In this activity, students are given three situations and asked to determine which situations are true and which are not. To do so, they need to carefully make sense of the quantities in each story and how they are related (MP2). Students may explain why a situation is true by writing one or more expressions or equations to represent the relationships and perform the calculations to check. Students also may reason, using estimation and mental computation when explaining why a situation must be false.

• Select students to share their responses and reasoning.
• Record the expressions or equations they wrote to represent the situations. Highlight different ways of representing the same situation.
• “For which situations did you need to find the actual values in order to tell if they were true or not true? Why is that?” (I tried to estimate for Situation A and I knew it would be close, so I did the multiplication and added to find out if the total height was really 610 feet. I needed to write equations to make sense of Situation C. I just did the multiplication and the subtraction to check if it really could be $54.)
• “For which stories was it possible to tell by estimation and mental math?” (I could do some estimation for all of them, but for Situation B I could tell that even if he washed only 10 windows, the window washer would be almost out of time and couldn’t do 17.)

In this activity, students interpret situations that involve equal groups and require making sense of a remainder. Students solve problems, using their understanding of multiplication, and by connecting their solutions to the quantities in the situation (MP2). Although parts of the task could be solved by dividing a multi-digit number by a two-digit number, students are not expected to perform division with these numbers until grade 5. Students may access this task, using multiplication and addition.

Encourage students to use the Three Reads routine as needed to solve problems. 

• Select students to share their responses and reasoning. Record the different representations students used to solve the problems.
• Consider asking:
  • “How did you decide how many buses you would need from each company?”
  • “Do all the buses carry the same amount of passengers? How can you see that in your representations or equations?”
  • “How did you decide what operations to use to answer each question?”