We had just finished a problem where they had to round 315 and 558 to the nearest ten and hundred. My students were getting stuck on rounding 3-digit numbers to the nearest ten but they started getting the hang of it. That was when I posed the question. I was hoping they would see the pattern and then we could discuss why. Well, it didn't quite go as I planned.
In the past, after about 15 minutes I would have just told them the answer I wanted to hear, but today I made them press on. It was uncomfortable for them and me! I made them take a stretch break. I told them there are mathematical questions in the world that still have never been answered, like the Hailstorm Sequence we worked on the first week from the www.youcubed.com Week in Math. (I assured them there was an answer to this question.)
They used open number lines on their dry erase boards to find the nearest tens and hundreds and I recorded the results on the board. At first I only had written the 315 and 558 on the board. They sat there looking back and forth and couldn't notice anything! I gave them more numbers to round and they told me how to sort them on the board. I could tell this was the first time they were asked to think about a problem like this. I made sure to give them numbers that had 2, 3, 4, 6, 7, 8 and 9 in the tens place.
I was hoping they would notice the pattern in the tens place. The only thing they noticed that they could explain was that when rounding to the nearest ten, the hundreds place always stays the same and when rounding to the nearest hundred the hundreds place can stay the same or go up.
A couple of times I told them that we should stop and try again later or another day because I seemed more interested in figuring it out then they were. They didn't want that.
Eventually I had to stop them. I took out my phone and took the picture and told them to keep thinking about it because we would be looking at this again next week. They were mostly shocked that I ended it with explaining the answer to them!
I was happy that they wanted to keep going and not give up (which I told them many times) but disappointed that I didn't know if there was more I could do to pull it out of them without giving it to them. I am looking forward to learning how to do this better this year!
Oh I have to add one thing. They did notice that when you round a number with a 9 in the tens place if it rounds up the hundreds place changed also and the nearest tens and hundreds would be equal! Even though they didn't get where I wanted them to be they really got rounding to the nearest ten which is awesome!
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