Noah's Ark by Fawn Nguyen
(click on the link above to check out Fawn's original post about this task and download a Word Doc of the task)
Mr. Noah wants his Ark to sail along on an even keel. The ark is divided down the middle, and on each deck the animals on the left exactly balance those on the right — all but the third deck. Can you figure out how many seals are needed in place of the question mark so that they (and the bear) will exactly balance the six zebras?
This task is pure gold. It's problem solving; it's balancing equations; it's systems of equations. And there are no numbers. A sixth grader could do this task (it was written by a 6th grade teacher), but it is engaging enough for a calculus student. Here are a few snippets of dialogue from my students as they were working on this task last year.
"So one bear equals three zebras."
"How many seals does the elephant equal?"
"Can you have half a kangaroo?"
"Get a smaller kangaroo!"
Student: So there are 6 zebras on that side, so then we take zebra out.
Me: Wait, you can't just take a zebra off one side. Your ark isn't balanced any more.
Student: Well, we're not really taking it off. We're just saying 'Sit down, Zebra. Wait for us to catch up.'
This all sounds completely crazy, but believe me, it's very fun. Last year, I gave the task right before Thanksgiving. Many of my students figured it out in class, but for those who didn't, I informed them that it was NOT homework and they didn't have to do it over the break. The following Monday, a few of those students complained to me that I had ruined their holiday. They spent hours working on that task because they just had to figure it out.
Actually, Noah's Ark sort of took over my own family Thanksgiving last year too. My oldest nephew, Max, was in eighth grade at the time, so I printed out a copy of Noah's Ark and handed it to him before dinner. Intrigued by Max's intense frustration/determination, one by one, each of the adults in my family found a copy of the puzzle and started working on it. In case you think this sort of thing is a regular occurrence in my family, believe me when I tell you that I'm the mathy oddball in my family. We don't sit down and do math together. Ever. It was one of the most strangely awesome holidays I've ever spent with my family.