Representing Empty Groups, the Dealing out One at a Time: What is it?

Representing empty groups, then dealing out one of a time (fair sharing) is a partitive division strategy students use during the early stages of division.  

Overview

At the beginning of using this strategy to divide, a student will create empty groups first and then share counters out, equally, by one into the empty groups. The number of empty groups is determined by the divisor. As they become more proficient students may share equally by other numbers (ex. 2, 5, 10). Students will determine the quotient when they count the number of counters in each group (composite unit) once they are all shared. 

Supporting Students Using Representing Empty Groups, then Dealing out One at a Time

This strategy helps students see that division is about the whole (dividend) being shared equally. Creating the empty groups helps students identify the purpose of the divisor. Questions posed within a context allows students to connect their personal experiences to the mathematical structure of division. Students naturally understand fair sharing but do not naturally write this in a math sentence. An example question that often elicits this strategy is, “You have twelve cookies and share them between three friends.  How many cookies does each friend have?” This is an example of a partitive division question which gives the total number of items and the groups. The unknown is how many are inside each group (composite unit). Providing students with partitive division questions support the fair sharing strategy and using concrete materials to support learners.

To work more efficiently with this strategy, students may be encouraged to think multiplicatively and replace concrete materials with numbers. For example, "We have 56 soccer balls to share between 8 classrooms. How many soccer balls will each classroom receive?"

Where to Next?

As students grasp this strategy and begin to work with higher numbers, the teacher can encourage efficiency by challenging the student to use 'skip counting' with larger intervals or known multiplication facts. For example, 150 divided by 3 could be shared out by 10s.

Looking to learn more? Check out the recorded session!