Growing math minds... Changing math mindsets
Early Math Symposium  June 21, 2024, from 9 am to 1:30 pm (PST)
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Back to Learning Progressions
Back to Kindergarten
Age: First Grade
Learning Progression:
Kindergarten 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.
Here are some examples of children demonstrating an understanding of counting and cardinality.

Play hideandseek, 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
Learn more about the Math Domains related to your child's age: