We encountered a puzzling situation with remainders this week. Until now, the students expressed remainders as R4, for example, rather than as a fraction or decimal. The problem that arose this week helped build the conceptual understanding of what remainders are all about, and now we know why you express remainders as a fraction or decimal, not just that you express remainders as a fraction or decimal.
One strategy the students use to solve a division problem is to make an easier, equivalent problem by dividing the dividend and the divisor by the same number, which won't effect the quotient (12 / 2 = 6 / 1). When they used that strategy to solve 376 / 6, however, they encountered a problem--halving and halving didn't produce the same remainder as other strategies, but no one could find an error in their work. We revisited the problem today, and everyone tried to figure out why the remainders were different. We ended with a meeting to discuss our findings. Here's the original question as well a poster that shows our conclusions:
A Division Mystery
Students solved 376 / 6 in different ways on Wednesday. Two different answers came up, but there doesn’t seem to be a calculation error in either strategy. What’s happening here?
376 / 6
Strategy 1
60 x 6 = 360
2 x 6 = 12
376 - 372 = 4
376 / 6 = 62 R4
Strategy 2
376 / 6 = 188 / 3
60 x 3 = 180
2 x 3 = 6
188 – 186 = 2
188 / 3 = 62 R2
376 / 6 = 62 R2
The students worked together to come to the following conclusion, and several students volunteered to make this poster:
That's me!!
ReplyDeleteThat was a great project!!!
ReplyDeleteI also worked on that!:)
ReplyDeleteGo math because math is GREAT!
ReplyDeleteKaya Said....
ReplyDeleteits extremely clear and Its hanging up in the room!!!!! Like trevor
Math Is Great and I love it!!!
I didn't want to get in the way of the new blog but Lauren you should show the kids this poster when you get to that part of the year this year or next year
ReplyDelete