Counting Large Collections (Grades 3-6)
By Dee Crescitelli (University of Louisville)
Counting Collections, as described in Choral Counting and Counting Collections (Franke et al, 2018),
is a counting routine in which students organize and count a collection of items and then share or
record their counting and organizational strategies. Counting large collections asks students to work
in pairs or small groups to count a large collection of objects — quantities over 1,000. When counting
large collections, students will need to find effective ways to group and organize items into manageable
chunks. As they organize, students develop a deeper understanding of and make use of base-10 units
and coordinate between place-value units. (See Related Posts for how this Routine can be implemented
in K-2 classrooms.)
- counting by groups (such as 5s, 10s, 25s, 100s, etc.)
- knowing number names and the counting sequence beyond 1000
- using the structures of our base-10 number system to help keep track of the count
- coordinating between place value units (for example, organizing 10 groups of one hundred into a group of one thousand)
- noticing scale and proportional relationships, such as when a student compares the size of a bag with 1000 beads to a bag with 10 beads.
When students work in pairs or small groups to count large collections, it creates an opportunity for them to discuss the different ways they organize and group objects for counting. For example, students might compare using groups of 10 and 100 for counting 1,500 paperclips versus using groups of 25 and 250 when organizing the same count. This gives students the chance to think about quantities in larger chunks, which is important for moving from counting by ones to using additive and multiplicative reasoning to make sense of quantities.
One way to have students count large quantities is to have an ongoing class collection that students count over several days or weeks. Buttons, pony beads, paper clips, and puzzle pieces are suitable items for counts of this size. The teacher designates time for students to count and record their thinking and totals. The class total is recorded so that it can be revisited and updated as the count continues. Alternatively, the class might set up a Counting Station, as described in a related post below.
Counting Large Collections in Action
A class of third graders counted a large collection of pencil erasers. What do you notice about the different ways the students grouped and organized their erasers for counting?
The teacher had the students count all the erasers she had in the classroom. The students worked together to count the erasers in one class block, and were excited to determine that there were 1,049 erasers.
Counting Collections as a Professional Learning Activity
Counting large collections can make for great professional learning for teachers. I used this routine with math intervention teachers as we discussed building student understanding of place value and really conceptualizing larger numbers. Participants counted objects and made decisions about how to group and organize their items for counting. The toothpick pair counted out groups of 20 and then combined them in the cupcake liners in groups of 100.
The pair counting beads organized cups of 25, and the paper clips were counted in groups of 10.
Counting large collections provides opportunities for exploration and rich conversations through which students make sense of how larger numbers are structured.
Resources
- Counting Collections in Choral Counting and Counting Collections by Megan Franke, Elham Kazemi, and Angela Chan Turr (2018)
- Counting Isn't Just for Primary Grade Students, Part 4 - Teaching Children Mathematics blog from NCTM with ideas for counting with older students
- Recording sheet for partner counting larger quantities