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I Count, You Count, We all Count!

Skills and Concepts in Counting Collections

Counting collections are rich, relevant cooperative learning tasks that also provide authentic formative assessment opportunities. Students in PK-2 apply many foundational skills while participating in counting collections: number list, cardinality, conservation, pairing one object to only one number name, place value, answering “how many?”.

Teachers can easily engage learners by curating creative collections and differentiating the collections by type of counters (complexity of attributes) as well as how many items are in the collection. After selecting their collection (they love this part!), students begin by estimating how many are in the collection, they may sort by attribute to count or organize in number groups such as 2s, 5s, or 10s to make counting easier. Finally, they use pictorial and symbolic recordings to represent how they counted their collection and their total.

Thinking Like Mathematicians

In addition to developing mathematical skills and concepts, students are engaging in the mathematical practices while working with counting collections:

  • Students make sense of problems and persevere in solving them when they study the collections, make a plan(s) how to count it, persist in finding the total, and assess the reasonableness of their total.
  • They reason abstractly and quantitatively when they consider the meaning of the quantities and represent them with pictures, numbers, words, and equations.
  • Young children construct viable arguments and critique the reasoning of others when they explain their counting reasoning and critique the counting reasoning of others.
  • Students use appropriate tools such as ten frames, cups, number paths, etc. to help them organize and count the collection efficiently and accurately.
  • They attend to precision with grade appropriate mathematical language verbally and in unit labels.
  • Young children also look for and make use of structure as they consider organizing collections into groups such as ten and ones to make counting easier.

Mathematical Discourse & Community

Counting collections are highly engaging because students LOVE discussing their collections and collaborating with other young "mathematicians" to find efficient and accurate ways to organize and count. They involve group work, promoting communication and collaboration as students discuss strategies and solutions. Students discuss with their peers how to count the collection and they explain their counting methods, allowing teachers to assess their understanding and correct any misconceptions. Counting collections prompt students to find and compare diverse ways of counting the same collection. This encourages flexible thinking and exposes students to multiple strategies for solving a problem.

Counting Collection Procedure

  1. Students select from differentiated collections of engaging objects. The collections range in total count and complexity of attributes.
    1. Students explore the collection, consider their attributes, make an estimate, organize, count, and record how they found the total.
      1. They may label their collections with numeral cards, place value cards, or place value disks.
    2. Extensions such as adding and comparing 2 collections may be offered. Students may even graph their collections.
  1. As students are working and sharing, the teacher has an excellent opportunity to observe, question, and take notes.
    1. It is amazing what you can learn about student understanding and misconceptions in the areas of counting, skip counting, addition, unitizing, place value, attributes/sorting, patterns, etc.
    2. With counting collections, students are not just getting a problem right or wrong - they are engaging in mathematical practices while applying grade level standards to the task. This allows teachers to note not only what they DON'T know but what they DO know!
    3. They can be repeated even monthly to note student growth and instructional opportunities.
  1. The teacher selects student work (the organized collection and/or the recording) to share and facilitates a math talk in which students discuss and question their organizational reasoning, strategy explanation, and solution justification.
    1. Students should be encouraged to ask questions of one another, agree or disagree on totals or solution paths, and consider new, more efficient ways of organizing and counting.

Counting Collections Resources

Of paramount importance to student engagement and for differentiation of academic skills is to have many intriguing collection choices: varied totals (10, 50, 100, 1000, etc.), number of attributes (1, 2, many), and attribute type (color, size, shape, etc.), theme, feel, etc. Some of my personally tested, kid-loved counting collections and organizational tools from Didax include:

To learn more purchase and read, Choral Counting and Counting Collections

More Than Just Counting

Counting Collections is more than just a counting exercise; it is a powerful instructional routine that builds a solid foundation for mathematical thinking and problem-solving. Through hands-on experiences with real objects, students develop numerical fluency, critical thinking skills, and a deeper understanding of numbers and their relationships. By integrating this approach into the classroom, teachers can create an environment where students actively engage with mathematical concepts, fostering a lifelong love for learning and a genuine appreciation for the beauty of mathematics.

Reach out to our sales team at sales@didax.com to create custom counting collection kits for your school. Happy Counting for ALL!

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Christine is a veteran educator, instructional coach, professional developer, and math curriculum writer with a passion for ensuring all students have access to engaging mathematics.