Table 3 Progression of four fraction schemes
From: Learning progression toward a measurement concept of fractions
Scheme | Associated actions |
|---|---|
Part-whole scheme (PWS) | Produce any proper fraction, m/n, from a given whole by partitioning the whole into n parts and disembedding m of the parts. |
Measurement scheme for unit fractions (MSUF) | Determine the fractional size of a unit fraction, relative to a given unpartitioned whole, through iterating the unit fraction to produce the whole. |
Measurement scheme for proper fractions (MSPF) | Produce an unknown whole from a proper fraction, m/n, by partitioning the proper fraction of the whole into m equal parts to produce a unit fraction, 1/n, and iterating 1/n to determine the whole. |
Generalized measurement scheme for fractions (GMSF) | Produce an unknown whole from any fraction, m/n, including improper fractions, by partitioning the fraction into m equal parts to produce a unit fraction, 1/n, and iterating 1/n to determine the whole. |