When asked to "find three forks", adult speakers of English use the noun "fork" to identify units for counting. However, when number words (e.g. "three") and quantifiers (e.g. "more", "every") are used with unfamiliar words ("Give me three blickets") noun-specific conceptual criteria are unavailable for picking out units. This poses a problem for young children learning language, who begin to use quantifiers and number words by age 2, despite knowing a relatively small number of nouns. Without knowing how individual nouns pick out units of quantification--e.g. what counts as a "blicket"--how could children decide whether there are "three blickets" or "four"? Three experiments suggest that children might solve this problem by assigning "default units" of quantification to number words, quantifiers, and number morphology. When shown objects that are broken into arbitrary pieces, 4-year-olds in Experiment 1 treated pieces as units when counting, interpreting quantifiers, and when using singular-plural morphology. Experiment 2 found that although children treat object-hood as sufficient for quantification, it is not necessary. Also sufficient for individuation are the criteria provided by known nouns. When two nameable things were glued together (e.g. two cups), children counted the glued things as two. However, when two arbitrary pieces of an object were put together (e.g. two parts of a ball), children counted them as one, even if they had previously counted the pieces as two. Experiment 3 found that when the pieces of broken things were nameable (e.g. wheels of a bicycle), 4-year-olds did not include them in counts of whole objects (e.g. bicycles). We discuss the role of default units in early language acquisition, their origin in acquisition, and how children eventually acquire an adult semantics identifying units of quantification. (Contains 4 footnotes and 7 figures.)