Division: One-digit Divisors

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Objective

SWBAT apply the steps of the division algorithm to find the quotient of a three-digit dividend and a one-digit divisor and use estimation to gauge the reasonableness of the quotient.

Big Idea

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

Think About It

7 minutes

Students work on the Think About It problem with their partners.  After three minutes of work time, I call the class to attention for a class conversation.

Students worked on long division in 5th grade (5.NBT.6), but it generally is an area of weakness for my students at the start of each year.  This lesson will ask students to find whole number quotients, and quotients with remainders.

This Think About It problem is designed to get kids thinking about long division, and to give me a platform on which to outline my work product expectations.  I describe those in the next section of this lesson.

Intro to New Material

15 minutes

To start each of the problems in the Intro to New Material section, I have my students read and annotate, draw a bar model, and make an estimate before we start to divide.  My students are proficient in these skills, and I don't spend time in this lesson teaching them how to do these things.  I reinforce my expectation that these components be a part of the solutions by asking students questions about each piece and modeling them in my own work. For context, this is an example of what the students produce.

The focus of this lesson is on the conceptual understanding of division, and how to set up the standard algorithm.  I find that students sometimes come to me knowing how to set up the algorithm, but without a firm understanding of what's happening.  This leads students to make mistakes - for example, not including a 0 in the tens place of the quotient, when warranted.

I don't want students to complete their work like this, using arrows.  This is the way I was taught as a child.  I learned the process, but I'm not convinced I would have been able to tell you why I was taking the steps that I was taking.

I ask a series of questions about place value that gets students to produce work that looks like this model.  For the example provided here, I'd say things like "we're looking at the hundreds place.  We have a 7 in the hundreds place of the dividend, which stands for 700.  We need to determine how many groups of 3 can fit into 700, thinking in multiples of 100.  What's 3 x 100?  What's 3 x 200?  What's 3 x 300?  Oh, that's too much.  We need 200 groups of 3, to get us as close as we can to 700 without going over, using multiples of 100.  200 groups of 3 is 600, let's take that away from the dividend.  Now, on to the tens place.  How many groups of 3 will fit into 160 tens, thinking in multiples of 10.  What's 3 x 10, 3 x 20, etc...."

Once we have our quotients, we always reference back to our estimate and compare the actual quotient to the estimate.  Students also must check their work, using multiplication.

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 annotating?
  • Are students drawing a bar model?
  • Are students estimating?
  • Are students correctly using the standard algorithm?
  • Are students completing the check step?
  • Are students explaining their thinking to their partner using the language of place value (e.g. groups of 10) and regrouping?
  • Are students answering in a complete sentence?

 

I am asking:

  • Tell me about your bar model.
  • Explain you determined this answer. 
  • What does this # mean?  How many groups of (XX) did you use?
  • How did you check your work?
  • How do you know that your quotient is reasonable?
  • What does this number mean, given the context of the problem? 

 

This early in the year, I do have a number of students who are not yet fluent with their multiplication facts.  I allow a small number of students to use a multiplication chart during this lesson.  I don't want them to miss out on mastering the division algorithm in this lesson.

 

 

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  

This is a problem set with only 5 problems.  It takes students awhile to complete all of the components of a top quality answer.  Of the 5 problems, 2 have remainders.  I will teach an entire lesson on interpreting the remainders.  If students are having difficulty with the sentence for questions 1 and 4, I affirm their numerical answer and let them know that we'll be working on figuring out what the remainder means in different situations soon.

As I circulate, I am looking to be sure that every problem contains:

  • annotation
  • a bar model
  • the actual expression and an estimate, using compatible numbers
  • the standard algorithm
  • a multiplication check
  • a full sentence answer

Because there are so many components to what I am looking for in student's work today, before the lesson I complete the five problems in this practice set exactly the way I expect to see them from students.  I carry my work with me as I check in with kids, so that I have my strong model to reference.

Closing and Exit Ticket

7 minutes

After independent work time, I cold call on students to read their full sentence answers for each of the 5 problems.  As a student reads his/her answer, I display my work for the problem so that students can see all of the required components. 

Students then independently complete the Exit Ticket to close the lesson.

The exit ticket contains 2 problems that do not have real-world contexts; students are simply asked to divide.  Exit tickets give me data about what students have mastered, and what they need more help with.  I included these 2 problems on the exit ticket so that I have a clear idea of where students are getting stuck.