On Wednesday afternoon he observes Betty Mathison, an experienced sixth-grade teacher. The teacher selects a task that allows students to use what they have previously learned about fractions. Betty has prepared transparencies of 100-square grids that are partially shaded. By having the students write their estimates, the teacher is involving all the students in the lesson. The teacher is providing the students with an opportunity to share their mathematical reasoning.
Students write their guesses and their reasoning on a sheet of paper.
Betty walks around the room and observes what they have written after showing each transparency. Betty then randomly selects students and asks them to indicate what their guesses are and to share their rationales for the guesses. The students begin to appreciate the strategies that their classmates are using. I saw three rows but didn't have time to count the other ones. In the second one, I think there were 8 rows of ten and then 7 more.