Thursday, January 15, 2004

1000 grains of rice

The day began with a 6:30 am IM from another teacher-blogger in NYC... we were both on-line hoping to find that school had been cancelled or at least delayed due to snow & extreme cold. I don't think we should have had a snow day, but a 1-hour delay would have been helpful. Attendance was about 50% today among students. One sign of the dedication of teachers at my school is that we all arrived (narrowly) on time!

Thursday is my light teaching day - 3 preps, 2 teaching periods. I got a lot of grading done and made one beautiful bulletin board showcasing the best graphs from earlier this week, with little text-arrows pointing out the features that made these top-notch graphs.

I had been planning to give the sixth graders one day of free-review time, and it worked even better with class sizes of 12, because each student could get lots of personal attention. Don't know how the kids who stayed home will fare on the quiz, though... I set up three stations so that students could choose to review whatever they felt they most needed to practice.

But it was last period that was truly remarkable: one of those transcendent lessons that just makes you think, "This is why I like teaching," and "This is what they mean by 'teachable moment' and 'student-centered inquiry.'"

We were going over the vocabulary sentences, and I asked the kids to suggest some things that might have a mass close to five kilograms. The responses: Two of our chairs, 2 bottles of water, and 1000 grains of rice. Hmmm. I reminded them of an earlier discussion about what the mass of a newborn baby might be - probably between 2-5 kg. The children re-thought their estimates and decided that two chairs would be more than 5 kg, they weren't sure about two bottles of water, and 1000 grains of rice was probably not quite 5 kg, but they weren't absolutely sure.

I told them if they wanted to count out 1000 grains of rice and bring them in on Friday, we would measure the mass and check. Then, I saw an opportunity to get a real discussion going and develop/review some math concepts.

"Are there any other ways we could figure out the mass of 1000 grains of rice without counting out all that rice?"

I made them all think for one minute before putting up their hands. I could see flickers of "I got it!" pass across many of their faces as the minute ticked by. For those who are not teachers, waiting a whole minute before accepting answers is extremely rare in classrooms. Average "wait time" as measured in classrooms is just a few seconds; schools of ed. constantly tell teachers to extend that even by just a few seconds to give students who don't know it right away time to think. For important or tricky questions, I tell the ones who get it quickly not to raise their hands at all until I say ok, because a bunch of hands waving around pressures the kids who are still thinking, and many of them let themselves "off-the-hook" knowing that someone else already has done the thinking for them.

The first child suggested measuring the mass of one grains of rice, then multiplying by 1000. The other kids agreed that this would work. Then I asked if they had other methods. Kids suggested measuring 10 grains and multiplying by 100, or 100 grains and multiplying by 10.

I was starting to move the discussion towards a close, telling them that we could try it all if they brought in rice on Friday, when a little girl who is extremely quiet raised her hand. She said that we could have 10 people each bring in 10 grains of rice. I asked the other children if that would work. "Yes... no!" I asked the girl if she could modify it slightly to make it work, and after much thought, she suggested 20 people each bringing in 50 grains of rice, or 10 people each bringing in 100 grains. Let me interject here to say that this little girl is years behind in anything to do with language, to the point of being refered for special education. She is much stronger in math - quite quick, actually - but her difficulties expressing herself made this suggestion of a new method quite an accomplishment for her.

I could see that I was starting to lose kids' attention (though up until now, most had been thoroughly engaged in the conversation), so again I started to wrap it up and go back to the vocabulary. Another boy - one who usually has trouble with math - raised his hand and suggested that we should take the 1000 grains and divide by the number of students in the class, and that would tell us how many each child needed to bring in.

So, I set them all to work calculating how many grains each child would need to bring in... which led to a discussion of using a decimal versus a remainder (in this case, using a remainder is more useful, since no one is going to bring in 38.4 grains of rice) and how many grains we would each need to bring in to be sure we had enough.

It was fabulous. The kids, because they wanted to know, were giving themselves more and more math problems, and these were real math problems, the thinking kind, plus some arithmetic.

Let's see how many students bring in rice tomorrow!


One little addendum: I talked to a colleague about this wonderful period. We agreed that low attendance, the fact that I was relaxed, the fact that the lesson plan was pretty flexible today, and luck all helped bring it about. But then she asked if I thought that the city's new math program, which is based on a lot of problem-solving and discussion of math, made it more natural for the kids to engage in this kind of discussion. I have no way of knowing, but it's an important question given how quickly people started criticizing the math curriculum for being too liberal/constructivist.

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