Division: Two-Digit Divisors, Part 1

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Objective

SWBAT explain and apply the steps of the division algorithm to find the quotient of a three-digit dividend and a two-digit divisor.

Big Idea

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

Think About It

7 minutes

Students work in partners on the Think About It problem.  

After a few minutes of work time, I ask the class how this problem is different from the ones that we did in the previous lesson. 

I frame the lesson by telling students we will be dividing 3 digit numbers by 2 digit numbers by following exactly the same process.  The only difference is that the divisor will be 2-digits.  

Intro to New Material

15 minutes

The Intro to New Material section of this lesson is comprised of two examples.  For the first example, I model for the class how to complete the problem.  Once my work is complete, I have the students reference the list of 'must-haves' at the bottom of the page, to check my work.  We then work out the second problem together.  

 

Throughout this lesson, I am asking students to use repeated addition as a way to keep track of the multiples of the divisor.  Some students, who have strong number sense, will guess and check with multiplication (writing 56x4= 224, 56x5 = 280, etc) rather than showing repeated addition (56 + 56 = 112 + 56 = 178 + 56....etc).  I am okay with this!  Multiplication facts are more efficient than repeated addition.

Partner Practice

15 minutes

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

  • Are students explaining their thinking to their partner?
  • Are students drawing a bar model?
  • Are students using estimation to help them divide?
  • Are students making a list of repeated addition?
  • Are students using multiplication to check their work?
  • Are students answering in a full sentence?

 

I'm asking:

  • Explain you determined this answer. 
  • What strategy did you use?
  • How did you use estimation to help you divide?
  • How did repeated addition help you to find your quotient?
  • How did you check your work? 
  • What does this quotient mean, given the context of the problem?

 

After 10 minutes of partner work time, I ask a student to share the problem of his/her choice on the doc cam.  The student presents his/her work to the class, and the other students ask any clarifying questions they may have.

 

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  As they are working, I circulate around the room and look to see that students are including all of the expected components (annotations, bar model, estimate, repeated addition, standard algorithm, multiplication check, and full sentence answer).

Students who attended my school last year learned a variation of the standard algorithm to use when completing long division problems.  It relies  heavily on an understanding of the power of 10:

 

If I see students using this method, I ask them to pause.  I tell them that the method they're using certainly works and is a good resource.  But, in this lesson, I want them to practice using the standard algorithm.  I reinforce the idea that strong math students get good at multiple ways to solve problems.  

Closing and Exit Ticket

8 minutes

After independent work time, I have students share a problem of their choice with their partners.  The partner asks any clarifying questions (s)he has, offers feedback on the work space, and then presents her own problem. 

Students then work independently on the Exit Ticket to close the lesson.  A sample of the work space is included.   

I assign this Homework after this lesson, which includes an example for students and parents.