## A Locus of Points

26 Aug

(Part 1 – A Locus of Points) As we were finishing up our unit on constructions and special segments in triangles last week, I wanted to introduce the idea of a locus of points. But I wanted to do it through exploration. So we started with the following question:

Students were familiar with “equidistant” but they were not familiar with “locus of points”. I was proud that none of them got caught up with the terminology so much that they couldn’t try something. This is a fairly new question type in TI-Nspire Navigator. Students drop a point on the graph. If the point they initially drop isn’t what they want to answer, then they can grab it and move it where they want before submitting their response. I was expecting the majority of the students to submit the midpoint. And they did. But even then, the picture that we got was still beautiful:

Some students remembered that any point that lies of the perpendicular bisector of the segment with the given points as endpoints would be equidistant from the two endpoints. And then we were able to go in as a class and connect their submitted points with the equation of the line, y=1.

The next question I asked was for an equation:

So they moved away from the visual of dropping a point to writing an equation, and most students were successful.

Looking back, I realize that I need to add “in a plane” to both of my questions. But that is one reason I am blogging this year. Reflecting on the lessons that I am presenting to my students will make me a better teacher.

(Part 2 – The Summative Assessment) Students took a summative assessment on our first unit in class at the end of the week. We had studied triangles during the unit, but we had a question on the assessment that extended the content of the unit to quadrilaterals.

I am proud of my students for their work. It may seem simple, but ultimately I want them to learn how to problem solve while they are taking their tests…to not be intimidated by questions they haven’t exactly seen before in class. They are off to a good start.

And so the journey continues…

Posted by on August 26, 2012 in Geometry, Tools of Geometry

### 2 responses to “A Locus of Points”

1. August 27, 2012 at 6:24 am

I really like how you took them from points on a paper to a real world response with some of the same language that they could now solve. It would be interesting to have them do a similar task first like the fire hydrant problem and compare their results to he hydrant problem after learning the concept. Another problem at the end could be cool too where there is a grid, like streets and the they have to come up with equtions of the locus and see where they intersect.

2. September 1, 2012 at 10:41 am

Thanks for including the screen shots – I have not used the NSpire and I appreciate seeing how everything was set up for your students. Neat stuff!
–Lisa