Products in the Hundredths Place

10 min

Narrative

The purpose of this What Do You Know About ____? is for students to think about 0.1×0.10.1 \times 0.1 before working with this kind of expression more formally in the lesson. Students know that 0.1 is the same as 110\frac{1}{10} and they know how to find products of fractions. The goal of the Activity Synthesis is to highlight this understanding before students find products of decimals in the lesson.

Launch

  • Display the expressions.
  • “What do you know about 1×0.11 \times 0.1 and 0.1×0.10.1 \times 0.1?”
  • 1 minute: quiet think time
Teacher Instructions
  • Record responses.
  • “How could we represent these expressions?” (I could use a hundredths grid or area diagram.)

Student Task

What do you know about these expressions?

  • 1×0.11 \times 0.1
  • 0.1×0.10.1 \times 0.1

Sample Response

Sample responses:
  • 1×0.1=0.11 \times 0.1 = 0.1
  • 0.1 is 110\frac{1}{10} so 0.1×0.10.1 \times 0.1 is 110×110\frac{1}{10}\times \frac{1}{10} which is 1100\frac{1}{100}
  • 0.1×0.10.1 \times 0.1 is going to be smaller than 0.1.
Activity Synthesis (Teacher Notes)
  • “Can you find the value of 0.1×0.10.1 \times 0.1?” (Yes, 0.1 is 110\frac{1}{10} so that’s 110×110\frac{1}{10} \times \frac{1}{10} and I know that’s 1100\frac{1}{100}.)
Standards
Addressing
  • 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.
Building Toward
  • 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>

15 min

20 min