Overview of Number, Relations, and Operations Core
The Number Core: Perceive, Say, Describe/Discuss, and Construct Numbers
Cardinality: giving a number word for the numerosity of a set obtained by perceptual subitizing (immediate recognition of 1 through 3) or conceptual subitizing (using a number composition/decomposition for larger numerosities), counting, or matching.
Number word list: knowing how to say the sequence of number words.
1-to-1 counting correspondences: counting objects by making the 1-to-1 time and spatial correspondences that connect a number word said in time to an object located in space.
Written number symbols: reading, writing, and understanding written number symbols (1, 2, 3, etc.).
Coordinations across the above, such as using the number word list in counting and counting to find the cardinality of a set.
The Relations Core: Perceive, Say, Describe/Discuss, and Construct the Relations More Than, Less Than, and Equal To on Two Sets by
Using general perceptual, length, density strategies to find which set is more than, less than, or equal to another set, and then later.
Using the unitizing count and match strategies to find which set is more than, less than, or equal to another set, and then later.
Seeing the difference between the two sets, so the relational situation becomes the additive comparison situation listed below.
The Operations Core: Perceive, Say, Describe/Discuss, and Construct the Different Addition and Subtraction Operations (Compositions/Decompositions of Numbers)
Change situations: addition change plus situations (start + change gives the result) and subtraction change minus situations (start − change gives the result).
Put together/take apart situations: put together two sets to make a total; take apart a number to make two addends.
Compose/decompose numbers: Move back and forth between the total and its composing addends: “I see 3. I see 2 and 1 make 3.”
Embedded number triads: Experience a total and addends hiding inside it as a related triad in which the addends are embedded within the total.
Additive comparison situations: Comparing two quantities to find out how much more or how much less one is than the other (the Relations Core precedes this situation).