In Topic B, students use tape diagrams and area models to analyze their work from earlier in the module and begin using multiplication to create an equivalent fraction that comprises smaller units (4.NF.1). Based on the use of multiplication, they reason that division can be used to create a fraction that comprises larger units (or a single unit) equivalent to a given fraction. Their work is justified using area models and tape diagrams and, conversely, multiplication is used to test for and/or verify equivalence.
Students use the tape diagram to transition to modeling equivalence on the number line. They see that, by multiplying, any unit fraction length can be partitioned into n equal lengths and that doing so multiplies both the total number of fractional units (the denominator) and number of selected units (the numerator) by n. They also see that there are times when fractional units can be grouped together, or divided, into larger fractional units. When that occurs, both the total number of fractional units and number of selected units are divided by the same number.
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