to explore proportions in similar triangles MA 12.4.3 The student will evaluate characteristics and properties of 2- & 3- dimensional geometric shapes Homework & practice HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Provide problems for proving similarity of triangles. Provide proportion problems that include solving quadratics. Skills (): Classify shapes in terms of similarity Explanation Prove triangles are similar. Homework & practice Questions, cues and advance organizers AVERAGE PERFORMING STUDENT Activities: Provide problems with triangles marked and prove similarity. LOW PERFORMING STUDENT Activities: Provide examples, sketches, and correct formulas for identifying similar triangles and solving proportions. Nonlinguistic representation ELL Activities: Provide sketches for all theorems and properties. 3
ASSESSMENT RECOMMENDATIONS Standard: Benchmark MA 12.4.5 The student will apply right triangle trigonometry to find length and angle measures.. Skills Skills Skills Skills Pythagorean Theorem Trigonometry Possible Assessments FOR Learning Selected response Classify triangles as right, obtuse, or acute. Solve for missing measures using trigonometry. Required Assessments OF Learning Selected Response Multiple choice (right, acute, or obtuse?) Essay Assessment Find missing measures using Trigonometry, Pythagorean Theorem, or special right triangles. Personal Communication 4
Standard: Benchmark: SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Use geometric sketchpad to explore Pythagorean Theorem and its converse MA 12.4.5 The student will apply right triangle trigonometry to find length and angle measures. Summarizing & note taking HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Have students explain the converse of Pythagorean Theorem and how it can be used to classify a triangle as right, obtuse, acute. Skills (): Selected response Classify triangles as right, obtuse, acute Solve for missing measures in right triangles Homework & practice Cooperative learning Nonlinguistic representation AVERAGE PERFORMING STUDENT Activities: Provide problems with missing measures in right triangles for them to solve. LOW PERFORMING STUDENT Activities: Have students work together to determine the best methods to solve right triangles. ELL Activities: Provide sketches for all examples. 5
ASSESSMENT RECOMMENDATIONS Standard: Benchmark MA 12.4.6 The student will apply geometric properties to solve problems. Skills Skills Skills Skills Segments, lines, and points in circles. Use angles and chords in circles Explanation Possible Assessments FOR Learning Selected response Identify types of segments and lines in circles. Find angle, arc, and segment measures in circles. Required Assessments OF Learning Selected Response Matching types of segments in circles. Fill in the blank - theorems Essay Assessment Find missing angle measures using theorems Find segment lengths using theorems Personal Communication 6
Standard: Benchmark: SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Use geometers sketchpad to explore various types of angles in circles. MA 12.4.6 The student will apply geometric properties to solve problems. Homework & practice HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Provide examples that require solving quadratics (ex. tangent & secant segments) Skills (): Explanation Identify and classify segments, lines, and points in circles Use theorems to find angle, arc, and segment measures in circles. Homework & practice Questions, cues, and advance organizers Nonlinguistic representation AVERAGE PERFORMING STUDENT Activities: Provide examples that require basic algebra to solve (angle measures, segment lengths in circles) LOW PERFORMING STUDENT Activities: Provide correct formulas needed to solve problems. ELL Activities: Provide sketches for vocabulary words and theorems. 7
REQUIRED KEY CONTENT WORDS Ratio Proportion Means Extremes Geometric mean Scale factor Similar polygons Pythagorean triple Trigonometric ration Pythagorean Theorem 45-45-90 Theorem 30-60-90 Theorem Circle Secant Tangent Radius Diameter Point of tangency Central angle Arc Inscribed angle Measure of an arc Intercepted arc Standard equation of a circle 8