Divide Decimals by Whole Numbers

10 min

Narrative

The purpose of this Estimation Exploration is for students to consider quotients of a decimal to the hundredth by a whole number. Students can draw or visualize a diagram or they may reason about place value in order to make a meaningful estimate. 

Launch

  • Groups of 2
  • Display the expression.
  • “What is an estimate that’s too high? Too low? About right?”
Teacher Instructions
  • 1 minute: quiet think time
  • 1 minute: partner discussion
  • Record responses.

Student Task

What is the value of 0.42÷50.42 \div 5?

Record an estimate that is:

too low about right too high

Sample Response

Sample responses:

  • too low: range 0.07 to 0.08
  • about right: range 0.08 to 0.09
  • too high: range 0.09 to 0.1
Activity Synthesis (Teacher Notes)
  • “How do you know 0.42÷50.42 \div 5 is more than 8 hundredths?” (I know 5 groups of 8 hundredths is 40 hundredths. That’s 0.4 which is 2 hundredths less than 0.42.)
  • “Why is 8 hundredths a good estimate for the value of 0.42÷50.42 \div 5?” (40 hundredths is really close to 42 hundredths.)
Standards
Building Toward
  • 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