Unit Plan Day 3: 5 Practices Park Problem
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1 Unit Plan Day 3: 5 Practices Park Problem Grade/Class : Geometry SOL: G.6 The student, given information in the form of a figure or statement, will prove two triangles are congruent. Content Objectives: Students will be able to form congruent triangles. Students will be able to prove why the triangles are congruent. Learning Targets: I can construct two congruent triangles. I can prove that two triangles I constructed are congruent. Key Vocabulary: congruence Materials: straws, protractors, scissors, pencil, tape, poster paper, post-it notes SIOP Features Preparation: Scaffolding : Group Options : _X Adaptation of content _X Modeling _X Whole class _X Links to background _X Guided practice _X Small groups _X Links to past learning _X Independent practice _X Partners _X Strategies incorporated _X Comprehensible input _X Independent Integration of Process : Application : Assessment: _X Reading _X Hands-on _X Individual _X Writing _X Meaningful _X Group _X Speaking _X Linked to objectives _X Written _X Listening _X Promotes engagement _X Oral Lesson Sequence Warm Up (5 minutes): We will have a quick review of when a triangle does and does not exist, in hopes of avoiding this pitfall during the main activity. Two sets of measurements will be posted and the
2 students will have to determine which triangle exists and be able to explain their reasoning to the rest of the class. Set 1: AB = 5 cm BC = 7 cm AC = 10 cm Set 2: DE = 3 cm EF = 7 cm DF = 11 cm Discussion Questions: Which triangle exists and why? When we say a triangle does not exist, what does that actually mean? If two of the side lengths summed together equals the other side length, is it a triangle? Explain. Engage/Explore (45 minutes): Students will be given the follow task statement: Task Statement - You and some neighbors are landscaping a community park. The organizer of the project selects an area for two congruent triangular rock gardens. You agree to be in charge of placing the pieces of wood to outline the gardens. The only tools you have are a saw, a protractor, and two very long pieces of wood. Describe one way to guarantee that the triangular outlines will be congruent. Justify your answer. With this task, students will work in pairs and follow the A,E,I,O,U format to use communication and clarity in their work and explanations. They will be graded based off of the A+E+I+O=U rubric at the bottom of this plan. They will be able to cut and move straws to form their two congruent triangles. From here, they will be able to paste them on poster board in an organized fashion. Anticipated Student Responses: Correct Responses - 1. Side - Angle - Side 2. Side - Side -Side 3. Angle - Side - Angle 4. Angle - Angle - Side Discussion Questions for these responses - Will this information always give congruent triangles? Can you create a counterexample with the same information you have to create a triangle that is not congruent? Can you think of another way to create two congruent triangles?
3 What s the least amount of information you need to prove congruence? How do you know the two triangles are congruent? Incorrect Responses - 1. Angle - Angle - Angle 2. Angle - Side - Side Discussion Questions for these responses - Will this information always give you congruent triangles? Can you create a counterexample with the same information you have to create a triangle that is not congruent? Would one more piece of information give you triangles that are always congruent? What pieces of information would suffice for a congruent triangle? Why do these pieces of information not always give you congruent triangles? Explain (20 minutes) : At this point, student groups have finished up creating their posters and writing their explanations for the congruent triangles. We will have the student groups present their work in gallery walk style where groups walk around and look at the posters. Each student must leave 2 comments on two different posters with either follow-up questions, or a comment regarding the work. Once we have completed the gallery walk, groups can go back to their posters and look at the comments left on their posters. I will give them 5 minutes to change anything on their poster based off of the questions/comments that their peers left. Elaboration (20 minutes): Once this has been completed, I will pick certain student groups to present in front of the class. While students are presenting, I will ask them the connecting questions. The goal is to have a student group doing one of each type of congruence theorem. I would have the SSS group present first, because I feel that this is the most relatable and approachable student response. From here, I would sequence the responses with the other correct congruence theorems and then at the end, if a group felt comfortable, I would ask them to explain why their reasoning for using AAA or SSA would not always result in a congruent set of triangles. Discussion/Connecting Questions during this section: How many pieces of information did you need to prove congruence of your two triangles? How do you know the triangles are congruent? How do these different approaches relate to one another?
4 How are these approaches different from one another? Is there anything that could be made clearer within their explanation? Does the orientation of the triangles make a difference on congruence? Why/not? Evaluate: Students will be monitored throughout the class with discussion, clarifying, and follow-up questions to judge their understanding of the material. They will also, as a group be graded using the A+E+I+O=U rubric below for their posters discussing triangle congruence.
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