Represent Situations with Multiplication and Division

10 min

Narrative

This Number Talk encourages students to think about multiplication and division involving a whole number and unit fraction. While the order of the factors does not matter for multiplication, as seen in the first two expressions, it does matter for division, as seen in the second pair of expressions. Monitor for students who find the value of the two division expressions using multiplication since the relationship between multiplication and division is the focus of this lesson.

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.

  • 3×1103 \times \frac{1}{10}
  • 110×3\frac{1}{10} \times 3
  • 110÷3\frac{1}{10} \div 3
  • 3÷1103 \div \frac{1}{10}

Sample Response

  • 310\frac{3}{10}: It’s 3 tenths.
  • 310\frac{3}{10}: It’s the same as 3×1103 \times \frac{1}{10}.
  • 130\frac{1}{30}: It’s 13×110\frac{1}{3} \times \frac{1}{10}.
  • 30: There are ten 110\frac{1}{10}s in 1 and 3 times as many in 3.
Activity Synthesis (Teacher Notes)
  • “How did you find the value of 3÷1103 \div \frac{1}{10}?” (I know that there are ten 110\frac{1}{10}s in 1 so there are thirty 110\frac{1}{10}s in 3.)
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>

15 min

20 min