Does It Make Sense?

10 min

Narrative

The purpose of this True or False? is to elicit the strategies students have for estimating. Students' reasoning here helps to deepen their understanding of how rounding can be used to estimate. It also will be helpful later when students determine a reasonable estimate.

Launch

  • Display one statement.
  • “Give me a signal when you know whether the statement is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record answers and strategies.
  • Repeat with each statement.

Student Task

Decide if each statement is true or false. Be prepared to explain your reasoning.

  • 132+115>200132 + 115 > 200
  • 228+195>400228 + 195 > 400
  • 217+151>400217 + 151 > 400
Solution Steps (3)
  1. 1
    Estimate 132+115 vs 200
    →100+100=200, still have 32+15 left, so TRUE (>200)
  2. 2
    Estimate 228+195 vs 400
    →200+100=300, then 28+95>100, so total >400, TRUE
  3. 3
    Estimate 217+151 vs 400
    →200+100=300, then 17+51≈70, total≈370<400, FALSE

Sample Response

  • True: 100+100100 + 100 is 200, but we still have to add 32 and 15, so it would be more than 200.
  • True: 200+100200 + 100 is 300. When we add 28 and 95, it’s going to be more than 100, so it would be more than 400.
  • False: 200+100200 + 100 is 300. When we add 51 and 17, it’s only about 70, so it wouldn’t go over 400.
Activity Synthesis (Teacher Notes)
  • “How can you explain your answer without finding the value of each side?”
  • Consider asking:
    • “Who can restate ___ 's reasoning in a different way?”
    • “Does anyone want to add on to _____ ’s reasoning?”
    • “Can we make any generalizations based on the statements?”
  • “For which problems was rounding helpful? For which problems did you not need to round?” (For the first problem, I didn’t need to round after I knew that the number was over 200. For the last problem, I rounded to add 17 and 51 to see if it would go over 100.)
Standards
Building Toward
  • 3.NBT.1·Use place value understanding to round whole numbers to the nearest 10 or 100.
  • 3.NBT.A.1·Use place value understanding to round whole numbers to the nearest 10 or 100.

15 min

20 min