How to Annoy a First Grader

I'm sure there are other ways too, but one really good way is to ask children to make an estimate.

First, present a "how many" question where the answer's clearly more than 10 or 15 or so: how many cubes in a bag, how many times they can hop in one minute, how many pages in a book, that kind of thing.

Then, ask them to estimate the total, but insist that they give you a "round" number--that is, a multiple of ten (10, 20, 30...).

From a math perspective, asking for a round number makes plenty of sense. Part of the purpose of an estimate is to use numbers that are easy to work with. "If this bag has about 20 cubes, and this one has about 60 cubes, about how many are there in both bags together?" is easier to deal with than "If this bag has about 19 cubes, and the other one has abut 63 cubes..."

But from a kid's-eye perspective, it's frustrating (or "fruster-rating," as some children say) to have to give a round number. That's because children of this age tend to view the purpose of estimation as "guessing the right answer," not simply coming up with a number you can use when you don't need, or can't get, an exact answer. By limiting their choices to multiples of ten, I make it very difficult to choose the correct total.

And they hate that. Recently I insisted that kids give me a round number for an estimate. "How many say it's about 10?" I said. "About 20? About 30? Who says about 40? Raise your hand..." Several of the children refused to vote. (Insurrection!) And when the true total was revealed to be 42, one child said to me reproachfully "No fair! You didn't let us pick that one!"

So enforcing a round number estimate is one good way to annoy a first grader. Here's another way, related to the first. Today we were working on probability. Partners were given an envelope with five cards. They recorded the number of red cards and the number of black cards, and then made estimates of how many of each color they would get if they pulled a card from the envelope 25 times (replacing the card after pulling it, of course). Next, they tried it out and recorded the results. Finally, they needed to decide if their initial estimate was "close" or "not very close."

One pair predicted 22 blacks and 3 reds. Not a bad prediction, given that they had 4 black cards and just 1 red one in their envelope. These children were not just interested in the results; they were invested. "Come on, BLACK!" they'd say, pulling out a card and discovering that it was...the two of spades. (Fist-pumping ensued.) Then, after a while, one of them commented "We need another couple of reds," and lo and behold, whaddaya know, the next card out of the envelope was the five of hearts! (More fist pumps.) And amazingly enough, after 25 pulls they had--wait for it--22 blacks and 3 reds. An astonishing coincidence, to be sure.

"The page just says 'close' or 'not very close,'" they complained to me after they were finished. "Where's the one for 'we got it exactly right'?"

"Oh, there isn't one," I said. "You can mark 'close.' The point of a prediction like this is to be close, that's all. That's what we care about."

"Yeah," they said, "but we got it exactly right."

"So you did," I agreed, "but when you make an estimate or a prediction you are just trying to get near the real total. Your estimate was a good one. But it would have been just as good if you had predicted 21 blacks and 4 reds. Or even 20 blacks and 5 reds. Just circle 'close.'"

Fist-pumping was now over. The two exchanged unhappy glances, returned to their seats, and circled 'close.' Against their wills, of course.

Oh well-they'll get there eventually. I hope! In the meantime, feel free to annoy your own personal first grader all you like with these methods...