Sharing

In division, sharing refers to a way of thinking of division that is also referred to as partitive division. It is one of the ways in which division is thought of and taught, with the other being measurement division.

Sharing involves dividing a given number of objects into a known number of groups, where the number of items in each group is unknown.

When first introducing the concept of sharing, one way to do it is to give a student a set of objects and to have them count objects into each group. This can be done 1 object at a time, or by 2s, 3s, or any convenient number that the student is comfortable with. The figure below is a representation of sharing in which 4 objects are evenly shared between 4 groups, 1 object at a time.

The arrows indicate counting the respective object into 1 of the 4 groups with the result being that 4 objects can be divided evenly into 4 groups if there is 1 object in each group. If there were 8 objects instead, we could count 1 into each of the 4 groups, then another to find that each group will contain 2 objects each, or 8 ÷ 4 = 2.

Below are some word problems that can provide some more practice.

Examples

1. There are 12 cookies. They are divided equally among 4 people. How many cookies does each person get?

12 ÷ 4 = 3

Thus, the size of each person's part, or share, is 3.

2. Daynna, Taylor, and John went blueberry picking. Together, they picked 15 pints. When they got ready to go home, they shared the blueberries equally. How many pints did each person get?

15 ÷ 3 = 5

Thus, each person's share of blueberries was 5 pints.

Sharing vs measurement division

Measurement division (also referred to as quotitive 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 some 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.