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Subject Area: Algebra Grade Level: 7th Benchmark Period: III Duration of Lesson: 1 hour Standard(s): M&G3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of figures. Learning Objective: Students will determine whether or not two polygons are congruent. Big Ideas involved in the lesson: The nature of congruence As a result of this lesson students will: Know: Vocabulary: Polygon, line segment, endpoints, sides, vertex/vertices, congruent, corresponding sides, corresponding angles, bisect, regular polygon, triangle, quadrilateral, pentagon, hexagon, diagonal, consecutive/non-consecutive, angle, postulate How to write a line segment AB , an angle ABC , and a triangle ABC . How to write the measurement of an angle ( mA =…). The symbol for congruent ( ). Understand: How to write an informal proof for the congruence of two polygons There are different methods to prove that two polygons (namely triangles) are congruent. That two polygons are congruent if their corresponding sides and their corresponding angles are congruent. (They must be same shape and same size). That a number of diagonals can be drawn depending on the number of sides of the polygon. Diagonals can be drawn to help prove that polygons are congruent. Regular polygons (i.e. Regular hexagons) are not always congruent, though they have congruent angles. Be Able To Do: Name angles, segments, and points. Name polygons by listing their vertices in order. Identify corresponding angles for congruent polygons. Identify congruent angles. Identify congruent sides of polygons. Identify corresponding sides for congruent polygons. Write an informal proof for congruent polygons. 1 M&G 3.4 Assessments: What will be evidence of student knowledge, understanding & ability? Formative: ABWA Checking for understanding during lesson Independent Practice (Teacher created worksheet) CFU Questions What is congruency? Why is knowing if two shapes are congruent important? How do we name lines? How do we name segments? How do we name rays? How do we name angles? How do we identify a triangle by its sides? How do we identify triangles by their angles? Summative: How do we differentiate between polygons? Teacher created Tell me whether or not each pair of triangles is congruent. If quiz/test, DWA, CST they are congruent, write a statement of congruency and tell me how you know that they are congruent. Are the parallelograms pictured below congruent? How do you know this? What information is necessary to prove two triangles congruent? What information is necessary to prove to polygons congruent? Lesson Plan Anticipatory Set: Show powerpoint anticipatory set file - add more real life reasons for learning a. T. focuses students congruency if you deem it appropriate or needed. b. T. states objectives c. T. establishes purpose of CFU – What are we going to learn? Why are we going to learn this? the lesson d. T. activates prior Preview/Review – As this lesson is to be implanted in a 7th grade honors Algebra knowledge 1 course, it may not occur directly after another geometry lesson. So a review of some geometric terms may be necessary. See the attachment Preview-Review M&G3.4 file. Project the file and go over with students. 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 2 CFU Questions – How do we name lines? How do we name segments? How do we name rays? How do we name angles? How do we identify a triangle by its sides? How do we identify triangles by their angles? How do we differentiate between polygons? All instruction is included in a form that is ready for projection. It is in the file M&G3.4 instruction. CFU Questions (in above file): On your white board, tell me whether or not each pair of triangles is congruent. If they are congruent, write a statement of congruency and tell me how you know that they are congruent. Are the parallelograms pictured below congruent? How do you know this? M&G 3.4 examples Use participation 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 (semiindependent) 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 3 Teacher and Students begin working guided practice (See file M&G 3.4 Guided Practice.doc) together. Teacher gradually releases the students to do the problems on their own. CFU – What information is necessary to prove two triangles congruent? What information is necessary to prove to polygons congruent? Lecture, note-taking, pair-shares and written responses during CFUs, guided practice, etc. Review vocabulary and concepts learned. Have students do 2 exit problems on post-it notes or scratch paper and have them turn it in on their way out (this way the teacher can tell if re-teaching is needed). On board, teacher draws two triangles with sides measuring 3, 8, 13 with different orientations. 1) Determine if the two triangles are congruent. If they are, write a statement telling why they are congruent. On board, teacher draws a regular quadrilateral, ABCD. 2) Draw a diagonal, BD, and prove that ABD CDB. See M&G 3.4 Independent Practice file. M&G 3.4 Resources: materials needed to complete the lesson 4 M&G 3.Anticipatory Set file. M&G 3.4 Instruction file. M&G 3.4 Guided Practice file. M&G 3.4 Independent Practice file. M&G 3.4