Counting All, Grouping, then Counting Groups

Counting All, Grouping, then Counting Groups? What is it?

Counting All, grouping, then counting groups, is a quotative division strategy students may use when they know how many are in the grouping (composite unit).

Overview

This strategy is used when students come across a quotative 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 to arrive at an answer. Concrete materials such as counters are used to represent their thinking.

For example, this student makes 15, makes groups of 3 until all are grouped, then counts the number of groups

Counting All, Grouping, Then Counting Groups FINAL.mp4

Supporting Students Using Counting All, Grouping, then Counging Groups

At this stage students will benefit from exploring division problems, in a context, using manageable amounts with manipulatives. Exploring division within a familiar context allows students to create an understanding of the process of dividing. For example, the context could have been: Mr. Allan 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.

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.

Where to Next?

Once students are confident with 'Counting All' and partitioning, educators can encourage students to 'Model composite units and Count by Ones' using manipulatives.

Using Concrete Tools

When students are exploring the early stages of division, the use of concrete tools is essential. Providing as much hands on opportunity will support students to deepen their divisional understanding.

Looking to Learn More? Check out the Recorded Session!

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