Component 2: Number Relationships and Operations

Learning Goal 2.a: Children learn to use numbers to compare quantities and solve problems.

By 9 months, most children:

  • Hold two objects, one in each hand

By 18 months, most children:

  • Demonstrate early one-to-one correspondence (e.g., filling containers with objects by dropping them in one at a time)
  • Will usually choose a set that has more of something they prefer over a set that has less, when given the option
  • Create larger and smaller sets of objects by grouping and ungrouping items (e.g., placing and removing rings on a vertical peg)

By 24 months, most children:

  • Begin to say or gesture the number “two” when asked how old they are
  • Put objects in accurate, one-to-one correspondence when supported by the context (e.g., placing one plastic egg into each indentation of an egg carton)
  • Compare collections that are quite different in size (e.g., one that is at least twice the other)
  • Notice when another child has more of something and gesture or verbalize “want more”
  • Put groups of objects together and begin to subtract (i.e., share) objects by offering one or more to a friend or adult

By 36 months, most children:

  • Use visual cues to approximate which of two sets of objects has more
  • Understand that putting two sets of objects together makes “more” and taking sets of objects apart will make less
  • Add and subtract with sets of objects smaller than three

By 48 months, most children:

  • Understand that a entire set of objects is more than its parts when the set is divided into smaller groups
  • Use toys and other objects as tools to solve simple addition and subtraction problems when the total is smaller than five
  • Use one-to-one correspondence to compare small sets of similar objects

By 60 months, most children:

  • Use counting to compare two sets of objects and to determine which set has more, less, or the same than the other
  • Understand that adding one or taking away one changes the number in a group of objects by exactly one
  • Use toys and other objects as tools to solve simple addition and subtraction problems with totals smaller than ten