The purpose of this study is to examine three, five and seven-year old children`s understanding of quantitative invariance. Young children were expected to transform five times according to three different domains. The subjects of this study were 60 children in three groups(each group had 20 children). Fifteen items were given to them to judge how they could transform according to three domains. The data were ananlyzed by ANOVA using SPSS PC^+ Program. The results of this study were as follows. First, the three, five and seven-year old children showed differences according to their age in understanding quantitative invariance and measurement competence. We will be able to help children develop their competence to understand and measure quantitative invariance through their rich experiences at each age. Second, the subjects of this study did not show differences in the five transformations according to the three domains. We will be able to help children develop their competence to understand and measure quantitative invariance through their experiences of various domains(length, weight, area, volume etc.). Third, there were differences in the ability to understand the quantitative invariance through five transformations(color, positional change, roll out, number, superimpose). We ought to give the children various experiences of making easy and hard judgements for transformation.