Reflection: Connection to Prior Knowledge Loci and Analtyic Geometry - Section 1: Activate Prior Knowledge (Kinesthetic Sense)

After teaching this lesson, I really liked the aspect of having students play the role of a point in a locus and going through the process of determining their position. However, the classroom space was somewhat confining and only a few students were actually able to get physically involved.

So the idea occurred to me that this could be a nice activity to do outside on the cement or blacktop. I would bring sidewalk chalk and explain to each student that they will be playing the role of a point. First I would draw a large dot on the ground and label it A. Then I would tell of the points, "Points, arrange yourself so that you are all equidistant from A. Hopefully we'd see some semblance of a circle.

Then I'd introduce another large dot on the ground and label it B. Next I'd say, "Points, arrange yourselves so that you are each equidistant from A and B." I would then stand back and watch as students worked together to make it happen. I would also check for understanding by asking individual students to explain how they know they are standing in a correct place.

Finally, I would do my best to draw a straight line through A and B (hopefully I'd pass this sobriety field test) and another point F adequately removed from line AB. And of course I would then say, "Points, arrange yourselves so that you are each equidistant from F and line AB". Then, I would most likely be having to earn my money as a teacher because there is no telling what I would see next. But I'm confident, we could work toward seeing something parabolic.

So while I didn't get to try this this year, I am looking forward to the next time I teach the course so I can try it and refine it so that it becomes a regular component of the lesson. I think it will really solidify students' understanding of the locus definitions of these figures.

An idea for enhancing this lesson with kinesthetics
Connection to Prior Knowledge: An idea for enhancing this lesson with kinesthetics

Loci and Analtyic Geometry

Unit 9: Analytic Geometry
Lesson 3 of 7

Big Idea: Which came first, the algebra or the geometry? After this lesson, students will interplay between these two branches of mathematics.

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90 minutes

Anthony Carruthers

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