Mathematics

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