Children at particular ages/grades may exceed the specified numbers and be able to work correctly with larger numbers. The numbers for each age/grade are the foundational and achievable content for children at this age/grade. The major types of new learning for each age/grade are given in italics. Each level assumes that children have had sufficient learning experiences at the lower level to learn that content; many children can still learn the content at a level without having fully mastered the content at the lower level if they have sufficient time to learn and practice.

Beginning 2- and 3-Year-Olds Learn the Number Core Components

Cardinality: How many animals (crackers, fingers, circles, …)? uses perceptual subitizing to give the number for 1, 2, or 3 things.

Number word list: Count as high as you can (no objects to count) says 1 to 6.

1-to-1 counting correspondences: Count these animals (crackers, fingers, circles, …) or How many animals (crackers, fingers, circles, …)? counts accurately 1 to 3 things with 1-1 correspondence in time and in space.

Written number symbols: This (2, 4, 1, etc.) is a______? knows some symbols; will vary.

Later 2- and 3-Year-Olds Coordinate the Number Core Components

Cardinality: Continues to generalize perceptual subitizing to new configurations and extends to some instances of conceptual subitizing for 4 and 5: can give number for 1 to 5 things.

Number word list: Continues to extend and may be working on the irregular teen patterns and the early decade twenty to twenty-nine, etc., pattern: says 1 to 10.

1-to-1 counting correspondences: Continues to generalize to counting new things, including pictures, and to extend accurate correspondences to larger sets (accuracy will vary with effort): counts accurately 1 to 6 things.

Written number symbols: Continues to learn new symbols if given such learning opportunities.

Coordinates counting and cardinality into cardinal counting in which the last counted word tells how many and (also or later) tells the cardinality (the number in the set).