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Counting & Cardinality


Several learning progressions originate in knowing number names and the count sequence. One of the first major concepts in a student’s mathematical development is cardinality.


Cardinality can be explained as knowing that the number word spoken tells the quantity and that the number on which a person ends when counting represents the entire amount counted.


For example, if a child is counting to make sure there are enough chairs at the table for dinner, they may or may not say the correct number of chairs. Even though the child knows the count sequence, the idea of a number meaning that many objects may not have been learned yet. The idea is that numbers mean amount, and no matter how you arrange and rearrange the items, the amount is the same. Students can generally say the counting words up to a given number before they can use these numbers to count objects or to tell the number of objects.


Students compare the number of objects in one group (with up to 10 objects) to the number of objects in another group. Students need a strong sense of the relationship between quantities and numerals to accurately compare groups and answer related questions. They may use matching strategies or counting strategies to determine whether one group is greater than, less than, or equal to the number of objects in another group.

What it looks like:


Jorge lined up his cars and his brother’s cars to see who had more. Both brothers could see that Jorge had more cars than his brother.

How can you tell if a child understands these concepts? Here are some examples of children demonstrating an understanding of counting and cardinality.


  • Play hide-and-seek, counting to 20 before looking

  • Ask child to count as high as she can

  • Children say how old they were, are, and will be

  • Painting numbers

  • Playing puzzles that match numbers with sets of objects

  • Children correctly use the word “zero”

  • Lining up toys and counting them

  • Asking a child to count the number of people in a small group

  • Passing out items, one to each member of the group (e.g. passing out 6 stickers to a group of 6 people)

  • Dividing or sharing a group of items with a friend

Vocabulary List:


Here is a list of important vocabulary words, from the California Mathematics Frameworks, that children can learn to use correctly by the end of their kindergarten year.


  • Number words up to 100

  • Count

  • Count by/from

  • Next number

  • How did you figure that out?

  • Zero

  • How many?

  • One more

  • All together

  • In all

  • Total

  • More

  • Fewer

  • Less

  • Same as

  • Greater than

  • Less than

In kindergarten, Counting and Cardinality includes knowing the names of numbers, counting, and comparing numbers. The end of kindergarten expectations include the following:


  • Count to 100 by ones and tens

  • Start counting in the middle of a known sequence (e.g. not starting at 1)

  • Write numbers from 0 to 20

  • Understand the relationship between numbers and quantities

  • Answer “how many?” questions up to 20

  • Compare groups by counting and matching

  • Compare written numerals from 1 to 10.

California Early Math Project