Make Sense of Decimal Subtraction

10 min

Narrative

The purpose of this True or False is for students to apply their understanding of place value to subtraction equations with decimals. The names of the decimals will likely suggest a strategy using whole number subtraction. For example 0.61−0.02=0.590.61 - 0.02 = 0.59 can be read as “61 hundredths minus 2 hundredths equals 59 hundredths,” which students will recognize is true. Alternatively, they can think about place value. For example, 0.5 is 5 tenths or 50 hundredths and 50 hundredths minus 1 hundredth is 49 hundredths.

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. Be prepared to explain your reasoning.

  • 0.5−0.01=0.40.5 - 0.01 = 0.4
  • 0.61−0.02=0.590.61 - 0.02 = 0.59
  • 1−0.07=0.931 - 0.07 = 0.93

Sample Response

Sample responses:

  • False: 0.5 is 50 hundredths so the difference is 0.49 not 0.4.
  • True: If I take 2 hundredths from 61 hundredths, that's 59 hundredths.
  • True: 1 is 100 hundredths and if I subtract 7 hundredths, that leaves 93 hundredths.

Synthesis

  • Display the first equation.
  • “How did you use what you know about place value to decide if the equation is true?” (I know 5 tenths is 50 hundredths and if I subtract 1 hundredth that’s 49 hundredths. So, it’s false.)
Standards
Addressing
  • 5.NBT.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
  • 5.NBT.B.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

20 min

15 min