Fraction Division Situations

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for dividing a whole number by a unit fraction and a unit fraction by a whole number. These understandings help students develop fluency and will be helpful later in this lesson when students solve division problems.

Launch

  • Display one expression.
  • “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 strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 6÷36 \div 3
  • 6÷136 \div \frac{1}{3}
  • 13÷6\frac{1}{3} \div 6
  • 13÷12\frac{1}{3} \div 12

Sample Response

  • 2: I just know it.
  • 18: 6×3=186 \times 3 = 18.
  • 118\frac {1}{18}: 13÷6=118\frac {1}{3} \div 6 = \frac{1}{18}.
  • 136\frac {1}{36}: There are twice as many pieces as in the previous expression so the pieces will be twice as small.
Activity Synthesis (Teacher Notes)
  • “How are the expressions 6÷136\div\frac{1}{3} and 13÷6\frac{1}{3} \div 6 the same? How are they different?” (They both have a 6 and a 13\frac{1}{3} but 6÷136 \div \frac{1}{3} is greater than 1 and 13÷6\frac{1}{3} \div 6 is less than 1.)
Standards
Addressing
  • 5.NF.7·Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
  • 5.NF.B.7·Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.<span>Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.</span>

20 min

15 min