The most interesting thing my third graders did today was learn how to find averages. Let me explain:
We've been growing plants in the classroom. They're a specially-bred plant called Wisconsin Fast Plants. They're supposed to go through an entire life-cycle, from seed to seed, in about two months. Perfect for a third grade unit on plant growth.
My students observe, measure, draw and write about their plants each day. They also make graphs each day, comparing each one of their four Fast Plants. After about three weeks, I introduced the concept of averages. I had them find the average size of their four plants.
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Young students usually need to learn new concepts with concrete materials. So I had them measure each plant - in centimeters - and then build a corresponding tower of centimeter-sized cubes. when they were finished, they had four towers lined up, each with a slightly different height. I talked about the idea of average being a way to describe their four plants with just one number.
So we "evened out" the towers; moving some cubes from the taller ones until each tower was about the same height. Coincidentally, we were working on fractions in our math unit, so when the towers couldn't be evened-out completely, we used fractions to express the leftover cubes.
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This worked for awhile, but today my students found that some of the plants grew like crazy over the weekend. It was no longer practical to use cubes to represent each plant. This was the moment I'd been waiting for!
I showed them how by adding up the height of all four plants and then dividing the total by four we were actually doing the same thing we had been doing with the cubes, but far more efficiently. I also showed them that using a calculator made a lot more sense than trying to get the addition and division right by hand.
It worked. My students learned how to compute averages. More importantly, by starting with the use of concrete objects - the cubes - and by measuring something they were interested in - their plants - the concept of average made sense to these students.