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The study we describe in this paper builds on recent studies within early algebra that have shown that early elementary school students can generalize and use variable notation to represent situations that involve both variable and fixed unknown quantities. We will answer the following question: In what ways do Kindergarten and Grade 1 students use variable notation as a way to represent indeterminate quantities and relationships between indeterminate quantities in algebraic problems? We present results from 16 students who participated in a 7-week classroom teaching experiment focused on generalized arithmetic. Our results indicate that after a brief teaching experiment most interviewed students were able to use variable notation to represent indeterminate quantities.