The 2 “conceptual” methods of division

Sharing (Way 1) vs Measurement (Way 2)

Let’s say I have the problem: .I can do this in 2 ways:

Way #1: “Sharing”

1) I know the number of groups or people to share with: it is the divisor 3.

Share with 3 people the 12 items*-- First give them each one….

Then give them each another, and so on

	*
			* * * *

Until all 12 items have been given away:

2)The answer (remember we just used the sharing method) is the group size- 4.

Way 2: “Measurement”

1) Measure out 3 items at a time- this is the group size. We do not know how many groups will be formed (i.e. how many people we will share with). Do this until no items are left.

Here go the first three:

I still have 9 items left.

The next three:

* * *

I still have 6 left. The next three

I have 3 left to form my final group:

* * *

2) To finish up, I ask: how many groups were formed? I can see that 4 groups were formed so 12/3 is 4.

Table: differences between sharing and measurement for a divided by b

	Group size	Number of groups
Sharing	Unknown to start. Whatever it is after you share the dividend (evenly) of a items amongst your b groups is the answer. The number of the things in each group is the answer to the division problem.	You know it- use the Divisor b as the number of groups and then share your pieces
Measurement	You know it- use the Divisor b . Distribute the pieces by measuring them out evenly into groups of size b until they are all gone.	Unknown to start. After you measure out all the pieces evenly , look at how many groups you have. The number of groups you have is the answer to the division problem.

One more try:

With sharing, you start with knowing how many people or groups you want to share with and then give out pieces and ask “how many pieces does each group get?”

With measurement, you start with knowing how many you want in a group and ask “how many groups will be formed?”