Interpret Diagrams

10 min

Narrative

The purpose of this Estimation Exploration is to estimate the product of a fraction and a large whole number. Students know how to find the exact answer, but it would require many calculations. Making an estimate will help develop a sense that because 53\frac{5}{3} is greater than 1, the product has to be greater than the other factor. Students can make a better estimate by replacing the whole number 9,625 with a friendlier number that they can find 13\frac{1}{3} of mentally. Throughout this lesson, students will continue to compare the size of a product to the size of one of its factors. 

Launch

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

Student Task

53×9,625\frac{5}{3} \times 9,625

Record an estimate that is:

too low about right too high

Sample Response

Sample responses:

  • Too low: 3,000 to 12,000
  • About right: 12,000 to 18,000
  • Too high: 18,000 or greater
Activity Synthesis (Teacher Notes)
  • “How do we know the product is going to be greater than 9,625?” (53\frac{5}{3} is more than 1, so the product is greater than the other factor, 9,625.)
  • “How do we know the product is going to be greater than 15,000?” (13×9,000=3,000\frac{1}{3}\times 9,000=3,000 so 53×9,000=15,000\frac{5}{3}\times 9,000=15,000, and we are trying to figure out 53\frac{5}{3} of greater than 9,000.) 
Standards
Addressing
  • 5.NF.5.a·Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
  • 5.NF.B.5.a·Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

20 min

15 min