In this activity, students subtract multi-digit numbers. They do so in two ways: by using the standard algorithm for subtraction and by finding unknown addends. Students find the value of a string of related differences that encourage them to look for and express regularity in repeated reasoning (MP8).

Students may notice that when a subtraction problem requires them to decompose multiple units to subtract in one place when using the standard algorithm—as is the case when the minuend has multiple zeros and the subtrahend has mostly non-zero digits—the standard algorithm for subtraction may not be the most practical. Students use their work in the lesson activity to discuss alternatives to the standard algorithm in these cases, including methods based on the relationship between addition and subtraction and on reasoning about sums and differences that are easier to calculate (MP7). 

• Select previously identified students to share the strategies they used to find the value of ​ ​.
• Ask students who didn’t use the standard algorithm to subtract why they chose another way.
• “How was finding the values of the differences in the first set of equations like finding the unknown addends in the second set of equations?” (Both had totals that kept adding a new place. The two-digit number in each did not have any zeros, but the total number in each had many zeros. There was a pattern in each. You could think about adding on and adding to a number like 100 first for each set.)

Previously, students used the standard algorithm for subtraction to find the differences involving minuends with multiple zeros. They also used the standard algorithm of addition to find an unknown addend that gives a sum with multiple zeros for its digits. In this activity, students make connections between these two ways of reasoning about differences. They also analyze another way to find differences between multi-digit numbers.

• See Lesson Synthesis.