Making assumptions..




Every year, I ask my students the same question at the end of a math problem. “What assumptions did you have to make in order to solve this problem?”.  It has always been one of my favorite questions, because it gets students questioning a problem and wondering if the answer they get is limiting those situations. Today one of those problems came up.

Textbook problem

We looked at the following problem, and worked through it.  And got the answer dictated to us by the Teachers Manual.  Almost immediately students began questioning these answers.  Not whether they are right or wrong, but if those were the only ones. Some student responses…

“What about when the ball hits the ground?”

“What about negative distances?”

“What about wind?”

“What if it’s deflected by another player?”

“What if players within that range aren’t in the path of the ball?”

“What if the defender is behind the quarterback?”

All really valid questions, and all assumptions we had to make in order to solve this problem.

We finally settled on an answer of: between 0 ft and 3.09 ft and also between 102.17 ft and 111.85 ft (when it hits the ground), assuming that the players are in a position to be in the path of the ball.