9.3: Introducing the Foundations
Introducing the Foundations
The California preschool learning foundations for math have been divided into five broad areas or strands.
- Number Sense
- Algebra and Functions (Classification and Patterning)
- Measurement
- Geometry
- Mathematical Reasoning[1]
Supporting Number Sense
The Number Sense strand refers to concepts of numbers and their relationships. It includes the development of counting skills, the understanding of quantities, recognizing ordering relations (which has more, fewer, or less), part-whole relationships, and a basic understanding of “adding to“ and “taking away” operations.
| 1.0 Children begin to understand numbers and quantities in their everyday environment. | 1.0 Children expand their understanding of numbers and quantities in their everyday environment. |
| 1.1 Recite numbers in order to ten with increasing accuracy. | 1.1 Recite numbers in order to twenty with increasing accuracy. |
| 1.2 Begin to recognize and name a few written numerals. | 1.2 Recognize and know the name of some written numerals. |
| 1.3 Identify, without counting, the number of objects in a collection of up to three objects (i.e., subitize). | 1.3 Identify, without counting, the number of objects in a collection of u to four objects (i.e., subitize). |
| 1.4 Count up to five objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. | 1.4 Count up to ten objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. |
| 1.5 Use the number name of the last object counted to answer the question, “How many . . . ?” | 1.5 Understand, when counting, that the number name of the last object counted represents the total number of objects in the group (i.e., cardinality). |
| 2.0 Children begin to understand number relationships and operations in their everyday environment. | 2.0 Children expand their understanding of number relationships and operations in their everyday environment. |
| 2.1 Compare visually (with or without counting) two groups of objects that are obviously equal or nonequal and communicate, “more” or “same.” | 2.1 Compare, by counting or matching, two groups of up to five objects and communicate, “more,” “same as,” or “fewer” (or “less”). |
| 2.2 Understand that adding to (or taking away) one or more objects from a group will increase (or decrease) the number or objects in the group. | 2.2 Understand that adding one or taking away one changes the number in a small group of objects by exactly one. |
| At around 48 months of age | At around 60 months of age |
| 2.3 Understand that putting two groups of objects together will make a bigger group. | 2.3 Understand that putting two groups of objects together will make a bigger group and that a group of objects can be taken apart into smaller groups. |
| 2.4 Solve simple addition and subtraction problems nonverbally (and often verbally) with a very small number of objects (sums up to