We are working on composed units and place value in my math course for future elementary and special ed teachers. We were discussing examples of composed units that are composed of things exactly like one another. A pack of gum is an example of this, while a car is not. A car is composed of a whole bunch of parts, but those parts are not all alike.
A student asked whether quarters being composed to make a dollar count. I said yes and then took a poll. I now share that poll with you, and invite discussion.
Both of the following are correct. However, one of them probably matches more closely how you think about this. So vote for the description that feels closest to how you think:
- A dollar is the original unit, and it is partitioned into smaller units called cents. In this case a cent is a partitioned unit.
- A cent is the original unit, and one hundred of them are composed into a larger unit called a dollar. In this case, a dollar is a composed unit.
I won’t tell you the results of my poll yet. I will tell that I had an instinct about it, that my students favored one of these outcomes by a ratio of to , and that my instinct about which would be more popular was correct.
So how about it? What are your thoughts? And what are the implications for using money to teach decimals?