Same Digit, Different Value

10 min

Narrative

The purpose of this True or False is for students to consider the value of the same digit in different places. This reasoning will also be helpful later in this lesson when students describe the relationship between different places in multi-digit numbers.

In this activity, students have an opportunity to look for and make use of structure (MP7) as they use commutative and associative properties of addition to compose numbers and determine equivalent sums.

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.

  • 4,000+600+70,000=70,4604,000 + 600 + 70,000 = 70,460
  • 900,000+20,000+3,000=920,000+3,000900,000 + 20,000 + 3,000 = 920,000 + 3,000
  • 80,000+800+8,000=800,000+80+880,000 + 800 + 8,000 = 800,000 + 80 + 8

Sample Response

  • False: the 4 in the number represents 400, but the equation shows 4,000.
  • True: the 900,000+20,000900,000 + 20,000 is equivalent to 920,000.
  • False: each number has the digit 8, but the values of all the 8s are different.
Activity Synthesis (Teacher Notes)

Focus question:

  • “How can you explain your answer without finding the value of both sides?”
  • “We can write numbers in different forms.”
  • “What is used to represent the numbers in this True or False?” (expanded form)
Standards
Addressing
  • 4.NBT.2·Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
  • 4.NBT.A.2·Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using <span class="math">\(&gt;\)</span>, =, and <span class="math">\(&lt;\)</span> symbols to record the results of comparisons.

20 min

15 min