Dividing with Decimals Day 2

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Objective

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

Big Idea

Where does the decimal point go in the quotient? Students use estimation and number sense skills to work on dividing with decimals.

Do Now

10 minutes

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.  A common mistake that students make when dividing with decimals is that they misplace the decimal point in their quotient.  Here, I want students to analyze the student’s work and explain their thinking.  Students should be able to use their number sense to easily identify that the answer is incorrect.  It may take students a little more time to determine what exactly went wrong.  Students are engaging with MP3: Construct viable arguments and critique the reasoning of others.

What about the decimal point?

10 minutes

As mentioned in the do now, a common struggle with students is that they do not know where the decimal point should go in their quotient.  We did a similar activity in the previous lesson (Multiplying with Decimals), so students should be used to the structure.  The first step is that they can estimate to see if their answer makes sense.

I have a volunteer read the task and pass out the calculators.  I give students 2-3 minutes to make their estimates and calculate their answers.  I walk around to ensure that students are on task and write neatly. 

We come back together as a class.  I ask students to think about what patterns they notice in their answers and what questions they have.  I read the directions for “Comparing Sets” and explain that they will participate in a Think Write Pair ShareStudents are engaging in MP8: Look for and express regularity in repeated reasoning and MP3: Construct viable arguments and critique the reasoning of others.

Then I ask for volunteers to share out with the class.  What patterns did you and your partner notice?  I want students to see how the answer changes when the divisor is made smaller by inserting or moving a decimal point.  Some students may look at Set B and think that they can count the number of decimal places in the dividend and that tells you how many decimal places are in the quotient à this does not work in all cases, like Set A.  I want students to make the connection between their estimation/number sense skills and where the decimal point goes.  This will help them check whether their quotients are reasonable.

I have a volunteer collect the calculators.

Problems

25 minutes

There are different strategies students can use to solve division problems with decimals (see Dividing with Decimals for specific examples).  I want students to work towards being able to efficiently use the standard algorithm to find quotients.  I continue to stress the importance of using number sense and estimation skills to check and make sense of solutions.  Students must use MP6: Attend to precision

These problems specifically address common mistakes that students make: forgetting to add a decimal point and bring down a zero when there is a remainder, forgetting to put a zero in the quotient when the divisor does not fit into the part of the dividend, and getting confused with a repeating decimal.  I have students work in partners on problems 1-3.  After 3-5 minutes we come back together as a class.  I present 1.35 as an answer for #2.  I ask for students to share their ideas.  I want students to recognize that that can’t be true, that it is way too small.  I have a student identify and remedy my mistake.  I present 13.33 as an answer to #3.  I want students to argue with me and for them to recognize that 13.33 is not the same as 13.3333…  We talk about whether this pattern will continue repeating.  I show them how to show that a digit in the quotient is repeating.

I have students work on problems 4-7 independently.  These questions address the same issues that were addressed in problems 1-3.  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 work on the “Radio Riches” Fast Finisher worksheet in partners.

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 6 and 7.  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 8-9 minutes left I pass out the Ticket to Go for students to complete independently.  Then I pass out the HW Dividing with Decimals Day 2