Another Look at the Standard Algorithm

10 min

Narrative

This Number Talk encourages students to think about the base-ten structure of whole numbers and the properties of operations to mentally solve subtraction problems. The reasoning elicited here will be helpful later in the lesson when students find differences of multi-digit numbers.

Launch

  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
Teacher Instructions
  • 1 minute: quiet think time
  • Record answers and strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each difference mentally.

  • 87−2487 - 24
  • 387−124387 - 124
  • 6,387−1296,387 - 129
  • 6,387−4,3296,387 - 4,329

Sample Response

  • 63: 80−20=6080 - 20 = 60, 7−4=37 - 4 = 3, and 60+3=6360 + 3 = 63.
  • 263: 300−100=200300 - 100 = 200, and we already know that 87−24=6387 - 24 = 63.
  • 6,258: We know that 387−124=263387 - 124 = 263. 129 is 5 more than 124, so 387−129387 - 129 would be 5 less than 263, which is 258.
  • 2,058: 4,329 is 4,200 more than 129, so the difference is 4,200 less than the previous difference. 6,258−4,200=2,0586,258 - 4,200 = 2,058
Activity Synthesis (Teacher Notes)
  • “How is each expression related to the expression before it?”
  • “How might the first expression help us find the value of the last expression?” (Knowing 87−2487 - 24 can help us find 87−2987 - 29. The latter is 5 less than the former. Then we can just find 6,300−4,3006,300 - 4,300.)
Standards
Addressing
  • 4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.
  • 4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.

15 min

20 min