By the end of Kindergarten, a child should count confidently, understand that numbers represent quantities, and compare small groups of objects. The year builds number sense (knowing what numbers mean, not just reciting them) and introduces addition and subtraction through hands-on work with objects. Children also begin to name and build the shapes around them.
Key learning topics:
Count to 100 by ones and tens; count forward from any number
Count objects accurately and tell "how many" (to 20)
Compare groups and numbers: more than, less than, equal to
Add and subtract within 10 using objects and drawings
Take apart numbers up to 10 in more than one way (7 = 5 and 2)
Identify, describe, and build basic 2-D and 3-D shapes
Sort and classify objects; compare length, weight, and size
Proficiency looks like: a child who can count a set of objects, say which group is bigger, and solve a simple "how many altogether" story with objects.