How Do You Compare Fractions?

10 min

Narrative

This Number Talk encourages students to use what they know about the meaning of fractions and about properties of operations to mentally relate fractions that are equivalent to whole numbers. 

Launch

  • Display one fraction.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategies. 
  • Keep fractions and work displayed. 
  • Repeat with each fraction.

Student Task

Find the whole number equivalent to each fraction.

  • 161\frac{16}{1}
  • 162\frac{16}{2}
  • 164\frac{16}{4}
  • 204\frac{20}{4}
Solution Steps (4)
  1. 1
    Find 16/1
    →16 parts of size 1 = 16
  2. 2
    Find 16/2
    →16 halves → 2 halves make 1 whole → 16 ÷ 2 = 8
  3. 3
    Find 16/4
    →16 fourths → 4 fourths make 1 whole → 16 ÷ 4 = 4
  4. 4
    Find 20/4 using 16/4
    →16/4 = 4, so 20/4 = 4 + 1 = 5 (add 4 more fourths)

Sample Response

  • 16: It’s 16 parts of 1, which is 16.
  • 8: I know 2 halves make 1, so I count by 2 halves, like 2 halves, 4 halves, and so on, to get to 16 halves. I counted by 2 halves 8 times.
  • 4: There are 4 fourths in 1, so there are 8 fourths in 2, and 16 fourths in 4.
  • 5: If 164\frac{16}{4} is 4, then 4 more fourths makes 5.
Activity Synthesis (Teacher Notes)
  • “How did the earlier fractions help you find the whole number for the last fraction?”
  • Consider asking:
    • “Did anyone have the same strategy but would explain it differently?”
    • “Did anyone approach the problem in a different way?”
Standards
Addressing
  • 3.NF.3.c·Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
  • 3.NF.A.3.c·Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. <span>Examples: Express <span class="math">\(3\)</span> in the form <span class="math">\(3 = 3/1\)</span>; recognize that <span class="math">\(6/1 = 6\)</span>; locate <span class="math">\(4/4\)</span> and <span class="math">\(1\)</span> at the same point of a number line diagram.</span>

25 min

10 min