In previous lessons, students used the area of rectangles to develop an understanding of factors and multiples. Students also worked on their fluency with multiplication facts. In this lesson, they apply these understandings to solve problems.

In some problems, the solutions are whole-number results of multiplying or dividing. For example: If eggs come in packages of 12, how many eggs are in 5 packages? (60 eggs). But in other problems, students need to make sense of products or quotients in terms of the situation. For instance: How many packages should we buy if we need exactly 50 eggs? Students reason that it is impossible to get exactly 50 eggs, since there are 48 eggs in 4 packages and 60 eggs in 5 packages.

As they examine the numbers in these situations, including interpreting remainders in division problems, students make sense of problems and persevere in solving them (MP1) and reason quantitatively and abstractly (MP2).

Math Community
Before the lesson, explain to students that norms are expectations that help everyone in the room feel safe, comfortable, and productive doing math together. Offer an example, such as: “It may help us share our ideas as a whole class if we have the norm ‘Listen as others share their ideas.’” Tell students to think about norms that help everyone do math as they work today, and that you will record these norms during the Lesson Synthesis.

What strategies do students use most often to decide if a number is a multiple of a given whole number?