Fraction Comparison Problems

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding and subtracting multi-digit numbers. These understandings help students develop fluency and will be helpful in later units as students add and subtract multi-digit numbers fluently using the standard algorithm.

When students make adjustments and create multiples of 10 for mental addition, they are looking for and making use of the base-ten structure of numbers (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.

  • 119+119119 + 119
  • 139+139139 + 139
  • 159+159159 + 159
  • 199+199199 + 199

Sample Response

  • 238: 119+1=120119 + 1= 120, and 120+120=240120 + 120 =240. I added an extra 1 to each addend, so 240−2=238240 - 2 = 238.
  • 278: 139+1=140139 + 1= 140, and 140+140=280140 + 140 =280. I added an extra 1 to each addend, so 280−2=278280 - 2 = 278.
  • 318: 150+150=300150 +150 =300,  9+9=189 + 9 = 18, and 300+18=318300 + 18 =318.
  • 398: 200+200=400200 + 200 = 400. I added 1 to each addend, so 400−2=398400 - 2 = 398.
Activity Synthesis (Teacher Notes)

“How did you use multiples of 10, such as 20, 40, and 60, to help you add these numbers mentally?” (I changed the addends to multiples of 10 by adding 1 more to each addend, and then subtracted the extra 2 from the final sum.)

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 expression in a different way?”
  • “Does anyone want to add on to _____’s strategy?”
Standards
Building Toward
  • 4.NBT.4·Fluently add and subtract multi-digit whole numbers using the standard algorithm.
  • 4.NBT.B.4·Fluently add and subtract multi-digit whole numbers using the standard algorithm.

15 min

10 min