Extend Cardinal Counting and Conceptual Subitizing to Larger Numbers

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.

Cardinality: Extends conceptual subitizing to 5-groups with 1, 2, 3, 4, 5 to see 6 through 10: can see the numbers 6, 7, 8, 9, 10 as 5 + 1, 5 + 2, 5 + 3, 5 + 4, 5 + 5 and can relate these to the fingers (5 on one hand). May do other such numerical compose/decompose patterns also.

Number word list: Continues to extend and learns the irregular teen patterns and extends the early decade twenty to twenty-nine, etc., pattern to higher decades: says 1 to 39.

1-to-1 counting correspondences: Continues to generalize to counting new things and to extend accurate correspondences to larger sets (accuracy will vary with effort): counts accurately 1 to 15 things in a row.

Written number symbols: Continues to learn new symbols if given such learning opportunities: reads 1 to 10; writes some numerals.

Reverses the cardinal counting principle (the count-to-cardinal shift) to count out n things (makes the cardinal-to-count shift): Must have fluent counting to have the attentional space to remember the number to which you’re counting so you can stop there.