Write Division Expressions

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting within 1,000, particularly with expressions that have the same difference. These understandings help students develop fluency for subtracting within 1,000. Consider drawing number lines as students share their strategies to emphasize that the difference of the two numbers in each expression is not changing.

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.

  • 225−100225 - 100
  • 227−102227 - 102
  • 230−105230 - 105
  • 220−95220 - 95
Solution Steps (4)
  1. 1
    Calculate 225-100
    →125 (count up: 100+100+25=225)
  2. 2
    Calculate 227-102
    →125 (both +2 from first, difference unchanged)
  3. 3
    Calculate 230-105
    →125 (both +5 from first, difference unchanged)
  4. 4
    Calculate 220-95
    →125 (both -5 from first, difference unchanged)

Sample Response

  • 125: The difference between 100 and 200 is 100 and then it’s 25 more to 225.
  • 125: I noticed that 2 was added to both numbers in the first problem. So now it’s 98 to 200, but it’s 27 more to get to 227. 98+27=12598 + 27 = 125.
  • 125: 5 is added to each number from the first problem, so the difference between the numbers is still 125.
  • 125: This time 5 was subtracted from both numbers. I added 5 to 95 to get to 100 and then it’s 120 more to 220, so the value is still 125.
Activity Synthesis (Teacher Notes)
  • “What pattern do you see as you look at the expressions and their values? Why is that happening?” (The values are all the same. This happens because when you add or subtract the same amount to both numbers in a subtraction expression, the difference does not change.)
  • As needed, record student thinking with a number line. Consider using smaller numbers to help test any generalizations students make about the pattern.
  • Consider asking:
    • “Did anyone notice a different pattern”?
    • “Did anyone notice the same pattern but would explain it differently?”
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.
  • 3.OA.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <em>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</em>
  • 3.OA.D.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <span>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</span>

15 min

20 min