LESSON PLAN Name: Rahul Bhandari Title of lesson: Congruent Triangles Conjectures. Length of lesson: Three 50 minute class periods Description of the class: Name: Grade level: Honors or regular: Geometry High School Honors TEKS addressed: (a) Basic understandings. 2) Geometric thinking and spatial reasoning. Spatial reasoning plays a critical role in geometry; shapes and figures provide powerful ways to represent mathematical situations and to express generalizations about space and spatial relationships. Students use geometric thinking to understand mathematical concepts and the relationships among them. (4) The relationship between geometry, other mathematics, and other disciplines. Geometry can be used to model and represent many mathematical and real-world situations. Students perceive the connection between geometry and the real and mathematical worlds and use geometric ideas, relationships, and properties to solve problems. (6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling, and justification and proof. (b) Geometric structure: knowledge and skills and performance descriptions. (2) The student analyzes geometric relationships in order to make and verify conjectures. Following are performance descriptions. (A) The student uses constructions to explore attributes of geometric figures and to make conjectures about geometric relationships. (B) The student makes and verifies conjectures about angles, lines, polygons, circles, and three-dimensional figures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic. The Lesson: I. Overview The goal of this lesson is to have students determine the minimum requirements needed for congruent triangles. II. Performance or learner outcomes The students will be able to: determine the minimum requirements needed for congruent triangles. They should be able to use properties like SSS, SAS, ASA, SAA, and the HL (only true for Rt. Angle Triangles) III. Resources, materials and supplies needed Rulers, scissors, papers, protractors, etc IV. Supplementary materials, handouts. Handout for Homework—Attached Five-E Organization Teacher Does Student Does Engage: Learning Experience Student Activity Prior Knowledge: Students are listening and answering Use of slides (pictures of Rhombus and questions. Square) to assess understanding of difference between similar and congruence. Questions Expected Student Answers 1. What are the characteristics you 1. Color, Maker, Hub-caps, etc. look for to determine similarity? Example: Is CAR-A similar to CAR-B? 2. Show them rhombus and square and 2. Yes/No ask if they are similar. 3. How can you tell if they are equal? 3. They have the same sides and angles. 4. What is a geometrical way to say 4. Congruent. equal? 5. What is the difference between 5. Similarity deals with the similar and congruent? appearance while the congruence deals with the measurement. Evaluate: Teacher will make sure students are on task and participating. Teacher Does Student Does Explore: Learning Experience(s) GAME: Students will be provided with index cards that have measurements for the triangle. Goal: Students will find at least one congruent triangle to theirs. However, none of them will be congruent. The students will have to find someone with the closest measurements to theirs. That will bring out the misconceptions like AAA and ASS. Questions 1. What approach are you using to solve this problem? 2. How do you know if the two triangles are congruent? Evaluate: What the students are doing Students are finding congruent triangles. Once students are done finding match, then they will construct and cut their triangle to see if they are congruent triangles. Expected Student Answers 1. Answer will vary depending on group. 2. They will try to relate the measurements between the triangles. The teacher will walk around the room to assess each group’s progress. Teacher Does Explain: Learning Experience(s) Teacher is listening to students’ ideas. Calling on different students to give their opinions. Student Does What the students are doing Groups are presenting their work. Students are listening and discussing opinions. Questions Expected Student Answers Address to class: 1. Do you agree this group has a 1. Yes/No; answer will vary match? Why? 2. What approach did your group use? 2. answer will vary (answers will be written on the board as “rules”) Teacher will call upon the groups that Students are explaining why AAA and have AAA and ASS congruent triangles ASS do not work. to clarify these characteristics are invalid. Evaluate: The teacher will ask questions to guide the discussion. Teacher Does Student Does Explore: Learning Experience(s) What the students are doing Problem: The City of Austin is putting a Listening to instructions. swing set in the park. Before they can put Working in groups to solve the problem. the top bar on, they need to make sure the supports will balance the swing. (supports are triangles) Goal: Find the least number of equal characteristics and all the possible ways use the characteristics of the two triangles that make them congruent. (We will refer to the previous lesson that there is more than one way to get to point A to point B.) Recall that they cannot use AAA and ASS. Questions 1. What approach are you using to solve this problem? 2. How do you know if the two triangles are congruent? Evaluate: Expected Student Answers 1. Answer will vary depending on group. 2. They will try to relate the measurements between the triangles. The teacher will walk around the room to assess each group’s progress. Teacher Does Explain: Learning Experience(s) Teacher is listening to students’ ideas. Calling on different students to give their opinions. Questions 1. (Before presentations) How many different ways did your group find? Which are they? (Teacher will have every group present different ways based on their answers.) 2. (During presentations) Teacher will call on students to make sure they understand each group’s solution. 3. (After groups have presented) What are the similarities and differences between the presentations? Student Does What the students are doing Groups are presenting their work. Students are listening and discussing opinions. Expected Student Answers 1. Answer will vary. 2. Students are answering, paying attention to student ideas. 3. Answer will vary. 4. Teacher will call on a student and ask them to explain what we just learned. Evaluate: 4. Student should be able to explain that three characteristics are needed to find congruent triangles. Works: SSS, SAS, AAS, ASA Doesn’t: AAA, SSA or the reverse. The teacher will ask questions to guide the discussion. Teacher Does Student Does Extend / Elaborate: Learning Experience(s) Teacher will assign worksheet to the students that will ask them to use the properties to find if the triangles are congruent. What the students are doing Students are individually working on the worksheet. The last problem will have an equilateral Students will get back in the group to find divided into two right angle triangles. This the new rule that shortens SAS for the right will guide them to find the congruent angle triangle. triangle in case of right angle triangles (HL). Teacher will ask them to shorten the SAS property that will be valid for all right angle triangles. If necessary, teacher will ask students what every right angle triangle has common in it. This will guide them to realize they have a common angle i.e. 90 degrees. Evaluate: Teacher is walking around to assess each student’s progress.
