Divide Whole Numbers by Decimals

10 min

Narrative

The purpose of this Warm-up is for students to analyze statements about quotients of whole numbers by 0.1 or 0.01. Students compare the value of quotients by 0.1 and 0.01. They can analyze the statements either by calculating the value of the expressions or reasoning about the relationship between 0.1 and 0.01, namely that there are ten hundredths in a tenth. 

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.

  • 6÷0.01=606 \div 0.01 = 60
  • 6÷0.1< 6÷0.016 \div 0.1 < 6 \div 0.01
  • 6÷0.01 =60÷0.16 \div 0.01  = 60 \div 0.1

Sample Response

  • False: There are six hundred 0.01s in 6.
  • True: There are fewer tenths than hundredths in 6.
  • True: There are 600 tenths in 60 and 600 hundredths in 6.
Activity Synthesis (Teacher Notes)
  • Display the second statement.
  • “How can you prove this statement is true without finding the value of the expressions on both sides of the equal sign?” (I can think about the size of the quotients. They both show 6 being divided into groups, but the size of the groups is bigger in 6÷0.16\div0.1 so there will be fewer groups.)

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.

15 min

20 min