Multi-step Conversion Problems: Metric Lengths

10 min

Narrative

The purpose of this True or False? is for students to demonstrate the strategies and understandings they have for multiplying and dividing by powers of 10. They will use these operations when they convert measurements between different metric length units.

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.

  • 5,423×10=50,4235,423 \times 10 = 50,423
  • 5,423÷10=542.35,423 \div 10 = 542.3
  • 5,423÷100=54.235,423 \div 100 = 54.23

Sample Response

  • False: All of the digits need to shift one place to the left, so it should be 54,230.
  • True: Each digit in 542.3 has 110\frac{1}{10} the value of the corresponding digit in 5,423.
  • True: Each digit in 54.23 has 1100\frac{1}{100} the value of the corresponding digit in 5,423.

Synthesis

  • “How did you decide if the equation 5,423÷100=54.235,423 \div 100 = 54.23 is true?” (It's like dividing by 10 twice. 5,423÷10=542.35,423 \div 10 = 542.3 and 542.3÷10=54.23542.3 \div 10 = 54.23. Each number has digits 5, 4, 2, 3 in the same order. The values of the digits' places in 54.23 are 1100\frac{1}{100} the values of the corresponding digits' places in 5,423.)
Standards
Addressing
  • 5.NBT.1·Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
  • 5.NBT.A.1·Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

15 min

20 min