Counting Collections is a structured opportunity for students to count a collection of objects. In doing so, students develop strategies for organizing their collections, keeping track of their counting, and ultimately develop a concrete understanding of base ten place value system.
Today I had the pleasure of observing a wonderful teacher as she led her kindergarten class through a Counting Collections routine. With the students sitting on their carpet squares the teacher began by reviewing the expectations for how to participate in a Counting Collections. It was clear this was not their first experience with the routine because she referred to some counting strategies students used last time and encouraged the children to pick one of those strategies to make the counting process easier.
“Remember last time,” she said, “when Javier created rows of ten with his pebbles? And Tabitha stacked her blocks in towers of five? This time I want you to think about how you can arrange your objects to make counting them easier. We have ten frames, picnic bowls, and paper cups available to organize your counting.”
For this round of Counting Collections the teacher had the students working individually to count their collections. She called students to the front of the room to choose their baggie of items from the large bucket. The excitement was palpable as the students excitedly showed each other their bag of items. The excitement only increased when she announced that they would be counting their collections outside in the building courtyard.
Almost immediately students found their spots outside and began counting their collections.
What follows are some photos of strategies students used to organize their counting and a paraphrasing of the conversations I had with the students.
During this round of Counting Collections, some students began by sorting their objects by color. I asked this mathematician how sorting the tiles by color helped her find the total number of tiles.
She said, “Because now I can count them like this…1…2…3…”. As she continued counting the tiles I encouraged her to keep counting as I moved on.
Even though this student was not yet grouping the objects by fives or tens, she was practicing some valuable concepts:
- One-to-one correspondence
- Number names
- Cardinality
This student proudly announced his answer. When I asked him how he knew his answer was correct he said, “Because I counted them!”
“How can you be sure you are correct?”, I asked.
“Because I can count them again”, he replied.
I suggested that he try linking the cubes to make towers that are easier to count than counting the cubes one by one.
I later saw him making towers of five and then putting two towers together like a vertical ten frame.
This student sorted her 44 objects into a hopscotch game by placing one object in each box and continuing until she ran out of objects. Essentially, she created 44 ÷ 10 = 4 with 4 remaining. She continued sorting those 4 remaining objects by adding a fifth object into the first four boxes. When I asked her how many objects she had, she began counting all the objects one by one.
At this point her sorting strategy did not help her efficiently keep track of the number of objects.
This student was tricky for me because I wasn’t sure how to nudge her towards the base ten system while still using the hopscotch board. Essentially, I wanted her to put ten objects in each of the first four squares and the final four objects in the fifth square, but she really wanted to use ALL ten squares to organize her counting.
While I think about how to support this student during the next round of Counting Collections, she experienced many benefits of the routine nonetheless.
Ten frames were a very popular strategy for organizing the counting.
I had a great conversation with the girl counting noodle pieces. She told me there were 20 noodles, which indeed is clearly shown in the picture; twenty noodles neatly arranged in the two ten frames. But right next to the twenty noodles was a baggie with many more noodles waiting to be counted.
“What about those extra noodles?”, I asked pointing to the noodles in the baggie.
“Oh…we are just ignoring those”, she announced.
It seems that students who were using the ten frames had a difficult time continuing the counting once they ran out of ten frames. During this episode of Counting Collections, few students successfully transitioned from using ten frames towards using the bowls or cups, which were far more plentiful than the ten frames.
Once the ten frames were filled up, the counting generally stopped.
I imagine the teacher might consider NOT providing ten frames during the next round of Counting Collections. This will nudge students towards using bowls and cups which will allow students to count higher numbers more efficiently.
Here a student managed to use a bowl when she ran out of ten frames. She is one of the few ten-frame-using students to do so.
This student created piles of ten pennies to count his collection. What perseverance! Watch what happens once he reaches 100 pennies.
If you are a TK–2 teacher, please consider giving Counting Collections a try in your classroom. Here are some tips for getting started. Be sure to also visit the Teacher Education by Design website.
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