Students have divided four-digit divisors by one-digit dividends using place value understanding and the properties of operations. In this lesson, students work with division situations and expressions that don’t have whole-number quotients. Students connect remainders to the idea of “leftovers” when dividing. They conceptualize remainders by determining that an additional equal group cannot be made with the remaining part of the dividend, or by determining that the dividend is not a multiple of the divisor.

In these materials, division that results in a whole number with a remainder—for example, —is not expressed with an expression such as “20 R 5.” Instead, students will relate this result to a multiplication equation, .

What evidence of multiplication fluency can be collected from student thinking in this lesson? How might you use this evidence to support development of fluency for students who need support?