The purpose of this activity is for students to identify and correct common errors in using a partial-quotients algorithm. One error involves subtraction and two involve multiplication. Students may choose to correct the errors and continue the work that is there, or they may choose to find the quotient in a different way that makes sense to them. When students determine the errors and explain their reasoning, they critique and construct viable arguments (MP3).

• "How did you decide what the error was in each calculation?"
• Prompt them to evaluate the division expressions, and ask: "How is your solution the same as and different from the one in the activity?"

• Invite students to share where they notice errors and to describe the errors.
• “What can you do to make sure you are not making the same errors in your calculation?” (Before I calculate, I can estimate. While I work on the problem, I can double check when I subtract or multiply. After I calculate, I can multiply the quotient by the divisor and make sure I get the dividend.)
• Encourage students to consider what they can do before, during, and after they calculate.

The purpose of this activity is for students to divide three- and four-digit dividends by two-digit divisors. As the size of the dividend increases, students have an option to subtract multiples of 100 of the divisor. In order to calculate efficiently, this becomes essential for a quotient such as , as it will take many partial quotients that are multiples of 10 to reach the full quotient. Using a partial-quotients algorithm for greater numbers also requires fluency with subtraction.

• Ask a few students to share their work.
• “How was your work similar to or different from your partner’s?” (We both tried to subtract multiples of 10 or 100, and then when the remaining amount was small we subtracted smaller multiples. My partner used fewer steps.)
• "What did you notice in your partner’s work that shows they understand how to use a partial-quotients algorithm?” (My partner picked multiples that could mostly be calculated in their head and worked on subtracting the partial quotients.)