We pulled out some folder activities for school work today just to do something a little different and because almost everything else is packed in a box. Including the batteries for my camera, so please excuse the poor quality of my phone pics. Folder activities have a way of feeling like more fun than regular school work just by virtue of being in a colorful folder, and the kids feel a little bit like they're getting away with something when we do them.
With the perimeter folder, I had a really fun time just observing how very different their approaches are to math. The boys, when handed the same stack of materials, use them in completely different ways and still come to the right answer.
Yesterday I allowed the boys to just tinker with the perimeter folder. Basically, they take a card that tells them how many bricks around a rectangular building should be, and then they take that amount of bricks and make the rectangle. Sounds easy enough, but when you just randomly go at it, pretty much every time you'll either close the rectangle and have bricks left over or the ends will never actually connect.
I let the boys try and fail as long as they wanted yesterday, huffing that it just never quite worked out and determining to try again. Today, however, I guided them with some questions. "What do we know is true of all rectangles?" They agreed that they all have two sets of same length sides and that those sets are not the same length, or else it becomes a square.
I just randomly grabbed a handful of bricks from the pile and gave them to Hunter, and gave Haven what was left. "So, if Hunter's pile of bricks make up one set of sides and Haven's make up the other, what should you both do to determine how long your set of sides will be?" Again, both boys agreed that they needed to divide them equally.
But how they went about it was so different. Haven immediately started counting his bricks. Hunter watched for a second and the rolled his eyes and got busy dealing his like cards into two equal piles on opposite sides of his pencil.
|Doesn't he look like he's talking you into buying a car?|
Haven said, "I have twenty-two bricks. Now I just need to know what number I can add to itself to get twenty-two!" Haven was proud of himself for his plan, but Hunter huffed, "You mean you want to divide twenty-two by two and then the answer will be eleven. Okay?" I explained that those were two ways of saying the same thing, so technically Haven was on the right path.
Haven wasn't at all bothered by this kind of interruption. In fact, he looked wowed by his brother's quick assessment and just said, "Hmm, I think you're right! Eleven!" and began to count out eleven.
Hunter just counted the bricks on one side of the pencil and called it a day. I would normally consider Hunter's approach of just sorting out physical objects and counting them later to be a lower order approach, but he clearly demonstrated that he understood Haven's way, and just preferred not to use it. Haven tried Hunter's way on the next round, didn't like it, and went back to his way.
Once they had both come up with the size of their walls, they put their bricks together to make a rectangle on the table. They both seemed a little shocked that it worked out after all of the trying and failing to construct a simple rectangle with a given perimeter the day before. They stayed at the table and did a few more and Haven came into my room and said, "Mom, it works like every single time! Isn't that weird?"
"Nope! It's math! It really works every time once you figure out how to approach it instead of just guessing." He beamed a super proud smile, puffed his chest out a little, and exited with a little more swagger than he had when he came in. He was feeling all math proud and that made me feel all Momma proud.
It got me thinking about the trend to have kids solve every math problem 4 ways. I think it stems from the very positive realization that there is more than one way to get to the right answer and that all ways to that answer are valid. Still, if we understand that kids all think differently, maybe we should allow them to arrive at the answer in their own way without forcing them to learn everyone else's way. I mean, for some kids, we're just lucky if they find one way that works for their brain. Why then burden them with an obligation to get the right answer 3 other ways that are less intuitive for them?
I'm feeling happy that the boys have the luxury of doing it how they do it without worrying about having to do it some other way. I did mention to them, though, that with the Common Core testing, they'll probably be asked to do it several ways, so it wouldn't be a bad idea to just make mental note of what the other one is doing.
Hands-on lessons like these always teach me so much about how the kids learn. So much fun!