## ABSTRACT

Like other numbers, fractions are fundamentally representations of magnitude. Nevertheless, children find it much more difficult to interpret fractions than whole numbers as representations of magnitude. There are two major obstacles to understanding fraction magnitudes. The first is appreciating that the two numbers that comprise a fraction (numerator and denominator) together specify a single magnitude (Behr et al., 1984). The second obstacle is understanding how that magnitude is related to the magnitudes of the numerator and, especially, the denominator (Behr et al., 1984; Ohlsson, 1991). The potential for confusion about this relationship is apparent from the observation that the relative magnitude of two fractions in some cases does correspond to the relative magnitudes of the numbers within them (e.g., 2 5 < 3 5 and 2 3 < 4 5 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315085654/f87c6c6e-2571-41ea-a545-06c895a22c0c/content/inline_math6_1.tif"/> ), but very often does not (e.g., 2 3 > 2 5 , and 3 4 = 6 8 even though 3 < 5 , 4 < 8 , and 3 < 6 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315085654/f87c6c6e-2571-41ea-a545-06c895a22c0c/content/inline_math6_2.tif"/> ).