Measurement division

Measurement division, also referred to as partitive division, is one of two common approaches to division. The other is referred to as sharing, or partitive division.

Measurement division involves determining the number of groups that a set of objects can be divided into given that the number of objects in each group is known.

One way to approach measurement division is to think of it in terms of repeated subtraction. Given that you have 10 objects, and want there to be 2 objects in each group, you can determine the number of groups of objects there will be by subtracting 2 from 10 until there are no objects left. The number of times you subtracted 2 is the number of groups of 2 you will have, which reflects the divison sentence 10 ÷ 2 = 5. However, it is worth noting that this division sentence is also applicable to the sharing approach to division, and the difference between the two is entirely based on how division is conceptualized.

The figure below provides a visual representation of the concept of measurement division.

At each stage, 2 objects are subtracted from the total number of objects, forming 1 group. This process continues until all the pairs of objects are in separate groups, after which we count the number of groups to determine how many there are.

Measurement division vs sharing

Sharing (also referred to as partitive division) is another way to think of division. The key difference between sharing and measurement division is that in sharing, the number of groups is known, but the number of objects in each group is unknown. In contrast, in measurement division, the number of objects in each group is known, but the number of groups is unknown. In both cases, the total number of objects is known.

In the case of sharing, we are trying to determine the number of objects that will evenly fit within each group. In measurement division, we want to know how many groups we can have given that each group has a known number of objects. Below is a figure that depicts this based on the division sentence: 8 ÷ 2 = 4.

Both approaches to conceptualizing division are valid. Whichever method is more intuitive or comfortable for a given student should be used.