The purpose of this activity is for students to divide decimal numbers by 0.1 and 0.01. They are given diagrams to help see that there are 10 tenths in each whole and 100 hundredths in each whole. The diagrams are not labeled with the whole so that the same diagram which shows can be interpreted as whole number division showing . This dual way of interpreting one diagram is highlighted in the Activity Synthesis. When students interpret the diagram as representing two different equations, they attend to precision in the meaning of each part of the diagram (MP6).

• Ask selected students to share their reasoning for each problem.
• Display:
• “How does the first diagram show that this equation is true?” (If each large square is a whole then the number of shaded strips is . If each large square is 100, then the number of those strips is  . The same diagram represents both expressions so they are equal.)
• Display:
• "How does the second diagram show that this equation is true?" (If each large square is a whole, then the number of small pieces represents  . If each large square is 100, then the number of small pieces represents  .)

In this activity, students practice finding quotients of decimals divided by 0.1 and 0.01. Students find the value of different expressions without the scaffold of a diagram. Monitor for these approaches:

• Diagrams
• Whole number quotient facts
• Multiples of the divisor

• Display:

• “How can we use the meaning of decimal place values to explain these equations?” (5 tenths is the same as 50 hundredths. So, that’s 5 groups of 0.1 or 50 groups of 0.01.)
• “How can we use the meaning of decimal place values to help find the value of ?” (The 3 is in the hundredths place so there are 3 one hundredths in three hundredths. The 5 is in the tenths place and there are 10 hundredths in each tenth. So, that's 50 more hundredths. There are 100 hundredths in one whole. That's 153 hundredths altogether in 1.53.)