Dividing Decimals by Decimals

I’m going to have the students review how to multiply by the powers of 10. The purpose of this activity is to help students make the connection to dividing decimals by decimals.  If students are struggling with this, I am going to remind them to use their tool box notes to help refresh their memories on how to do this.  There is no need for students to be multiplying this out.  (SMP1 and 7)

Before beginning the examples, I am going to explain to students that it is impossible to divide by decimal.  For example, there is no such thing as 1 and 2 tenths equal parts.  Therefore, we must alter our problem to reflect a division by a whole number.  Mathematics is based upon balance, so if we alter our divisor, we have to alter our dividend in the same way to maintain the balance.   With that said, I will begin modeling, out loud, how to divide decimals by decimals.  Each time I do an example, I will be asking the students how I can make the divisor into a whole number.  I’m looking for the students to tell me what power of 10 will make that happen.  Then I will remind them that since we multiplied our divisor by a power of 10, we also have to multiply our dividend by a power of 10 to maintain our balance.  Then we can divide like normal and move our decimal place straight up into our quotient.  This process will repeat for each example. (SMP 1 and 2)

Students should work independently to try a few division problems on their own.  Be sure to remind them to use their notes to help keep them on track.  As students are working, I will be walking around to make sure they are dividing correctly.  I will be looking to see that students are moving the decimal point both inside and outside of the division house.  I will also be looking to see that they are placing the decimal in the quotient.  I will also be making sure students are moving the decimal the correct amount of spaces.  I like to ask students, "is your divisor a whole number"? If not, "what will it take to make it a whole number"?  I will also be asking the students why they are moving the decimal (SMP 1 and 6) As students wait for me to check their work, they can check their own answers by multiplying the quotient by the divisor.  (SMP 6)

As students finish working on the problems, have them write down the steps it takes to divide decimals by decimals.  Students can share their responses with a  tablemate. (SMP 3)

The students will be working on decimal division word problems in this NHT.  The purpose of this common core strand is to have the students fluently compute with decimals.  Part of fluently computing is to know how and when to use different operations.  Even though these are all division problems, it will give the students exposure to what the problems look and sound like.  (SMP 1,2,3, 4)

Working on word problems is always difficult for students.  I always like the students to circle the key words that tell them it is division.  This helps build fluency.  Additionally, studetns struggle knowing which number is the dividend and which is the divisor.  Students have been taught that the larger number goes inside the division house and this is the rule they live by.  We know that is not always the case.  In trying to help students figure this out, I like to ask them to look for the number that says " I need this many equal parts" or something like that.  The number that needs to be divided into that many parts is the dividend (inside the house).  The number that makes the equal parts is the divisor (outside of the house)

The students will be working on a domino worksheet.  The domino worksheet is a nice tool to use as the students can quickly self-assess if their solution is correct.  Students work out the first problem in the first box.  The answer they get goes into the next small box and then into the larger box.  This becomes a new problem in the second box.  Students should follow the arrows and solve each new problem they get.  The solution to the domino is in the circle in the end. 

(SMP 1 and 5)