The purpose of this activity is for students to explain the steps for using a partial-quotients algorithm to divide a three-digit number by a two-digit number. Because the size of the dividends is greater and the numbers are less friendly, the problems encourage students to reflect on which partial quotients will be the most efficient for making the calculations. Monitor for students who begin with partial quotients that are multiples of 10. This strategy helps make the calculations simpler, and students have seen and used multiples of 10 for these calculations throughout the last several lessons.

When students share and compare their methods with their partner and with other groups, they explain and improve their calculations (MP3).

• Ask selected students who used different strategies to divide.
• “What questions do you have about partial-quotients algorithms?”
• Consider displaying sample responses from Student Responses for the quotient .
  • “How are the strategies the same? How are they different?” (All subtract 1 group of 19 at the end. Before that, all subtract multiples of 10.)
  • “How is the 30 in Solution C represented in the partial quotients in Solutions A and B?” (Solution A uses 20 and 10 and Solution B uses 10, 10, and 10 more. These add up to 30.)

The purpose of this activity is for students to practice using a partial-quotients algorithm to divide multi-digit numbers by two-digit divisors. Before finding the quotient, students estimate the value of the quotient, which helps students both decide which partial quotients to use and evaluate the reasonableness of their solution (MP8). For example, if students estimate that the value of  is a little more than 20, that means that a good choice for the first partial quotient is 20. Whenever possible, ask students to explain the steps they are taking.

To add movement to the activity, after students have solved each problem, they can partner with other students who used different partial quotients or got a different solution. This gives students the opportunity to explain their reasoning to one another and make adjustments to their work, as needed.

• Ask 2–3 students to share their work showing different partial quotients for the same problem.
• “How can you make sure that the whole-number quotient you got at the end is reasonable?” (It should be close to my estimate. I can multiply the quotient and divisor and that should give me the dividend.)
• If students share with other partners, ask: “How did explaining your work to others help you today?” or “What did someone say today that helped you in your understanding of division?” (I learned that it’s okay to take more steps because I was comfortable with the multiples I used.)