Subtraction Algorithms (Part 1)

10 min

Narrative

The purpose of this Number Talk is to elicit the strategies students have for subtracting within 1,000. These understandings help students develop fluency and will be helpful later when students choose between using an algorithm or another strategy to subtract.

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.

  • 100−98100 - 98
  • 101−99101 - 99
  • 200−98200 - 98
  • 204−98204 - 98
Solution Steps (4)
  1. 1
    100-98: Count up from 98
    →98→99→100, counted 2 → answer is 2
  2. 2
    101-99: Notice pattern
    →Both numbers increased by 1, difference still 2
  3. 3
    200-98: Count up in chunks
    →98→100 is 2, 100→200 is 100, total is 102
  4. 4
    204-98: Build on previous
    →Like 200-98=102, plus 4 more → 106

Sample Response

  • 2: I counted up from 98 to 100 and called out only 2 numbers, so the answer is 2.
  • 2: I counted up from 99 to 101 and called out only 2 numbers, so the answer is 2. I saw that both numbers in the subtraction expression just went up by 1 from the first expression, but the difference is still 2.
  • 102: This is like the first expression, but I counted up 2 to get to 100, and it's up 100 to get to 200, so the difference is 102.
  • 106: I counted up 2 to get to 100, then 100 to get to 200, and 4 more to get to 204. Altogether, I counted up 106. It’s like the third expression, but the 200 went up 4 more, so the difference would be 4 more, so it’s 106.
Activity Synthesis (Teacher Notes)
  • “How did the first couple of expressions help you find the values of later expressions?” (When I noticed that the numbers had adjusted a little, it was easy to adjust the difference the same way. Sometimes it looked like a new problem, but both of the numbers had gone up the same amount so the difference was the same.)
  • 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.

15 min

20 min