In this lesson, students continue to reason about place value and the base-ten structure in division. Instead of using base-ten representations, they use partial quotients.

Students begin by recalling that division can be done in parts, by decomposing the dividend. For instance, we can calculate by calculating  , , and . These partial quotients can be recorded as a series of equations, as students may have seen in earlier grades.

Next, students analyze a method of recording division that also involves partial quotients but is arranged vertically. Students make sense of the steps for subtracting parts of the dividend below the original number and the adding of partial quotients stacked above it. The vertical calculation foreshadows the long division algorithm.

Finally, students use this method to divide multi-digit numbers. While the dividends, divisors, and quotients are whole numbers, the challenges here are in using an unfamiliar algorithm and in looking for efficient ways to decompose each dividend. Students are likely to recognize that it helps to decompose the dividend by place value, as was the case when dividing using base-ten blocks or diagrams.