KCM HUB COLLECTION

Choral Counting

Counting is an essential foundation for all mathematics. Furthermore, the ways and range in which students count is always expanding. Students count forward or back, by 1s or by multiples, by 10s or 100s, even by fractions! As they count, they uncover patterns and structures in our number system.

• Choral Counting Overview
  Choral Counting, as described in Choral Counting and Counting Collections (Franke et al, 2018) is a whole class-counting routine that makes these patterns visible to students. As the class counts, the teacher records each count in a planned and organized way, pausing with questions such as "What patterns do you notice?", "Did the pattern you noticed before continue?", "If the pattern continues, what will happen?" At each step, the teacher annotates the patterns students are noticing, highlighting important relationships.
• Choral Counting with Fractions
  In this example of a Choral Counting routine, third-grade students count by one-fourth, finding patterns in the counting sequence and in the way fractions are written with a numerator and denominator.
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• Choral Counting by 4s: Noticing Patterns to Build Multiplicative Reasoning
  Explore how a teacher might use the Choral Counting routine with a skip counting sequence. In this video, we walk through planning a skip count by 4s, supported by concrete representations using towers of 4 unifix cubes, alongside a teacher's annotation of the pattern. Learn how to help students recognize structure, describe patterns across the count, and build a foundation for reasoning with equal groups and early multiplication.

Counting Collections

By counting small collections, young learners develop early counting principles, such as 1-1 correspondence and cardinality. As students grow more sophisticated in their thinking, they can count larger and “messier” collections, they develop a deeper understanding of the structure of numbers.

• Counting Collections (Grades K-2)
  Counting collections, as described in Choral Counting and Counting Collections (Franke et al, 2018), is an activity in which students count a collection of objects and represent that count in ways that make sense to them. For early learners, this activity supports their developing understanding of core counting principles such as 1-1 correspondence and cardinality. As students grow more sophisticated in their counting and work with larger collections, they develop an awareness of and make use of the structure of numbers.
• Counting Large Collections (Grades 3-6)
  Counting large collections asks students to work in pairs or 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.
• Counting Collections: Implementing a Counting Station in a Third-Grade Classroom
  Learn more about how one third-grade classroom found joy and agency as they worked together to determine the number of buttons in a large collection.
• Counting Collections: When Collections Get Fractional (Grades 3+)
  Counting collections with fractions is a powerful way to deepen mathematical thinking and support students in building a more flexible understanding of quantities and fractions as numbers. Counting collections with fractions offers a rich opportunity for students to explore equivalence, part-whole relationships, and unitizing while redefining units and wholes, all of which support the development of flexible thinking about quantities.