Reflection: Quizzes Proving Theorems involving Similar Triangles - Section 4: Assessment


When I gave the quiz after this lesson, there were about 20% of the students who got at least one of the proofs incorrect. I noticed that changing the lettering of the vertices from what I had originally used in class tripped many of these students up. They wanted to rename the vertices the way they were named on the original proof I used in class, and I purposely did not allow that. This let me know that they had basically memorized the proofs line by line, which is not what I wanted for them to do.

While I have always emphasized the importance of knowing and understanding the overall plan of the proof as opposed to merely memorizing the statements and reasons, I have not been consistently checking to see if students are taking my advice. If I were to teach this lesson again, I would definitely include an activity in which students would be required to lay out the overall plan for the proofs. I might also have students write these plans on the quiz as well.

The proofs on this quiz were just long enough to be beyond what many students could memorize their way through and so the results made me aware of the issue of students trying to memorize proofs rather than really knowing them.

  Memorize plans, not proofs
  Quizzes: Memorize plans, not proofs
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Proving Theorems involving Similar Triangles

Unit 6: Similarity
Lesson 5 of 8

Objective: SWBAT prove that a line parallel to a side of a triangle divides the other two sides proportionally, and conversely.

Big Idea: 9 steps for one and 3/4 of a dozen for the other. In this lesson students will learn to write two 9-step proofs that involve similar triangles.

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Math, similar triangles, Triangle proportionality theorem
  75 minutes
partition segment construction
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