Solve and Interpret Division Problems

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SWBAT solve word problems involving division and interpret remainders in context

Big Idea

The division algorithm is an efficient way to determine a quotient given any division context.

Think About It

7 minutes

Students work with their partners to complete today's Think About It problem.  

After 4 minutes of work time, I ask students to share out.  I ask:

What were you solving for?

How might you do that?

How did you figure out the number of packages?

What does the quotient of 29 R 10 mean? Why?  

I tell students that in this lesson, they're going to have the chance to use everything they've learned so far about division to solve real-world problems.  

Guided Practice

10 minutes

Rather than lead students through an Intro to New Material portion, this lesson has Guided Practice.  The lesson requires students to use everything they've learned up until this point about division, but does not contain any new material.

I cold call on students, using the following sequence of questions: (selected student answers in parentheses) 

What do we do first? (annotate)

What is the problem asking us to find?

What do we know?

What do we need to do, as a first step?

What does that look like, visually?

What operation do we use?

How much trash is there in total? 

Are we done?  What next?

What do we know?

How can we represent this as a bar model?

What operation do we use? 

What is the quotient? (20 R 8)

So what is our answer? (21 bags)

Why not 20?

Partner Practice

15 minutes

Students work in pairs on the Partner Practice problem set.  As students work, I circulate around the room and check in with each group.  I am looking for:

  • Are students explaining their thinking to their partners?
  • Are students representing the problems with bar models?
  • Are students using estimation to help them divide?
  • Are students using multiplication to check their work?
  • Are students correctly interpreting the quotient and remainder?
  • Are students using the correct operations?
  • Is student work clear and organized?

I'm asking: 

  • Explain how you determined this answer.
  • How did you know which operation to use first?
  • How did you use estimation to help you?
  • How do you know your calculations are correct? 
  • What steps were needed to solve this problem?
  • What does the remainder mean in this problem?

I did not include a Check for Understanding for this lesson.  I have the chance to go around to each group multiple times while they're working.  Before students start Independent Practice, I'll ask a group to present their work on one of the Partner Practice problems to the class.  We, the class, will make sure that the work has all of the components I expect in top quality work.

Independent Practice

18 minutes

Next, students work on the Independent Practice problem set.  

At the start of work time, I tell students that they have the freedom to decide the order in which they complete problems.  Students always have this option in my class.  In this problem set, there is a variety of problem types (although all division word problems).

As students work, I am looking to see that their work meets my Criteria for Success (CFS).  I'm looking for: 

  • annotations
  • bar model
  • expression and estimate
  • scratch work (neat)
  • standard algorithm
  • multiplication check
  • equation with answer
  • answer in sentence

Closing and Exit Ticket

8 minutes

After 15 minutes of independent work time, I have students turn to their partners and present the work for a problem of their choice.  Partners are checking their peer's work to be sure that the work space includes everything expected, as outlined in our Criteria for Success

Students work independently on the Exit Ticket to close the lesson.  A sample is included here.