Solve Problems Involving Large Numbers

10 min

Narrative

This True or False prompts students to look carefully at the sum and difference of the digits in each place and to remember to compose units when needed. It also prompts students to make use of structure (MP7). For example, the last expression would be cumbersome to calculate with the standard algorithm. Recognizing that 99,999 is 1 less than 100,000 would enable students to find the difference much more quickly. Likewise, students who notice that 300,000+99,999300,000 + 99,999 is only 1 away from 400,000 would know that 311,111 is far too high and cannot be the difference between 400,000 and 99,999.

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 strategy.
  • Repeat with each statement.

Student Task

Decide if each statement is true or false. Explain your reasoning.

  • 7,000+3,000=10,0007,000 + 3,000 = 10,000
  • 7,180+3,920=10,1007,180 + 3,920 = 10,100
  • 423,450−42,345=105423,450 - 42,345 = 105
  • 400,000−99,999=311,111400,000 - 99,999 = 311,111

Sample Response

  • True:  7,000+3,000=10,0007,000+ 3,000 = 10,000
  • False: 7,000+3,000=10,0007,000+ 3,000 = 10,000 so 7,180+3,9207,180+ 3,920 has to be more than 10,100.
  • False: the difference between 420,000 and 42,000 is more than 300,000 so the difference between 432,450 and 42,345 cannot be 105.
  • False: 99,999 is just 1 away from 100,000, so the difference between 400,000 and 99,999 should be just 1 over 300,000, not 11,111 over 300,000.
Activity Synthesis (Teacher Notes)
  • “How can you explain your answer without finding the value of both sides?”
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

20 min