Basic fraction concepts are viewed as the seedbed for many important mathematical ideas including the notions of equivalence, inverse, decimals, probability, ratio, and proportion. It is viewed that a critical component of children's mathematical knowledge necessary for success in certain fractional number contexts appears to be intellectual mechanisms for dealing with systems of units. Twenty-nine children were interviewed in May 1979 using sets of partition and fraction problems. This group consisted of 9 fourth-grade, 10 sixth-grade, and 10 eighth-grade children, all of whom were average or above average in mathematics. Data from seven of the fourth graders and two of the sixth graders were analyzed for this document. Among the results, it is found that the children who did not succeed at solving the given problems had not been able to take advantage of their knowledge of units, because either (1) such knowledge was not integrated into their existing fraction knowledge, or (2) knowledge of units was not the basis for whatever meanings these pupils had for fractional numbers. (MP)