Lesson 8

This Number Talk encourages students to think flexibly about numbers to divide. The understandings elicited here will be helpful throughout this unit as students divide whole numbers and build toward fluent multiplication and division.

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”

• 1 minute: quiet think time
• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “How did you use the first few expressions to help you find the value of the last expression?”
• “How might you use multiplication to find the value of each quotient?”

In this activity, students are given three situations and asked to determine which ones could be 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 may also reason using estimation and mental computation when explaining why a situation must be false.

• Groups of 2–4
• 5 minutes: independent work time

• 5 minutes: group discussion
• Monitor for different ways students represent and prove how each situation could be true or false, including using reasoning based on estimation and mental math.

• 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 on 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 subtraction to check to see if it could really 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 that even if he washed 10 windows the window washer would almost be 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. 

• Groups of 2

• 5 minutes: independent work time
• 5 minutes: group work time
• Monitor for the different ways students represent and solve the problem, including how they discuss how to treat any unfilled buses (the remainder).

• 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?”