The purpose of this activity is for students to consider two subtraction algorithms. In Algorithm A, students first look for any place-value units they need to decompose to get more units, and then they subtract from right to left. In Algorithm B, subtraction also occurs from right to left, but units are decomposed as the need arises. Students try each algorithm and consider potential advantages and disadvantages of each algorithm. 

In the Activity Synthesis, students carefully analyze and discuss the two algorithms, explaining the motivation behind them, how they are the same, and how they are different (MP3, MP6).

• Select students to share how they used each algorithm to find the value of .
• Keep algorithms from the first problem displayed.
• “Even though the algorithms may look the same after a few steps, they started out differently. Think about the advantages and disadvantages of using each algorithm.”
• 1 minute: quiet think time
• “Now discuss the advantages and disadvantages of each algorithm with your partner.”
• 1 minute: partner discussion
• Invite students to share advantages and disadvantages they come up with. (In Algorithm A, I look for decompositions first, so I probably won’t mix up the order of subtracting. In Algorithm A, I could subtract from left to right or from right to left. In Algorithm B, I can start subtracting right away. That means I don’t have to worry about decomposing until I know I need to do it.)

The purpose of this activity is for students to make sense of an algorithm in which a number with non-zero digits is subtracted from a number with a zero in the tens place. In the given problem, it is necessary to decompose a greater unit to have enough ones to subtract. There are no tens to decompose, but prompt students to consider whether subtraction is possible, and if so, how it could be done.

When students make sense of Elena’s reasoning, they construct viable arguments and critique the reasoning of others (MP3).

• Select students to share their responses.
• Display students’ work that shows a hundred decomposed into tens, and then a ten decomposed into ones (or show the example in Student Responses).
• “How does the work here show that we could have enough ones to subtract even though there is 0 in the tens place of 301?” (Crossing out the 3 and writing 2 in the hundreds place and writing 10 in the tens place shows a hundred decomposed to make tens. Crossing out the 10 and writing 9 in the tens place and writing 11 in the ones place shows a ten decomposed to make ones.)