Steps in the Number Core

Step 1 (ages 2 and 3): Beginning 2- and 3-year-olds learn the number core components for very small numbers: cardinality, number word list, 1-1 counting correspondences, and written number symbols; later 2- and 3-year-olds coordinate these number core components to count n things and, later, say the number counted.

Step 2 (age 4/prekindergarten): Extend all four core components to larger numbers and also use conceptual subitizing if given learning opportunities to do so.

Step 3 (age 5/kindergarten): Integrate all core components, see a ten and some ones in teen numbers, and relate ten ones to one ten and extend the core components to larger numbers.

Step 4 (Grade 1): See, say, count, and write tens-units and ones-units from 1 to 100.

Steps in the Relations (More Than/Less Than) Core

Step 1 (ages 2 and 3): Use perceptual, length, and density strategies to find which is more for two numbers ≤ 5.

Step 2 (age 4/prekindergarten): Use counting and matching strategies to find which is more (less) for two numbers ≤ 5.

Step 3 (age 5/kindergarten): Kindergartners show comparing situation with objects or in a drawing and match or count to find out which is more and which is less for two numbers ≤ 10.

Step 4 (Grade 1): Solve comparison word problems that ask, “How many more (less) is one group than another?” for two numbers ≤ 18.

Steps in the Addition/Subtraction Operations Core

Step 1 (ages 2 and 3): Use subitized and counted cardinality to solve situation and oral number word problems with totals ≤ 5; these are much easier to solve if objects present the situation rather than the child needing to present the situation and the solution.

Step 2 (age 4/prekindergarten): Use conceptual subitizing and cardinal counting of objects or fingers to solve situation, word, and oral number word problems with totals ≤ 8.

Step 3 (age 5/kindergarten): Use cardinal counting to solve situation, word, oral number word, and written numeral problems with totals ≤ 10.

Step 4 (Grade 1): Use counting on solution procedures to solve all types of addition and subtraction word problems: Count on for problems with totals ≤ 18 and find subtraction as an unknown addend.