By Sara Baranauskas, IM Lead Curriculum Writer, Grade 1 and IM Certified® Facilitator
Counting Collections is an engaging and playful mathematical routine that supports and builds students’ sense of mathematical identity and develops a joy for doing mathematics.
Young children are constantly making sense of their world, and counting is the perfect opportunity for joyful interaction with mathematics. Young children enter our classrooms with a plethora of mathematical ideas about counting and cardinality. They may subitize small quantities, know some number names, and know parts of the count sequence.
Let’s consider a scenario and think about what we can learn about this child’s understanding.
Counting Collections in Action: Molly and the Teddy Bear Counters
In a kindergarten math class, Molly dumps out teddy bear counters from a paper bag. She organizes the teddies into a line on her paper and begins counting, touching each object only once. “1, 2, 3, 4, 5,” she says aloud. “There are 5 teddies.” She is confident about this. She doesn’t need to recount.
Molly turns her attention to the act of recording her count, carefully drawing one circle under each teddy on her recording sheet. She counts aloud as she draws each circle. Then she recounts the five circles and writes “fv” on her paper.
What can we learn by observing Molly’s thinking about her Counting Collection? In thinking about Molly’s strengths, we can see that Molly knows several things about quantities to 5: she knows the count sequence and uses one-to-one correspondence to at least this quantity. She has a system for organizing her count (lining up the teddies). She can represent the quantity with drawings, which she did by matching a circle to each teddy. She knows the number names. She may trust her count to 5.
After observing Molly, we can ask many questions. Does Molly trust that the last number said represents her count? Does she trust her count when representing it? Does Molly connect her count with the numerals that represent the quantity? These questions can be answered in time as Molly is provided multiple playful counting experiences and supported in comparing her thinking with other students in her class.
Counting Collections is joyful as both a center and routine. It playfully provides students an entry point into mathematics into which they can use their funds of knowledge to do and make sense of mathematics. In the book Choral Counting & Counting Collections: Transforming the PreK–5 Math Classroom, the authors recognize that, “a child’s understanding of number grows rapidly over the course of these early years when they have access to, and support with, bags of Collections. Through Counting Collections, and recording their counts, children have opportunities to experience quantity and develop understanding for a wide range of early ideas about number” (Franke, et al., 2018)
When I was on the writing team for IM K–5 Math’s Grade 1 curriculum, Counting Collections was at the forefront of my mind. I wanted students to have opportunities to grapple with counting and organizing quantities. I did not want these quantities to be limited to smaller numbers, e.g. quantities within 20, as I have seen in many kindergarten and first grade classrooms. Instead, IM K–5 Math offers multiple experiences with bags of collections as a way to explore the relationship between counting and cardinality.
Counting Collections as a Routine
During the Counting Collections routine, students are given a collection of objects that are appropriate for early mathematicians. Students work with a partner or independently to count and represent how many objects are in the collection. In IM K–5 Math, this routine is first introduced to the whole class and then becomes a center.
During this center, IM K–5 Math provides checklists (checkpoints) for teachers to monitor student understanding. This way, teachers have a way to keep track of observations. For example, in early Kindergarten, teachers observe for the following understandings:
- saying the count sequence to 10
- saying one number for each object
- answering how many without counting again
By Unit 4 of Grade 1, teachers observe counting through a lens of place value:
- Represent the base-ten structure of multiples of 10 up to 90 using towers of 10, drawings, numbers, and words.
- Organize and count objects by ten.
- Represent a number in more than one way (cube towers, drawings, numbers, words, expressions).
Using these checklists, teachers are able to determine how students count, organize, and represent their counts. This allows for teachers to use an asset-based lens to adjust individual student’s collections and how they confer with students based on what they know.
During the activity synthesis, the teacher selects specific children to share their counting aloud and asks the other students what they notice about how they counted. Allowing students to develop, and share, their own strategies for counting a collection, such as touching and moving each item in the collection, allows important ideas—about counting, cardinality, and number—to emerge.
Counting Collections in Kindergarten
Counting Collections is introduced in the very first unit of Kindergarten with collections of up to 10 objects. Students are offered tools such as counting mats and 5-frames to help them organize their collections and count accurately. Choosing among these tools gives students practice in “using appropriate tools strategically” (SMP 5).
Teachers closely observe students as they count the collections. For example, the teacher will listen as students count aloud. Do students say one number for each object? Initially, some students may begin saying numbers that may or may not be in the counting sequence, gleefully counting out, “1, 2, 3, 4, 6, 7, 10!”
Teachers will also attend to how students organize their count. Some may dump the collection out and count the collection as is, randomly pointing to objects in no particular order. Others may touch each object in the collection, organizing each item into a line. Another student may move each object in the collection from one side of the counting mat to the other side. Regardless of how the student organizes their count, this gives the teacher insight into what students know about counting and cardinality right from the very start of kindergarten.
As students move through kindergarten, they are provided multiple opportunities to count collections up to 20 (K.CC.1, K.CC.4, K.CC.4a, K.CC.4b), and perhaps more, objects. As students develop their understanding of quantity, they begin to connect their collections to representations such as numbers, eventually representing their collection as drawings or numbers.
Counting Collections in Grade 1
For first graders, the sizes of the collections grow. Students grapple with how to organize the larger collections so that they can keep track. Children begin creating their own strategies for counting and organizing, such as using 10-frames and counting by 10s to quantities up to 120 (1.NBT.A.1). They will experiment with counting in groups. Students can be heard having mathematically productive conversations with each other as they defend and critique each other’s strategies and counts.
Counting Collections in Action: Chantelle and Stefan Count Cubes
Let’s consider a first grade example of Counting Collections in action.
Stefan, who is in first grade, dumps out a paper bag with a collection of centimeter cubes. The centimeter cubes fall about the floor. “Woah,” Stefan says to his partner Chanelle. “That’s a lot of cubes.”
Chanelle excitedly responds, “Yeah, I bet there are one hundred of them!”
Stefan reaches for the 10-frames. “I think we should use these,” he says, “otherwise we might lose our count.” Chanelle nods in agreement.
Stefan and Chanelle begin arranging the cubes on the 10-frames, one in each square, until all of the cubes have been placed. They fill 7 ten frames and 3 cubes are left over. They do not count the cubes individually.
Stefan counts “10, 20, 30, 40, 50, 60, 70, 71, 72, 73.”
Chanelle counts “1, 2, 3, 4, 5, 6, 7 ten frames and 3 left over. That’s 73.” Each student shares their answer aloud and explains their thinking.
There are so many things we can learn about each student’s understanding of counting and cardinality. Both show understanding of the underlying structure of tens and ones, but there is a difference between where each of them is in their continuum of learning. Stefan counts groups of 10s and 1s, showing his understanding of counting by groups and knowing the sequence of tens, but he may not be treating each group as one unit. Chanelle knows instantly when the number of tens and ones is known.
As the stories of kindergartner Molly and first graders Stefan and Chantelle show, Counting Collections supports the classroom community as it provides access to all learners and helps students see themselves as brilliant authors of mathematical ideas, no matter where they are on their development of counting and cardinality. Through counting collections, students are doing mathematics, engaging in the standards for mathematical practice in the Common Core, such as: reasoning abstractly and quantitatively (SMP 2), making appropriate use of tools (SMP 5), attending to precision in their use of language (SMP 6), looking for and making use of structure (SMP 7).
Counting Collections can be messy. It can be loud. Getting collections together can be time consuming. However, I invite you to leap head first into them anyway. I ask that you consider making them a regular center within your classroom to engage students joyful and playful sense-making. Your students will grow as classmates and friends. They will provide entry points for students at any level of mathematical understanding.
- Want to see counting collections in action? Check out https://vimeo.com/45953002
- Post photos of your students counting and representing collections using the hashtag #learnwithIM