The purpose of this activity is for students to convert from a smaller metric length unit to a larger metric length unit. In this activity, students divide a three- or four-digit number by 100. The measurements, in centimeters, are whole numbers, but the converted measurements, in meters, are decimals. To find the value of the quotients, students may reason about the meaning of each place value and how that changes when the value is divided by 100. They may also reason that each place value has the value of the place to its left, so shifting two places to the right gives the value for each place (MP2, MP7).

• Display:
  
  
  
• “What patterns do you notice?” (The measurements in centimeters are whole numbers but the measurements in meters are hundredths. All the digits in the numbers are the same, but they shifted 2 places to the right. So the 7 hundreds in centimeters is 7 ones in meters.)
• “Why does dividing by 100 represent how many meters are in the given centimeters?” (I know there are 100 centimeters in each meter, so each centimeter is of a meter.)
• “How did you find the result of 727 divided by 100?” (I went place by place. 7 hundreds divided by 100 is 7 ones. 2 tens divided by 100 is 2 tenths. 7 ones divided by 100 is 7 hundredths.)
• Invite students to share which unit of measure they found most informative for these distances and why.

This activity continues the work of the previous activity as students convert from a smaller metric length unit to a larger metric length unit. Students are given several different conversions and multiple numbers for each set of conversions. They observe that when converting different units, dividing by 100 shifts each digit two places to the right, while dividing by 1,000 shifts each digit three places to the right. This allows students to solidify their understanding that dividing by powers of 10 shifts each digit one place to the right for every power of 10 in the divisor (MP8).

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

• “Share with your partner your response as to whether or not Tyler’s strategy will always work. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion
• Repeat with 1–2 different partners.
• If needed, display question starters and prompts for feedback.
  • “Can you give an example to help show . . . ?”
  • “Can you add a diagram, a table, or a representation to show . . . ?”
• “Revise your initial draft, based on the feedback you got from your partners.”
• 2–3 minutes: independent work time