Carnival Bears

Part of what we do as "residents" at UTC is take classes. The math classes we are taking right now are, in a word, awesome. We are totally re-thinking math, what it is and how we teach it. I posted a little about this in the summer, but it has taken me personally from a stance of thinking math is a "plug and chug" subject to realizing it's more about logic, problem-solving and finding a short-cut. I'm kind of mad that I never experienced math this way before, and it makes a lot more sense to me now why I hated it for so long growing up (even though I was pretty good at it).

In summary, Math is really cool, and I'm really, really lucky to be in a position to teach other people about how cool it is.

Related: I've never felt like more of a nerd.

To give an idea about exactly how we approach math, I'm going to put a problem below. The problem isn't easy, but it's simple. The idea is you want to embrace the struggle that comes along with solving the problem. Once you break through, you have a "mathgasm," as some of the less mature members of our cohort like to call it.¹

Here's the problem. It's pretty standard but I really enjoyed it, and I think you will too. It took a group of 5 of us about 15 minutes to solve it completely, so feel free to kick our butts and then brag about it in the comments. All you need are 7 post it notes to denote equal space, 3 items that are exactly the same (pencils, plastic bears, moldy foods left in the refrigertar, etc.) and then 3 other items that are exactly the same but are NOT the items from the first group. So, a perfect example would be the post-its, 3 pencils and 3 paper clips. However, if you have access to bears or something more concrete, that makes it more fun. Maybe it's time to dust off those old Beanie Babies.²

Also, do this with other people. Good, old-fashioned, fun for the whole family!!³

Anyway, here's the problem:

Connie, Jeff, and Kareem saw bears do tricks. At the beginning of the trick, three black bears were on the left side of a long mat divided into seven squares, and three brown bears were on the right side. Each bear had its own square with an empty square in the middle. The bears could only do two different types of moves:

1.They could slide onto the next square if it was empty.

2.If the next square was not empty, they could jump over one other bear to an empty square. The black bears only moved from left to right, and the brown bears only moved from right to left. When the trick was over, the bears had switched places. All the black bears  were on the right side, and all the brown bears were on the left.

Can you get the bears to switch places?

BEFORE YOU START: Set up a table. Three columns. Column #1 = number of bears per side. Column #2 = jumps. Column #3 = "slides." Column #4 = total moves. You should be able to pick up a pattern after the second or third run through. If you can't figure out the first round, definitely start with 1 bear per side, then 2 bears per side, etc. until you are comfortable enough and find a pattern that solves for every number of bears per side.

Once you solve that part...

How many jumps and slides would it take for 5 bears on each side?

Next...

How many jumps and slides would it take for 10 bears on each side?

We would typically give our kids 30-35 minutes to solve. This is a grade 6-8 math problem, and doesn't really rely on any mathematical prowess at all until you get to the short-cut part, which makes the problem easier.

Guess what - that's math! Math makes things easier. Who knew.

Time to see if you're smarter than a seventh grader.

Enjoy.

-BD

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1 OK, maybe it's just me. I don't want to hear it. ^↩ 2 I always knew they'd be good for something.^↩ 3 I think I've turned a corner. Is this what a quarter-life crisis feels like?^↩