The Commutative Property

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting within 100. It also provides an opportunity to observe student strategies as they work toward becoming fluent in addition within 1,000.

When students use strategies based on place value to subtract, they look for and make use of structure (MP7).

Launch

  • Display the first 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.

  • 70−1070-10
  • 68−1068-10
  • 70−1270-12
  • 68−1268-12
Solution Steps (4)
  1. 1
    Find 70-10 mentally
    →7 tens - 1 ten = 6 tens = 60
  2. 2
    Find 68-10 mentally
    →Like 70-10 but starting 2 less: 60-2 = 58
  3. 3
    Find 70-12 mentally
    →70-10-2 = 60-2 = 58
  4. 4
    Find 68-12 mentally
    →68-10-2 = 58-2 = 56 (or 6 tens - 1 ten and 8 ones - 2 ones = 56)

Sample Response

  • 60: Seven tens minus 1 ten would be 6 tens, which is 60.
  • 58: It’s just like the first one, but the number you’re subtracting from is 2 less, so the difference would be 2 less.
  • 58: This is like the first problem, but you’re subtracting 2 more from 70, so instead of 60, it would be 58.
  • 56: It’s like the first problem, but you’re starting with 2 less and taking 2 more, so it would be 4 less than the first answer. I subtracted tens from tens and ones from ones and ended up with 5 tens and 6 ones.
Activity Synthesis (Teacher Notes)
  • “How was place value helpful as you found the difference in these problems?” (I subtracted the tens first then adjusted my answer each time. I subtracted tens from tens and ones from ones.)
  • Consider asking:
    • “Who can restate _____'s reasoning in a different way?”
    • “Did anyone use 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
Building On
  • 2.NBT.5·Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • 2.NBT.B.5·Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Building Toward
  • 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