The purpose of this activity is for students to transition from reasoning about division concretely or visually (using base-ten diagrams) to doing so more abstractly (by writing equations). This activity also reinforces the connections between multiplication and division.

Students make sense of three different strategies for dividing 78 by 3 and attend to the connections between the visual and numerical representations of the same quotient. As students do so, they practice reasoning quantitatively and abstractly (MP2).

During the Activity Synthesis, discuss how place-value units play a role in all three strategies.

• Invite students to share how Lin, Priya, and Tyler’s work are alike and how they are different.
• Select previously identified students to share additional connections that they noticed.
• “Why does it make sense that Priya and Tyler wrote multiplication equations to find the value of a quotient?” (Multiplication and division can represent the same equal-groups situation. To divide 78 by 3 is to find how many are in each of 3 groups or how many groups of 3 there are. We can multiply up to 78 to find the answer.)
• Consider asking: “What new ideas about dividing numbers did you learn and would like to try? Talk to a new partner about why you’d like to try them.”

The purpose of this activity is for students to practice finding the value of division expressions using any strategy that makes sense to them. They may divide the dividend into equal groups or use the divisor to multiply up to the given dividend. They may choose to represent the division or multiplication with base-ten blocks or by drawing diagrams.

During the Activity Synthesis, students share and discuss strategies that rely on place value, properties of operations, and the relationship between multiplication and division (MP7).

• Have previously selected students share their responses. Display or record the strategies and representations students use.
• For each problem, consider polling the class on the strategy they used.

The purpose of this optional activity is for students to practice evaluating division expressions in order to make comparisons. Compare is a center that focuses on the procedural skills needed to solve single- and multi-step word problems. In this stage, students will use division to evaluate and compare quotients within 100.

• Display: and .
• “Suppose these are the two cards you draw. How would you decide which expression has the greatest value?”