I am teaching dividing fractions now and wanted to be clear in my own mind about the differences between these two ways of thinking about and describing division problems. I have found myself switching between these two different ways of describing division problems and I really did not understand why. I made the graphic below to help me understand why some problems make more sense with partitive division (sharing) and others with quotative division (measurement). And how the language used to describe a problem changes how you would draw a picture of the problem (model) and the meaning of the quotient.
Partitive Division
- Sharing Division
- I know the number of groups
- How many in each group?
Quotative Division
- Measurement Division
- I know how much will be in each group
- How many groups?
I find quotative division (measurement division) very helpful when describing fraction division problems. For example, how many 1/2s are in 10 wholes? However, partitive division (sharing division) makes more sense when the dividend is a fraction or mixed number and the divisor is a whole number. For example, 4 3/5 lbs of candy is divided among 6 friends. How much candy does each friend get?
This video helped me understand the difference between these two different ways of thinking about division problems.
