I’ve been working with my 4th graders on fractions during the last week or so. They LIKE fractions. The reason they feel this way is that I started them off with a game that they made themselves out of paper that they tore into halves, fourths, eighths, and sixteenths. It always surprises and delights me when I hear the “aha!” that emerges spontaneously. When you hear that, you know you hit the bullseye with one of your magic darts. I got to smile a few times last week when one of the boys, after we’d made these things and worked with them for about 45 minutes, said, “Hey! I just noticed something! These things go by 2’s.” Sometimes the teacher has to allow the experience to simmer before the soup is right.

Today I had another chance to lead them into territory on the edge of the map. Decimals. I had them use graph paper and color in the squares in a 10 by 10 grid. We discussed the relationship of decimals to fractions. During the lesson I got one of those good ideas that over the years I’ve learned to trust. Thinking that they needed to learn to trust these numbers and not just identify .25, .47, .50, etc. I decided that they may appreciate learning to count to 1. I had them start out writing 0.00, 0.01, 0.02, 0.03… by the time we got to 0.12 one of the resident geniuses spoke up and announced, “This is just like normal counting.” Aha!

When we were on the way to the Music teacher’s class, several of them told the third graders they met in the hall, “We just learned how to count to 1! By hundredths!”

Some days things work out better than others. At the end of the period I asked them to write down what they learned today. My favorite response was, “I learned that besides 0 there is a lower number than 1.”