The purpose of this lesson is for students to apply their understanding of division, multiplication, factors, and multiples to solve problems involving remainders.

In this lesson, students encounter problems about finding unknown factors and relate such problems to division. The context in this lesson allows students to apply their understanding of factors and multiples developed in an earlier unit. The dividends in this lesson are 3-digit numbers beyond 100.

Students continue to interpret division in terms of finding the number of groups (“If we write multiples of 5, how many numbers will we need to write to get to 105?”) and the size of a group (“What number are we finding multiples of if we get to 112 after writing 7 numbers?”). Students may solve the problems by multiplying in parts (finding partial products) or by dividing in parts (finding partial quotients). Through repeated reasoning, they notice that it helps to decompose a dividend into familiar multiples (MP2).

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, .