Decimal Quotients

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Objective

SWBAT divide a decimal or whole number by a whole number resulting in a whole number or decimal quotient (1 and 2-digit divisors).

Big Idea

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

Think About It

7 minutes

Students independently annotate the Think About It problem, draw the appropriate bar model, and represent the problem with an expression.

I ask students how this problem is different  from the numbers that we have been dividing with.  Students name that this problem has a decimal in the dividend.  I tells students that the problems we’ll work on in this lesson will require us to work with decimal numbers.  Before I move on to the next section of the lesson, I ask students where in the real world they might need to divide decimal number.  

Intro to New Material

15 minutes

To start the Intro to New Material section, I have students fill in the first Key Point:  When we divide a decimal by a whole number, we can divide just as we would with whole numbers.  The decimal point in the dividend moves up to be in the same place in the quotient.  I then have students guide me through the first example.

We then fill in the second Key Point:  We can annex zero to keep dividing.  I cold call on students to complete each step of the next example. 

I have students think about the question, ‘Will the quotient of 34.5 ÷ 45 be greater than, less than, or equal to 1?’ and ask for a few students to share their thoughts.  After hearing some ideas, I have students record this on the lines:  The quotient will be less than one because the dividend is smaller than the divisor, so you are dividing a number by a bigger number.  This becomes a fraction less than 1.

We fill in the final Key Point:  If the dividend is larger than the divisor, the quotient will be greater than one.  If the dividend is smaller than the divisor, the quotient will be less than one.  

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 partner?
  • Are students annotating the problems?
  • Are students creating bar models to represent the problems?
  • Ares students using estimation to check the reasonableness of their quotients?
  • Are students using multiplication to check their work?
  • Are students placing the decimal point in the correct place in their quotient?
  • Are students writing full sentence answers?

 

I’m asking:

  • Explain how you determined this quotient. 
  • Tell me about your bar model.
  • How did you use estimation to check the reasonableness of your quotient?
  • Will this quotient be bigger or smaller than 1? How do you know?
  • How did you use multiplication to check your answer?
  • How did you know where to place the decimal point in your quotient?
  • What does your quotient mean, given the context of the problem?

 

After 10 minutes of partner practice time, students complete the Check for Understanding problem independently.  I ask for a volunteer to present his/her work to the class, and have the class give positive and constructive feedback on the work.

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  As I circulate, I am checking to be sure that the work includes the following: annotations, a model, a number sentence, an estimate, the standard algorithm, a multiplication check, and a full sentence answer.

As students complete Problem 3, I am expecting them to reference the example we completed together.  

Problem 4 can be difficult for kids, as they have to be able to convert from minutes to hours.  While most of my students know that there are 60 minutes in an hour, they don't all immediately think to divide by 60 in this problem.  It's a great chance to have them persevere and make sense of the problem.  

Closing and Exit Ticket

8 minutes

After independent work time, I have the students turn to Problem 3.  I have students clap out the answer, as a way to quickly check for understanding.  I then cold call on a student to share his/her written answer on how (s)he knew which quotient would be less than 1.  I am looking for students to talk about how the size of the divisor, relative to the dividend, impacts the size of the quotient.

Students then complete the Exit Ticket independently to close out the lesson.  A sample response for the first problem has been included. 

On homework, I provide this example as a reference for students and parents.