Previously, students decomposed non-unit fractions into smaller unit and non-unit fractions. Here they continue to think about decomposing fractions, but they now use number-line diagrams to support their reasoning.

A number line can illustrate the number of unit fractions that make a whole number. This in turn allows students to see that a fraction greater than 1 can be decomposed into a whole number and a fraction less than 1, preparing them to work with mixed numbers. For instance, on a number line partitioned into fifths, the fraction is 7 fifths away from 0 and 2 fifths away from 1, so we can express as 1 and . One way to illustrate that sum is by drawing “jumps” on the number line.

Note that in grade 3, students came across mixed numbers in the context of measurement. For instance, they used inch rulers to measure lengths greater than 1 inch to the nearest half inch or fourth inch, and expressed them, using numbers such as  or , respectively. They did not, however, reason about mixed numbers as sums of lesser fractions or as sums of a fraction and a whole number.