Previously, students have found quotients by decomposing a dividend and finding the quotient for each decomposed part until all of the dividend is divided. Students also reasoned in terms of multiplication—adding partial products until they reach the value of the dividend—and in terms of place value. They also used area diagrams and base-ten diagrams—among other representations—to support their reasoning.

In this lesson, students use partial quotients and a couple of ways to record them systematically—by writing a series of equations, and by using an algorithm that uses partial quotients.