Division Situation Drawings

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 1,000, particularly around adjusting numbers in a sum to make them easier to add. These understandings help students develop fluency for adding within 1,000.

When students notice that the same value is being removed from one addend and added to the other and the value of the sum does not change, they look for and make use of structure (MP7).

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 strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 120+120120 + 120
  • 121+119121 + 119
  • 125+115125 + 115
  • 129+111129 + 111
Solution Steps (4)
  1. 1
    Calculate 120 + 120
    →240 (double 120)
  2. 2
    Notice pattern in 121 + 119
    →(120+1) + (120-1) = 240, same as 120+120
  3. 3
    Apply pattern to 125 + 115
    →(120+5) + (120-5) = 240
  4. 4
    Apply pattern to 129 + 111
    →(120+9) + (120-9) = 240

Sample Response

  • 240: I just doubled 120.
  • 240: I noticed that 121 is 1 more than 120 and 119 is one less than 120, so the value is the same as for 120+120120 +120.
  • 240: I took 5 from 125 and added it to 115. Then it’s 120+120120 + 120 again.
  • 240: I took 9 from 129 and added it to 111. Then it’s 120+120120 + 120 again.
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 you add an amount to one addend, but subtract the same amount from the other addend. Addition and subtraction are opposites, so the value will stay the same.)
  • As needed, record student thinking with expressions or equations. Consider testing any student generalizations with smaller addends to make the thinking accessible to all students.
  • 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>

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