This activity prompts students to interpret and represent situations about distances and use multiple operations to solve problems. In the third problem, a piece of information is withheld. Students will need to make sense of what’s missing and find out that information before the question could be answered. Throughout the activity, students reason abstractly and quantitatively as they interpret the diagram and use the information to solve problems (MP2).

• Consider collecting and displaying the different expressions students wrote for the first question and discussing what they tell us about the way the writer reasoned about the problems. For example:
  • suggests that the writer found the distance one way then doubled it.
  • suggests that the distances between classes were doubled first before being added.
• “How did you find out if Mai’s cousin traveled 2 miles each week? What did you do first? What did you do next?”
• Select students to share their responses and reasoning.
• Highlight how the strategies are alike and different.

This activity gives students another opportunity to use multiple operations to model the quantities in a situation and to solve problems involving large numbers. Students interpret the quantities in context, reason about them abstractly as they perform computations, and then return to the context to interpret the results. As they do so, students are reasoning quantitatively and abstractly (MP2).

Students may choose to answer the first problem by dividing a five-digit number by a one-digit divisor. Though finding a quotient of a five-digit dividend is not an expectation, this particular number ends in a 0. Students can use the division strategies they’ve learned so far and what they know about the structure of numbers in base ten to find the quotient (MP7).

• Invite students to share their responses and reasoning.
• Focus the discussion on how students found the number of steps Han took each day and how they found the last number in the table.
• “How would you know if your answer to the first question is correct?” (Multiply 4,650 by 7 to see if it equals 32,550.)
• “How would you know if your answer to problem 3 is reasonable?” (Add it to the other three numbers and see if the sum is 120,000.)