The purpose of this 5 Practices activity is to elicit students’ existing approaches for finding the value of quotients with greater numbers and encourage them to think about ways to multiply and divide in smaller parts. Students should be encouraged to use whatever approach makes sense to them. 

Monitor for and select students with the following approaches to share in the Activity Synthesis:

• Make groups of 4 with objects, drawings, arrays, or base-ten blocks. Add groups of 4 until they reach 48, and count to see how many groups they make.
• Multiply up starting with .
• Decompose the dividend into tens and ones and divide each part (using drawings or known facts).

The approaches are sequenced from more concrete to more abstract to help all students make sense of ways to find the quotient by multiplying or dividing in parts, especially by using what they know about place value. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently. If appropriate, discuss connections between the approaches as they are shared, rather than after all selected students have shared. It is not essential that all the listed approaches are discussed, as students will consider these ideas in upcoming lessons. The main goal here is to elicit what students currently understand, and to make connections to thinking about multiplying and dividing in parts if it comes up.

When students make sense of the contextual division problem, they reason abstractly and quantitatively (MP2). Students who use the relationship between multiplication and division make use of structure (MP7).

• Invite previously selected students to share in the given order. Record or display their work for all to see.
• As each approach is presented, invite the class to ask questions.
• Keep all the approaches displayed.
• Connect students’ approaches by asking:
  • “How are these ways of solving the problem alike?” (All the approaches used  to help break the problem into smaller parts. The approaches with division and multiplication equations both had .)
  • “How are they different?” (In some, students drew a representation. In others, students wrote multiplication or division expressions or equations.)
• If some approaches show breaking the problem into smaller parts, connect students’ approaches to the learning goal by asking:
  • “How did _____ think about breaking the problem into smaller parts? Why was that approach helpful for this problem?” (They thought about multiplying by 10 first because they know , and that's close to the total. It helped because they didn't have to add or skip-count by 4 as many times or draw as many things.) 

The purpose of this activity is for students to consider their strategies as they solve two other division problems involving equal groups with greater numbers. The divisor in the first problem is a low one-digit number. Students can see from the given situation that it is the number of groups. In the second problem, the divisor is a teen number, and the context suggests that it is the size of one group. Students are likely to adjust their strategy based on these observations. Focus the discussion on how students may have reasoned differently given a greater divisor or given what they understand about the situation.

• “What is the problem about?”
• “How could you represent the problem?”

• Invite students to share their responses. Display or record their reasoning.
• Poll the class on whether they used a different strategy for solving the second problem than they used for the first.
• Ask those who used a different strategy. “Why did you change your strategy?” (In the first problem, the 3 represents 3 groups. In the second problem, the 12 is how many in each group. In the first, the number used to divide is smaller. In the second, the number is larger.)