• Invite students to share different partial products for the first problem.
• Keep student work displayed or display the two solutions in Student Responses.
• “How are the solutions the same? How are they different?” (They both subtract some groups of 100, 10, and 1. They both show that the value of the quotient is 521. The first strategy takes out all the hundreds at once while the second strategy takes out 400 and then 100 more.)
• “Why are multiples of 100 good choices to subtract when you divide greater numbers?” (I can calculate them quickly and they make the number I’m dividing get smaller quickly.)

The purpose of this activity is for students to practice using partial quotients. Students compare their strategy with the strategies of their classmates. They reason about the similarities and differences, using their understanding of place value and balancing the complexity of calculations versus subtracting a large amount quickly.

• Ask selected students who used different partial quotients to share, or display or write work as shown here for all to see.
• Display:

  

  

• “How are the calculations the same? How are they different?” (They both show that the quotient is 71. One of them finishes faster because it starts by taking out 70 groups of 32. The other one takes longer because it subtracts smaller groups of 32.)
• “Which calculation do you prefer?” (I prefer the one that takes out larger groups of 32 because it is faster. I prefer the one that takes more steps because each calculation is easier to do in my head and I know I am not trying to subtract too much.)