Relate Division and Multiplication

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for multiplying a fraction by a whole number. These understandings help students develop fluency and will be helpful later in the lesson when students explore the relationship between multiplication and division.

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.

  • 3×123 \times \frac{1}{2}
  • 3×223 \times \frac{2}{2}
  • 3×323 \times \frac{3}{2}
  • 5×325 \times \frac{3}{2}

Sample Response

  • 32\frac{3}{2} : 3 groups of 12\frac{1}{2} is 32\frac{3}{2}.
  • 62\frac{6}{2}: 3 groups of 22\frac{2}{2} is 62\frac{6}{2}.
  • 92\frac{9}{2}: 3 groups of 32\frac{3}{2} is 92\frac{9}{2}.
  • 152\frac{15}{2} or 7127 \frac{1}{2}: 5 groups of 32\frac{3}{2} is 15 halves.
Activity Synthesis (Teacher Notes)
  • Display equation: 152=712\frac{15}{2} = 7 \frac{1}{2}
  • “How do we know this is true?” (They are both equal to 15÷215 \div 2 or 7 is 142\frac{14}{2} so 7127 \frac{1}{2} is 152\frac{15}{2}).
Standards
Building On
  • 4.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
  • 4.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Building Toward
  • 5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

20 min

15 min