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Lesson Design Subject Area: Geometry Grade Level: 9 – 12 Benchmark Period BM 3 Duration of Lesson: 2 days Standard(s): Find and use measures of sides and interior and exterior angles of polygons to classify figures and solve problems (12b) Learning Objective: Using theorems about the interior and exterior angles of convex polygons to solve problems. Use Polygon Interior Angles Theorem and Polygon Exterior Angles Theorem. Big Ideas involved in the lesson: Using angle relationships in polygons, using properties of parallelogram, and classifying quadrilaterals by their properties. As a result of this lesson students will: Know: Vocabulary: Diagonal, interior and exterior angles, polygon, vertices, consectutive and non-consecutive vertices, convex, concave, parallelogram, rhombus, rectangle, square, trapezoid, kite, congruent, and opposite angles. Understand: Polygon Interior Angles Theorem Interior Angles of a Quadrilateral Polygon Exterior Angles Theorem Classifying polygons Be Able To Do: Solve problems and classify polygons using measures of sides and interior and exterior angles. Assessments: Formative: Observation, quiz, CFU Questions: What will be evidence of student ABWA 1. What is the sum of the measure knowledge, understanding & of the interior angles of a convex ability? Summative: CST & Benchmark pentagon and hexagon? According Given a regular n-gon, draw (DWA) to the pattern, what is the measure diagonals, classify the triangles of the interior angles of a convex by their sides and angles, and heptagon? find the measure of the interior and exterior angles. Lesson Plan Anticipatory Set: T. creates set of index cards with the following figures on them (10). Have a. T. focuses students students work in groups of four. Each group is given a whiteboard and b. T. states objectives separates into polygons and non-polygons. Ask students to sort figures into c. T. establishes purpose of polygons or non-polygons and explain their grouping of the figures. the lesson d. T. activates prior knowledge Together as a whole class, write the definition of a polygon. Polygon: It is formed by three or more segments called sides, such that no two sides with a common endpoint are collinear. Each side intersects exactly two other sides, one at each endpoint. 1 Geometry 12b Lesson Plan Lesson Design QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. 7. Instruction: a. Provide information Explain concepts State definitions Provide exs. Model b. Check for Understanding Pose key questions Ask students to explain concepts, definitions, attributes in their own words Have students discriminate between examples and nonexamples Encourage students generate their own examples Use participation 8. 9. 10. 11. 12. T. States: You have already learned that the name of a polygon depends on the number of sides in the polygon. You also already learned to find the sum of the measures of the interior angles of quadrilaterals by dividing quadrilateral into triangles. You will use the triangle method to find the sum of the measures of the interior angles of any convex polygon with n-sides, called n-gon. Investigate Angle Sums in Polygons (Investigate AngleSum.doc) CFU: What is the sum of the measure of the interior angles of a convex pentagon and hexagon? According to the pattern, what is the measure of the interior angles of a convex heptagon? T. states: Polygon Interior Angles Theorem – The sum of the measures of the interior angles of a convex n-gon is (n-2)180°. The measure of each interior angle of a regular polygon is (n 2) 180 n T. models how to solve problem 11 step-by-step along w/students at the same time. Have students work in pairs, and complete problems 12 – 13. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. T. states: Polygon Exterior Angles Theorem – The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°. 360 The measure of each exterior angle of a regular polygon is . n T. models how to solve problem 11 step-by-step along w/students at the same time. Have students work in pairs, and complete problems 12 – 16. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. 2 Geometry 12b Lesson Plan Lesson Design Guided Practice: a. Initiate practice activities under direct teacher supervision – T. works problem step-by-step along w/students at the same time b. Elicit overt responses from students that demonstrate behavior in objectives c. T. slowly releases student to do more work on their own (semi-independent) d. Check for understanding that students were correct at each step e. Provide specific knowledge of results f. Provide close monitoring What opportunities will students have to read, write, listen & speak about mathematics? Closure: a. Students prove that they know how to do the work b. T. verifies that students can describe the what and why of the work c. Have each student perform behavior Independent Practice: a. Have students continue to practice on their own b. Students do work by themselves with 80% accuracy c. Provide effective, timely feedback Resources: materials needed to complete the lesson T. makes an overhead of the following problems. Have students complete problems 12 – 16. 3 Geometry 12b Lesson Plan QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Students will be answering questions, writing notes and problems, describing the process to the teacher and their peers, and reading problems. Explain in words how to find the measure of each interior angle and each exterior angle in a regular polygon. Explain how to find the sum of the measures of the interior angles of a polygon using triangles. Assign the following problems: QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Ruler Whiteboard & marker Index Cards Overhead projector