Monday, September 2, 2013

Roommate Problem

I'm teaching geometry for the first time this year and I must admit originally I wasn't all that enthused. I think this is mainly just because I've never taught it before and the geometry that I remember was memorization of endless theorems and two column proofs. I have an awesome group of kids though and I'm excited about that so it's giving me extra motivation to put time into planning things that are great.

This week I sat down to start planning and started to read through the standards. I came things that were exactly why I wasn't thrilled about geometry. Things like this:
From G.CO.9: "points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoint" 
Ouch. Such a terrible way to phrase an idea that's actually fairly intuitive. The last thing I want to do is have kids copy down a definition, then try to explain it to kids that are already turned off, and then give them a sheet of practice problems.

So this is my idea for a task that would address this idea, with a low entry point that establishes the need for the mathematics.

You and a friend have just gotten new jobs and have decided that you will live together.  You would like to find a place to live where you will be an equal distance from both of your jobs.  Use the map to decide where you could live.

these two points are completely random

The first place I'd expect them to go would be to find the midpoint.  In actually creating this task, I might try to make it so that there is a problem with the midpoint..maybe it's in the middle of a highway or lake or something so they would have to find other places that work.

My goal would be to get them to create a segment between the two jobs and then to create the perpendicular bisector, maybe by measuring or folding or whatever they decide.

To add more to the task, I may also put in a stipulation that says you only want to live at most some number of miles away so that they would have to construct circles as well. And ultimately I'd like to have them get on an actually google map, draw in their perpendicular bisector line and search for any apartment complexes that would be on their line. I think I'd try to design the map in a way so that there are a couple on the line to choose from too.

I also think that a great way to start this would be using Have students make predictions and then we could compare their estimates to the line.

I would wait until the end to add in the formal geometry of it. That:

  • the line they used to connect the jobs is a segment
  • the jobs themselves are the endpoints
  • the line of all the places they could live is perpendicular bisector (and why)
  • that all the points on the line are equidistant from both jobs

At this point, hopefully the ideas wouldn't be confusing because they would have informally have already thought about all these things on their own and developed their own meanings already. By discussing the formal language at the end, all it does is assign the vocabulary to things they already know.

At the moment I don't think it's an especially long task or one that's really all that challenging. I don't mind really that though. Unfortunately I don't have the time to draw every single topic out into a week long project so short tasks are ok with me. I think that it does a good job of giving the standard some context and making it relatable which I'm happy with.

So I'd like input on this. Is there anywhere else you could see it going? Any ideas to make it better or include more learning targets? I'm admittedly new to geometry, so apologies in advance for things that are less than's all a work in progress.


  1. I love this! I always breeze by that standard in favor of other aspects but this is a great way to intro perpendicular bisectors.

  2. My second thought about this is wondering if they want to live physically halfway between to time-wise halfway between. (My first thought was just forget it and move to Hoboken.) Can they take the train to work? It's not really geometry related but definitely involves math.

  3. THis is a cool idea. I might have to teach geometry next year so I look forward to your progress through your first year teaching it.

  4. Maybe this post will work....sorry if it repeated this is my first year doing ISN( thanks to your amazing blog). I also am only teaching Geometry this year since it can be a lot of info, I need tricks and tips on using isn with geometry. My original idea was to just use it when we do summaries of a section. Please any ideas would be greatly appreciated
    And love your blog!

  5. Just to throw an idea out there for introducing this concept, I picked 3 volunteers, A and B, and told C to stand at a place equidistant to both of them. Then, I asked C to start to walk away but to continue to remain equidistant. Then the kids repeated this on paper by finding multiple points that were equidistant from points M and N, and then imagining what the locus would look like. They were able to make the jump to formalism with no problem!


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