## 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

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