All of this was sensible to my students as well as straightforward. There was little abstraction involved. Once the winners explained their strategy to their peers, nearly everyone understood what had just happened. Now I wanted to make the task a bit more abstract. I showed the students that the tiles were exactly one yard wide and one yard long. I wondered aloud if there were yet another shortcut rather than counting the tiles in a row and counting the number of rows? Before long we were measuring to see how many yards wide and long the room was and then multiplying those measurements. When I questioned the students about the results, it became clear to me that they all knew that our answer represented the number of ceiling tiles (squares) that I would have to buy to change the color of our ceiling. None of the students told me that I should buy a certain number of yards or a certain number of feet of ceiling tile. It was clear that our measurement of the room in yards was an intermediate step in figuring out the number of square tiles needed. When we eventually developed the formula of it was merely a convenient shortcut to the concrete work we had been doing. The formula made sense, it meant something, and therefore, it was easy to remember. Furthermore, very few students forgot to label their area answers as square units.
This story illustrates the importance of understanding that the different units in which we measure are distinctly different from each other by nature. The illustration focused on the different nature of square units as compared to linear units, but we can generalize this point. There is a distinctly different nature of units of volume as compared to units of area. There is a distinctly different nature of units of weight as compared to units of volume, and so on. If we want our students to fully understand measurement, then we must be aware of these different types of units for different types of measurement, and we must teach in such a way as to help our students develop this same understanding. Teaching measurement is not a matter of simply assigning numbers to an attribute. It is a matter of exploring what those numbers actually mean.
Further enhance your math curriculum with more Professional Development Resources for Teaching Measurement, Grades K-5.
