Place-Value Patterns

10 min

Narrative

The purpose of this Warm-up is for students to discuss the multiplicative relationships between the place values of the digits in two numbers. This will be useful when students write multiplication and division expressions to represent place-value relationships in a later activity. While students may notice and wonder many things about these numbers, the place-value relationships between the digits in the numbers and between the numbers themselves are the important discussion points.

Launch

  • Groups of 2
  • Display the image.
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record responses. 

Student Task

What do you notice? What do you wonder?

8,200

820                     

82

8.2

0.82

0.082

Sample Response

Students may notice:

  • The numbers have the same digits.
  • The digits are in different places.
  • The numbers are getting smaller.
  • The value of each number is 110\frac{1}{10} the value of the number above.

Students may wonder:

  • Is it a pattern?
  • What other numbers can we write with those digits?
  • What number comes next?
Activity Synthesis (Teacher Notes)
  • “How does the value of 8,200 compare with the value of 820?” (It’s 10 times as much.)
  • “How does the value of 0.82 compare with the value of 0.082? How do you know?” (It’s also 10 times as much since there are 10 thousandths in 1 hundredth.)
Standards
Addressing
  • 5.NBT.A·Understand the place value system.
  • 5.NBT.A·Understand the place value system.

20 min

15 min