Children acquire exact meanings for number words in distinct stages. First, they learn one, then two, and then three and sometimes four. Finally, children learn to apply the counting procedure to their entire count list. Although these stages are ubiquitous and well documented, the foundation of these meanings remains highly contested. Here we ask whether children assign preliminary meanings to number words before learning their exact meanings by examining their responses on the Give-a-Number task to numbers for which they do not yet have exact meanings. While several research groups have approached this question before, we argue that because these data do not usually conform to a normal distribution, typical methods of analysis likely underestimate their knowledge. Using non-parametric analyses, we show that children acquire non-exact meanings for small number words like one, two, three, four and possibly for higher numbers well before they acquire the exact meanings.