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Table 2 Five subconstructs of rational number

From: Learning progression toward a measurement concept of fractions

Part-whole

Understanding a rational number or fraction, m/n, as m equal parts taken out of n equal parts

Quotient

Understanding a rational number or fraction, m/n, as dividing a quantity m into n equal parts

Measurement

Understanding a rational number or fraction, m/n, as being m measures of the unit fraction, 1/n, or m iterations of 1/n

Ratio

Understanding a rational number or fraction, m/n, as a relationship between the two quantities m and n, where either m + n = whole (part-part relationship) or n = whole (part-whole relationship, see part-whole subconstruct)

Operator

Understanding a rational number or fraction, m/n, as a function that multiplicatively maps a given quantity to another quantity, i.e., it operates on the given quantity

  1. Based on Kieren (1980)