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In IM Grade 4, students saw that a non-unit fraction can be expressed as a product of a whole number and a unit fraction, or a whole number and a non-unit fraction with the same denominator. For instance, can be expressed as , as , or as . In the previous section, students interpreted a fraction like as a quotient:...
In this section, students learn to see a fraction as a quotient, a result of dividing the numerator by the denominator. They solve a sequence of problems about situations that involve sharing a whole number of objects equally. Through repeated reasoning, they notice regularity in the result of division (MP8) and generalize that .
For example, 3 objects being shared...
In this section, students learn that they can reason about the area of a rectangle with a fractional side length the same way they had with rectangles with whole-number side lengths: using diagrams and multiplication.
To find the area of such rectangles, students work through a progression of fractional side lengths: a unit fraction (), a non-unit fraction (...