In Prekindergarten, instructional time will focus on three critical areas:
(1) Developing an understanding of whole numbers, including concepts of correspondence, counting, cardinality, and comparison: Children develop an understanding of the meanings of whole numbers and recognize the number of objects in small groups without counting and by counting – the first and most basic mathematical algorithm. They understand that number words refer to quantity. They use one-to-one correspondence to solve problems by matching sets and comparing number amounts and in counting objects to 10 and beyond. They understand that the last word that they state in counting tells "how many", they count to determine number amounts and compare quantities (using language such as "more than" and "less than"), and they order sets by the number of objects in them.
(2) Identifying shapes and describing spatial relationships: Children develop spatial reasoning by working from two perspectives on space as they examine the shapes of objects and inspect their relative positions. They find shapes in their environments and describe them in their own words. They build pictures and designs by combining two- and three- dimensional shapes, and they solve such problems as deciding which piece will fit into a space in a puzzle. They discuss the relative positions of objects with vocabulary such as "above", "below", and "next to".
(3) Identifying measurable attributes and comparing objects by using these attributes: Children identify objects as "the same" or "different", and then "more" or "less", on the basis of attributes that they can measure. They identify measurable attributes such as length and weight and solve problems by making direct comparisons of objects on the basis of those attributes.
Taken from Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (Reston, Va.:NCTM, 2006, p.11).