Previously, students learned how to write unit fractions, using numbers of the form . They also partitioned rectangles and used unit fractions to describe one of the parts. In this lesson, students use diagrams with multiple equal parts shaded to make sense of how non-unit fractions are made of unit fractions.

Students learn that a unit fraction is a fraction in which the numerator is 1 because it describes one of the equal-size parts. Students work with fractions that are greater than or equal to a whole number to see that all non-unit fractions are built from unit fractions in the same way. Students also notice that if all the parts are shaded, then the non-unit fraction is equivalent to a whole number. The terms “numerator” and “denominator” are not used until the next section.

How did students leverage their knowledge of unit fractions from previous lessons to make sense of non-unit fractions for the first time?