Mathematics

By 9 months, most children:

• Explore the size and shape of objects through various means (banging, mouthing, dropping, etc.)
• Explore volume as they wrap their fingers around an object or around an adult’s finger
• Explore weight as they pull a toy toward themselves
• Explore speed by moving hands or legs

By 18 months, most children:

• Notice large differences in size between two objects (e.g., pointing to the bigger ball)
• Use such words as “big” and “little” to differentiate sizes
• Explore relative size by trying to squeeze a large object into a smaller container (e.g., putting a doll into doll stroller and then trying to fit themselves into the stroller)

By 24 months, most children:

• Use words such as “big,” “small,” and “more” to indicate differences in quantity
• Understand and use general measurement words, such as “big” and “hot”
• Recognize when their food bowl is empty and gesture to indicate that fact, or say “more” or “all gone”
• Find and point to small objects (e.g., the tiny mouse on the pages of Goodnight Moon)

By 36 months, most children:

• Compare small quantities (e.g., knowing that “two” is more than “one” or choosing the larger bowl for cereal over the smaller one)
• Know the sequence of some parts of their daily routine
• Use language to compare the sizes of objects (e.g., “big” and “little”; and  “mommy,” “daddy,” and “baby”)

By 48 months, most children:

• Compare two small sets of objects (five or fewer)
• Make small series of objects (e.g., putting three or four objects in order by length)
• Recognize differences in measureable attributes by direct-comparison measuring (e.g., when trying to pour the same amount of juice into three cups, looking to see if one cup has more than the others)
• Use multiple copies of the same unit to measure (e.g., seeing how many “building blocks high” a pillow fort is)
• Use comparative language (e.g., “shortest,” “heavier,” “biggest”)

By 60 months, most children:

• Order (or seriate) four or more items by decreasing or increasing a relative attribute when differences are perceptually clear (e.g., arranging a rock collection from the largest to the smallest)
• Use some appropriate tools to measure different attributes (e.g., choosing a scale for weight and a cup for volume)
• Use measurement language to describe the attributes of objects (e.g., “This is three-blocks long.”)