Analyze Subtraction Algorithms

10 min

Narrative

The purpose of this Number Talk is to elicit the strategies and understandings students have for subtracting multi-digit numbers. These understandings help students develop fluency and will be helpful later in a subsequent lesson when students use strategies flexibly to subtract within 1,000.

Launch

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

Student Task

Find the value of each expression mentally.

  • 400−200400 - 200
  • 450−200450 - 200
  • 450−205450 - 205
  • 450−215450 - 215
Solution Steps (4)
  1. 1
    400-200
    →4 hundreds - 2 hundreds = 2 hundreds = 200
  2. 2
    450-200
    →Same as first plus 50: 200+50=250
  3. 3
    450-205
    →450-200=250, then 250-5=245
  4. 4
    450-215
    →Like third, subtract 10 more: 245-10=235

Sample Response

  • 200: I knew that 4 hundreds subtracted by 2 hundreds is 2 hundreds.
  • 250: This problem is just like the first one, but there are 5 tens left over. So 400−200400−200 is 200, plus 50 is 250.
  • 245: I subtracted the 2 hundreds first, and 450−200=250450−200=250. Then I subtracted the ones, and 250−5250−5 is 245.
  • 235: This is just like the third problem, but I had to subtract 10 more, and 245−10=135245−10=135.
Activity Synthesis (Teacher Notes)
  • “How did place value help as you subtracted these numbers?” (I subtracted hundreds from hundreds, tens from tens, and ones from ones. I was able to think about each place-value position separately, which helped me find the difference.)
  • Consider asking:
    • “Who can restate _____'s reasoning in a different way?”
    • “Did anyone have the same strategy but would explain it differently?”
    • “Did anyone approach the problem in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
Standards
Addressing
  • 3.NBT.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • 3.NBT.A.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

20 min

15 min