In case you missed it I gave my Geometry class this at the end of the period on Monday.
I am not expecting to come up with the magical fix to making this sorta question great. However, I want to use this post to look at what I was trying to get at in this problem and where it went wrong.
Let’s start by looking at the objectives I had in mind with this thing
- Position a figure in a coordinate plane.
- Prove a geometric concept by using coordinate proof.
To proves this students need to know one or more of the following
- Definition of a rectangle
- Distance Formula
A majority of the struggle probably came from the definition of a rectangle. When thinking about this I immediately jumped to proving lines perpendicular and congruent distances. A lot of my students were still stuck in the two column proof mindset.
There isn’t really anything groundbreaking in proving a shape is a rectangle. For some reason I was expecting this problem to challenge student’s thinking and encourage them never to just jump to conclusions about a shape.
What I am really interested in though is how to re-vamp this problem to meet the same objectives but approach them from a different angle.
The first type of problem that comes to my mind appears in my Fence Problem Part II post.
I am still working on how exactly this problem could be modified into a rectangle… But hey, it doesn’t necessarily have to be a rectangle.
Feel free to share your suggestions/comments, I would love some input!