Math Strategy: Counting all, partitioning, counting groups

What does counting all, partitioning, counting groups mean?

Math Strategy: Counting All, Partitioning, and then Counting the Groups
Math Strand: Number Sense and Numeration



Overview:
This strategy is used when students come across a division problem. A student would begin to use this strategy by first counting out the dividend (ex. all 15 objects). Then the student would separate the objects into the composition of each group (into groups of 3). When all of the items are sorted into groups the student would then count the number of groups.

Above: Student makes 15, makes groups of 3 until all are grouped, then counts the number of groups.

How to Support Student Learning:

At this stage students will benefit from exploring division problems, in a context, using manageable amounts with manipulatives.  Exploring division within a context allows students to create an understanding of the process of dividing.  For example, the context could have been: Mr. A has 15 pencils.  He wants to give 3 to each student. How many students will he be able to give 3 pencils to? Building with manipulatives allows the students to model the action of the problem and make the operation of division accessible.  Additionally, working with smaller amounts allows for students to grow confidence with dividing. With the repetition of putting the dividend into equal groups and then counting the groups, students will begin to identify that each group is a unit (made up of equal amounts). This is the beginning of understanding the key idea of unitizing.

Where to Next:

Students should be allowed to go through the process of counting all, sorting the composite units, and then counting the groups as needed.  The repetition of this process is required for students to gain an understanding of and trust the process of division.  Later, students may also try creating groups of the composite until they reach the total amount being divided.  Also, students may try to make the composite for each group and then skip count by the composite while tracking the number of groups.  To support the development of these strategies, try using real life scenarios where students can practice this strategy.  An example of this would be: "For the game today, we need groups of 5.  We have 20 students here today.  How many groups of 5 can we make?"

Share your classroom experiences with Counting All, Partitioning, & Counting Groups with us on Instagram and Twitter at @LKelempro #EngageLK!