Wednesday, June 29, 2016
My Favorite Math Problem
I had a number of great math ed professors, Dr. Brumbaugh is one. Sadly, I do not recall the name of the one whose materials I still, over 20 years later, look through for inspiration and help. (btw...UCF Go Golden Knights)
He made every one of his students submit 3 original problems. They had to be unique, which at the time meant that the problem, or one like it, could not be found within the class materials. The materials for this class were not a textbook, but a copy of 2 binders that the local Kinko's had. You walked in and told them you were in professor's class and they sold you 2 binders full of previous student's submissions as well as whatever the professor had added to them.
I was working with 5th graders and I wrote a problem that my students solved with little assistance in about 5-10 minutes.
We had to present our favorite problem in front of the class. My turn came up and I presented my problem, but because it was the last one of the day (and the professor had a thing about promptness) I didn't get to complete giving the explanation. He said that we should do the problem and bring a solution to class on Tuesday. It was Saturday (this being the lab for the Tue/Thur class). By Tuesday I had well over a dozen students ask me for help.
I've found that 5-6th graders rarely take more than 15 minutes to figure it out, whether they get the correct solution or not.
High school'ers take 30-45 minutes and rarely get a correct solution.
College people, especially those with STRONG math backgrounds fill pages and pages with work and get to the right answer, but are uncomfortable with the answer they have.
I call it the bionic bee problem. It hinders the student in that the more math they know, the more math they try to apply to finding a solution to it.
I love it for the same reason I love www.mathwithbaddrawings.com , its all about a bad drawing and a great story.
I wish I had his ability in my blog.... maybe I till see if I can draw something and add it later...
There's this bee. Not a normal, everyday bee; one which has been bionically enhanced by a secret governmental agency. Or maybe the illuminati. It has been enhanced to have perfect reflexes and the ability to fly at 200 mph.
In order to keep the bee from getting splatted, it is gyroscopically synchronized to turn 180 degrees in case of an imminent collision, returning exactly in the direction it was coming from.
For some reason the bee has been released on a straight railroad track, well ahead of an oncoming train. The train is travelling at 77 mph, so there is no way it should be a threat to the bee.
**At this point I ask if anyone has any questions. Invariably the question of why it was released in front of a moving train comes up. I tell them, "hey, its not like the (FBI, CIA, NSA, Etc) tell me why they do anything" Why do you think they released the bee on a straight section of railroad tracks?
A signalman accidentally transfers another train onto the same straight segment of tracks, this time 300 miles up the track. This train is travelling 73 mph right toward the bee and the other train.
I'm happy to say that just as the two trains collided together, the bee falls out of the way, exhausted but safe. Which is good, do you know how much bionic bees cost?
My question to you is, how far will the bee have flown when the trains crash together?
For high school students used to Algebra, that the tool they use.
College students use Calculus, and sometimes Algebra as well.
For them I add...
What will the flight of this bee look like (zig-zagging back and forth between the two trains).
I've never typed it out and given it to students. I may, depending on the class and usually only at the middle school or below level write everything on the board. (the bee, tracks and trains always get drawn).