Sunday, January 23, 2011

Estimation & Measurement in Grams

This year I decided that I was going to focus a good amount of attention on the metric system. When I taught 4th grade in the public school, we did a week or so on the metric system of measurements, which never did anyone any good. Learning a new system of measurement can only be done with a little bit of practice each day, spread over many days. For example, we switched the thermometer in my truck to read in Celsius instead of Fahrenheit and now I know C so well that I have to convert temperatures in my head before I have a good feeling for what other people are talking about. It's just more natural to me to think in C.

My big goal this year was to have my students completely internalize the gram. Once you have a good feeling for the gram, you know whether you should go down a step to mg or up a step to kg for the object you are measuring. (I wasn't looking to get into the math for the conversions, I just wanted them to know which unit would be the most appropriate for any given situation, and to have an understanding of the prefixes.) Daily practice in grams? This is how we did it.

When I first introduced the gram, I got out the Montessori Wooden Hierarchical material -- which is built to scale -- and told my students that the thousand cube would represent a gram. The unit cube was 1/1000 of a gram, called a milligram. The million cube was 1000 grams, called a kilogram. Then I told them that I would set out an object on a special tray each morning for them to feel and weigh in their hands, then write down their guess as to its weight in grams on a slip of paper and place the paper in a basket. At morning meeting I would weigh the object on the Triple Beam Balanceand we would see who was the closest to being correct.

The students all got to choose something from the classroom right then, for me to weigh and announce the weight of, just so they'd have a starting rough idea on which to base later estimates. Each morning for two weeks, I would set something on the tray and place the basket, slips of paper, and pencil alongside. Each day at morning meeting we would order the estimates from largest to smallest (duplicate guesses were placed below each other), talk about the Range and the Mode, and then I would weigh the object with great ceremony. As I moved the weights and eliminated guesses which were too low, we would turn those over. Finally we would look at the number to the left and to the right of the final answer and see which was closest... this is an unexpected benefit to this activity! Students were doing mental math and arguing with each other about who was closer, one child or another. For example, if the object weighs 302.6 grams and one person guesses 250 and another guesses 350, who was closer to being correct? I heard some great mathematical discussions and people explaining their reasoning to each other. The person who was closest was line leader for recess and I wrote a slip of paper with the name of the object and the correct weight in grams and taped it to the door. After a few days, these taped slips became crucial as students used them to fine tune their estimates. I would see students standing with a smooth red rock in one hand and a large beanbag in the other, then weighing the red rock against the tape dispenser. It was wonderful! (Recording and taping up the answers in order from lightest to heaviest was also an unexpected spur-of-the-moment idea, which came about because I saw students going to previous objects for comparison. So we just incorporated it into the activity.)

At the end of the two weeks I gave a test. Yes, a test. I had the students number their paper from 1 to 12. I set out the wooden hierarchical on the floor one more time and labeled the cubes (thousand cube was labeled "gram", unit cube was labeled "1/1000, milligram, mg", million cube was labeled "x 1000, kilogram, kg") and talked about how a student the day before came to me with a single Smartie and told me he had weighed it and it weighed zero. I reminded students that there were units of measurement for objects that wouldn't appropriately be measured in grams because they were way way too light or way way too heavy. (We never once did any estimating in mg or kg.) Then I asked them to tell me by writing g, mg, or kg what they thought would be the most appropriate unit of measurement for the following items. And I stated 12 items. When possible, I held up the item, such as a piece of dental floss, a tissue, or a sunflower seed. For kg I used examples such an elephant, a teacher, a car, and a bowling ball. I reminded students to think about using the triple beam balance. If something is ridiculously too light or ridiculously too heavy for the triple beam balance, then gram may not be the best unit of measurement for it. When I was done I collected and scored the tests and I was extremely happy with the results of our daily estimation practice.

Many thanks to my grandmother, who helped me come up with this activity at the breakfast table over Christmas break!

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