Compare to 1

10 min

Narrative

The purpose of this What Do You Know about _____? is for students to share what they know about, and how they can represent, the product 1514×2330\frac{15}{14}\times\frac{23}{30}. The numbers were intentionally chosen to make finding the exact value of the product challenging.

Launch

  • Display the expression.
  • “What do you know about 1514×2330\frac{15}{14}\times\frac{23}{30}?”
  • 1 minute: quiet think time
Teacher Instructions
  • Record responses.
  • “How could we find the value of the product 1514×2330\frac{15}{14}\times\frac{23}{30}?” (Find the product of the numerators and the product of the denominators.)

Student Task

What do you know about 1514×2330\frac{15}{14}\times\frac{23}{30}?

Sample Response

Sample responses:

  • It would be hard to multiply those fractions.
  • 1514\frac{15}{14} is a little bit greater than 1.
  • It represents a number that is a little bit greater than 2330\frac{23}{30}.
Activity Synthesis (Teacher Notes)
  • “Is 1514×2330\frac{15}{14}\times\frac{23}{30} less than, equal to, or greater than 2330\frac{23}{30}? Why?” (It is greater, since 1514\frac{15}{14} is greater than 1.)
Standards
Building Toward
  • 5.NF.5.b·Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
  • 5.NF.B.5.b·Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence <span class="math">\(a/b = (n \times a)/(n \times b)\)</span> to the effect of multiplying <span class="math">\(a/b\)</span> by <span class="math">\(1\)</span>.

15 min

20 min