Reflection: Exit Tickets Algebraic Proof of the Perpendicular Bisector Theorem using Coordinate Geometry - Section 3: Exit Ticket

 

The type of exit ticket I used in this lesson is very simple: students simply explain the purpose of our activity and how we went about achieving that purpose. This allows students to do some metacognition. It also gives me some insight into how they actually experienced lesson and lets me know what they learned and understood.

In looking at these exit tickets I can put them into two general categories. In the first category, students tend to concentrate on procedure and fail to address the purpose for the procedures. They'll write things like "We found the equation of the perpendicular bisector and then we put points into the distance formula and showed that the distances were equal. Then we used variables instead of numbers in the distance formula and they were still equal." This type of response indicates to me that a students has experienced the lesson as a series of procedures and has not fully appreciated the reason for doing those procedures or the implications of the findings of those procedures.

The second category of student focuses on purpose and within that category I look for the depth of knowledge communicated in their response and also the precision they use. An exemplary response would include the following components:

"We were attempting to show that all points on the perpendicular bisector of a segment are equidistant from the segment's endpoints (purpose). First we found the equation of the perpendicular bisector and determined the coordinates of some specific points that were on it. We used the distance formula to show that these specific points were each equidistant from the endpoints of the segment. Then we considered the general case where P was a generic point with coordinates (x, 3x+4) on the perpendicular bisector and found P was also equidistant from the endpoints of the segment. Since P represented all points on the perpendicular bisector, this proved that any point on the perpendicular bisector must be equidistant from the endpoints of the segment."

So the extent to which students can produce this type of response lets me know how well they have seen the big picture of the lesson. By the way, I do not expect them to read between the lines and infer the purpose of the lesson. I have basically been repeating this type of language and rationale very intentionally throughout the lesson. These exit tickets simply let me know who has been listening and how they have processed what they have heard.

  Knowing if my students actually saw the big picture
  Exit Tickets: Knowing if my students actually saw the big picture
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Algebraic Proof of the Perpendicular Bisector Theorem using Coordinate Geometry

Unit 9: Analytic Geometry
Lesson 2 of 7

Objective: SWBAT use algebra to verify that any point on the perpendicular bisector of a given segment is equidistant from the endpoints of the segment.

Big Idea: Feeling nostalgic? In this lesson students return to their Algebra roots in order to prove the perpendicular bisector theorem.

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