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 101 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?
Synthesis
“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.)