Fraction Multiplication and Division Situations

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for multiplying and dividing fractions. These understandings help students develop fluency and will be helpful later in this lesson when students solve problems about multiplying and dividing fractions.

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.

  • 5÷165 \div \frac{1}{6}
  • 5×165 \times \frac{1}{6}
  • 15÷6\frac{1}{5} \div 6
  • 15×16\frac{1}{5} \times \frac{1}{6}

Sample Response

  • 30: I multiplied 5 by 6.
  • 56\frac{5}{6}: I just knew it.
  • 130\frac{1}{30}: I found 16\frac{1}{6} of 15\frac{1}{5}.
  • 130\frac{1}{30}: I found the product of the numerators and denominators.
Activity Synthesis (Teacher Notes)
  • “How are the last two problems related?” (Dividing by 6 and multiplying by 16\frac{1}{6} give the same result.)
Standards
Addressing
  • 5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 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.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 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