Fourth Grade · Math · week 5

Subtraction with regrouping chains

Subtract multi-digit numbers using the standard algorithm, regrouping across one or more zero columns.

Subtraction sometimes needs to regroup (borrow) from the next column over. That is easy when the next column has something to lend. But when the next column is a zero, it has nothing to give, so the borrow has to travel further left, column by column, until it finds a digit that can lend. That traveling borrow is a regrouping chain.

Once a column further left lends a 1, it turns into 10 for the column right next to it, which can then pass a 1 along, and so on, all the way back to the column that first needed it.

📋 For the teacher
Teach it (10–15 min):
  • When the column above cannot lend (it is a 0), keep moving one column further left until you find a digit that can.
  • Cross out and rewrite each digit as it changes during the chain so nothing gets lost along the way.
  • Check every subtraction answer by adding it back to the number that was subtracted; it should rebuild the original number.
  • Go slowly through a chain the first several times; speed comes later, accuracy comes first.
Talk about it:
  • What do you do when the column you want to borrow from is a zero?
  • How can addition check a subtraction answer?
  • Why does 50,204 minus 27,568 need more than one regrouping step?

Mastery looks like: They subtract multi-digit numbers accurately, correctly chaining the regrouping through one or more zero columns.

Common stumbles: Stopping the chain at the first zero instead of continuing left; forgetting to reduce the lending column by 1 after it lends; subtracting the smaller digit from the larger one regardless of position instead of regrouping.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
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