Dividing with Decimals

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Objective

SWBAT: • Make estimates of division problems • Divide whole numbers and decimals • Interpret a remainder

Big Idea

How can you split $27 equally between 4 people? Students apply what they know about division to divide with whole numbers and decimals.

Do Now

10 minutes

Notes:

  • Before the lesson you will need to copy, cut, and organize the Division Matching cards.  I like to label cards in sets (write #1 on all of first set, etc.) so that students know which cards are theirs.
  • I use the data about division from the pre-test in Unit 1 to Create Homogeneous GroupsFor the do now I have students work in partners or groups of 3.

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Here, I want students to connect what is being described in the word problem with a picture.  Students must think about what is going on and what the action will look like. 

After most students have finished most of the matches, I call the class together.  I ask students to share their number sentences and pictures for #4 and #8.  There is a subtle difference in these problems, which I want students to notice. A common mistake is that students confuse the situations that represent 24/4= 6 and 24/6= 4

Estimation

5 minutes

Here I want students to quickly review the vocabulary word quotient and then work on estimating.  I give students a couple minutes to make and write explanations for their estimates.  I stress to students that estimates need to be relatively quick. 

I walk around and monitor student work.  I’m looking to see what strategies students are using.  Some students may round numbers to whole numbers and divide.  Other students may make connections to multiplication.  I am interested to see what students do with #3.  If they struggle I ask, “Do you think the quotient is going to be bigger or smaller than 1.89?  Why?”

I call one student to explain one of their estimates.  These students are students I observed using a particular strategy as I was walking around.  I am not giving exact answers at this time.  We will work on finding exact quotients later in the lesson.  It is important that students are able to use their number sense to make reasonable estimates.

Practice

15 minutes

We do number 1 together.  I ask students how they want to find the exact quotient.  I also show them the algorithm.  I stress that students need to use their number sense and the patterns they noticed earlier to decide if their final answer makes sense (MP1)

Students work independently on the rest of the problems.  They can check in with their partner if they are stuck.  I Post A Key so that students can check their work when they finish a page.  I am looking that students are making reasonable estimates and that they are successfully dividing using a strategy of their choice. 

If students successfully complete the practice problems, they can play the Leftovers From 100 game.

If students are struggling, I may intervene in one of the following ways:

  • Ask them what their estimate is and how they got it.
  • Let them use a multiplication chart.
  • Give them a word problem situation that represents the problem.
  • Have them use the grids to organize their problems.
  • Pull a small group of students who are struggling to work together.

 

Sharing $$

10 minutes

I have students participate in a Think Write Pair Share.  Working with money forces students to interpret the remainder.  I have a few students share and explain their strategies.   Some students will use the picture, others will use the algorithm, others will make connections to multiplication.  Here students are using MP 6: Attend to precision.

We move on to the next page where I ask students to take a couple minutes to analyze the examples.  What do they notice?  What are the similarities? The differences? I give the students a couple minutes to jot down notes.

I want students to see that all of the answers are technically correct, although not as useful as others.  Problem A solves the problem but the answer doesn’t help. I also want students to start moving away from the partial quotient method and towards the standard algorithm.  Problem B turns the remainder into a fraction, but we then need to figure out how to do that. 

A common struggle is that students don’t know where to put a decimal point.  This can be easily remedied if students are able to make reasonable estimates.  For example, offer $67.50 as an answer.  Hopefully students will quickly eliminate this as a possibility, since it is way too big!

I want students to notice the differences between C and D.  In problem C the person ignored the decimal point until the end, and then used estimation to decide where it goes.  Problem D kept the decimal point in the dividend and brought it up to the quotient.  I ask students how could these students check their answers.  I want students to get into the habit of using multiplication to check their answers.

More Practice

10 minutes

Just like the previous Practice section, we do number 1 together.  I ask students how they want to find the exact quotient. I stress that students need to use their number sense and estimates to decide if their final answer makes sense. 

Students work independently on the rest of the problems.  They can check in with their partner if they are stuck.  I Post A Key so that students can check their work when they finish a page.  I am looking that students are making reasonable estimates and that they are successfully dividing using a strategy of their choice. 

If students successfully complete the practice problems, they can play the Leftovers From 100 game.

If students are struggling, I may intervene in one of the following ways:

  • Ask them what their estimate is and how they got it.
  • Let them use a multiplication chart.
  • Give them a word problem situation that represents the problem.
  • Have them use the grids to organize their problems.
  • Pull a small group of students who are struggling to work together.

 

Closure and Ticket to Go

10 minutes

I begin the Closure by asking students to look at questions 3 and 4.  What was your estimate? Why?  How did you find the exact quotient.  I look for students who used different strategies and I have them show and explain their work. If there is a common mistake I see students making, I will present it and ask students to address it here.  I am also interested to see what students estimated with #4.  Even if students struggle with estimating, they should be able to see that they answer is going to be smaller than 2.34, since you are dividing it by a number that is larger.

With about five minutes left I pass out the Ticket to Go for students to complete independently.  Then I pass out the HW Dividing with Decimals. I may also assign one of the “Facts about College” or “Working During College” pages for homework, depending on how much students finished.