How I Used Midpoint Formula to Install a Ceiling Fan

Summers in Florida can be brutally hot, and my darling children, 4 and 1, love nothing more than to dump out every toy they own play in our living room. Without a ceiling fan, that room quickly became a sauna, so this summer we decided to install a ceiling fan. Well we paid electricians to install a ceiling fan - I know my limits. Although I wanted no part of running wire through the attic - I could put my math skills to use for positioning the ceiling fan. Here is our Living Room:

To get the maximum air flow and for purposes of symmetry, we wanted to ceiling fan centered in the room.

Suddenly, my living room became a coordinate plane and I calculated to the nearest eighth of an inch where the fan should go.

When the electricians came the next day, they wanted to check my math (even though I told them I was a math teacher). He whipped out his tape measure and also measured the width of our living room to be 193 1/4 inch. Then he simply folded his tape measure in half and found the middle to be 96 5/8 inches and did the same thing with the length of our living room.

I quickly made a mental note to model this for my students - what a great visual for midpoint and a great way to conceptualize what we are doing : finding the halfway point between the x-coordinates (in this case the width) and the y-coordinates (in this case the length) and then finding where they intersect. Whether you use the formula or not, you are using the same steps. 

When I introduce midpoint this year, I am definitely going to tell students this story about hanging the fan. I think I will tell them that we want to hang a fan centered in the living room and ask them what information they would need to accomplish this.

Then I will give them the dimensions and see what they come up with. I feel like midpoint is intuitive enough that they could accomplish it. Because not all midpoint problems start at the origin, I want to extend their thinking with this scenario: My living room and dining room are actually connected into one long room. How would this change the coordinates of the midpoint (helping them to see we are still finding the middle of the length and the width of the living room, but translating it up 132 inches to account for the dining room).

Off to enjoy the cool breeze in my living room for the next week or so until school starts!