Give Me the Wrong Answer

The other day I had the following warm-up on the board:

It takes 8 elephants 8 minutes to drink 8 pints of water. If they drink at the same rate, how many elephants would you need to drink 16 pints of water in 16 minutes?

(What is it with me and elephants?)

This isn't a difficult problem if you take the time to think about it. But as I walked around the room, I saw quite a few students had it wrong. Some students were thinking proportions and assumed that the number of elephants would also double. Some students noticed that 16 was evenly divisible by 8 and wrote 2 elephants. (As if I would give them something that easy.) And some had the correct answer of 8.

So after walking around, I asked, "How many elephants?" And not surprisingly, not many hands went up. Even the students who had 8 seemed to be a bit reserved.

For me, it's a little disappointing because I've had these kids all year and I would hope that at this point I could get a little more participation out of them. Obviously some students are still not very confident and don't like putting themselves out there in front of their classmates.

When this happens, I try a different approach. After seeing that only a few hands were raised, I said, "Wait. I didn't mean to ask that. Let me try again. What do you think is a common wrong answer?"

Then, a beautiful thing happened. About half the class had their hands raised. Many of these students did not know the right answer, but at some point during the process, they figured out what wasn't right. These students now felt like they had something worthwhile to contribute and were more comfortable in becoming a part of the discussion.

A student gave one of the incorrect answers I was looking for. I asked, "Why is it wrong?" She said something about rates not being the same (1 pint per 8 minutes versus 1 pint per 16 minutes). Using that, I follow up with, "Many of you thought that it would only take 2 elephants. Can someone explain why that doesn't work either?"

More hands went up.

Finally, I asked my original question, "So how many elephants?" At this point, many more students were ready to share. The students that had it wrong fixed their mistakes. The students that were right in the first place were more confident in their answers and willing to share.

On a related note: I always hate those pictures in educational magazines that show a smiling teacher in the front of a classroom, filled with students, all of whom have their hands raised high in the air. Why do I get the feeling that these pictures are all staged with the photographer telling the kids, "OK everybody! Pretend to be really excited about class today and put your hands high in the air!" I find this photo to be especially irritating because A) there's no way those kids are old enough to be learning about quadratic equations and B) no teacher would let their students have bottles of water on their desks. Someone would be asking to go the bathroom every five minutes!