**Question:**
I've been studying p. 39, Teacher Note, and I'm somewhat confused. I thought that the two kinds of division were partitive and measurement division. It was my understanding that partitioning and sharing were the same. I have used two college math methods books to explore the issue. They are *Learning Mathematics in Elementary and Middle Schools* by Cathcart and *Elementary and Middle School Math* by Van de Walle. Any insight you can shed on this would be greatly appreciated.

**Answer:**
Thank you for pointing out the confusion about the division terms in the Teacher Note. The Note is confusing because partitioning sounds a lot like partitive which it isn't. For example, consider 24 divided by 3.

How many for each of 3 people is sharing/partitive.

How many groups of 3 is measurement/grouping.

Tom Carpenter et. al. define these this way, in *Children's Mathematics: Cognitively Guided Instruction*:

Partitive Division [sharing equally or dealing out]: Gene has 4 tomato plants. There are the same number of tomatoes on each plant. Altogether, there are 20 tomatoes. How many tomatoes are there on each tomato plant?

Measurement Division [making groups of a certain size]: Gene has some tomato plants. There are 6 tomatoes on each plant. Altogether there are 24 tomatoes. How many tomato plants does Gene have?

Cornelia Tierney, TERC

November 2002

*This information was reprinted with permission of CESAME, Northeastern Univ., and the Educational Alliance, Brown University.*