Tips for Teaching Long Division

Discussion in 'General Education' started by Ms.Holyoke, Sep 15, 2018.

  1. Ms.Holyoke

    Ms.Holyoke Connoisseur

    Joined:
    May 14, 2012
    Messages:
    1,915
    Likes Received:
    690

    Sep 15, 2018

    I am teaching long division to my 6th graders next week. The majority of them have never done long division with the standard algorithm before -- they only used partial quotients. I am going to assume that they know nothing, especially because some kids could not even multiply using the standard algorithm.

    I am going to use the acronym (Does McDonalds Serve Cheeseburgers?), have them write it on their paper, and cross off when each step is done. Does anyone have other tips? I am also looking for any activities people might use when teaching this topic.
     
  2.  
  3. rpan

    rpan Cohort

    Joined:
    Mar 19, 2017
    Messages:
    706
    Likes Received:
    542

    Sep 15, 2018

    Keep the pace slow and use small numbers To start with and then build up from there. Long division can seem difficult and overwhelming so they need to feel they can conquer it. Also, maybe the “I do” “we do” “you do” method may be helpful. Students who have got it can move on to the “you do” phase while those who need more help can stay on the “we do” phase.
     
  4. Hokiegrad1993

    Hokiegrad1993 Comrade

    Joined:
    Dec 6, 2017
    Messages:
    262
    Likes Received:
    98

    Sep 15, 2018

    I have seen people use decks of cards where they can visually see and move the cards down when needed.
     
    futuremathsprof likes this.
  5. mathmagic

    mathmagic Enthusiast

    Joined:
    Nov 20, 2012
    Messages:
    2,418
    Likes Received:
    1,174

    Sep 15, 2018

    You might consider showing with a model while you do it via the algorithm so they learn what's happening at each step. As you were mentioning, you might start with partial quotients / "big 7" to build up the conceptual understanding behind the algorithm if you feel they need that.
     
  6. futuremathsprof

    futuremathsprof Phenom

    Joined:
    Jun 27, 2014
    Messages:
    4,398
    Likes Received:
    1,304

    Sep 15, 2018

    This.

    Also, explain to them that long division, like “short” division, is just repeated subtraction in that you are really just trying to figure out how many groups/parts you can make by dividing the dividend (whole) by the divisor (part).

    Another thing that might help is asking students how many parts remain after removing a “grouping” of the divisor. Do a few examples of this and they should hopefully notice that the quantity that remains is the difference of the dividend and the groups.
     
  7. futuremathsprof

    futuremathsprof Phenom

    Joined:
    Jun 27, 2014
    Messages:
    4,398
    Likes Received:
    1,304

    Sep 15, 2018

    Excellent idea. This would be especially helpful to visual and kinesthetic learners.
     
    Hokiegrad1993 likes this.
  8. otterpop

    otterpop Phenom

    Joined:
    Jun 14, 2013
    Messages:
    4,257
    Likes Received:
    1,826

    Sep 15, 2018

    Some things in math require a lot of repetition. I strongly feel that this is one of them. If it were me, I'd: Do two on the board; do three or so together; have them do one, check together, do one, check together, and so on.

    Ultimately, I Do, We Do, You Do.

    Also, use simple, repetitive language. Know exactly what you'll say for each step, and then use that language repeatedly as you're showing what to do. They will eventually hear that language in their heads as they're doing the problems on their own.

    Note on above: some might take issue with "use simple, repetitive language", and it might seem like you're talking down to the kids. I disagree 100%. Having a simple chant to say as you go through a process can help immensely. For example, even as an adult, I still say the "I before e, except after c" rhyme in my head when writing certain words.
     
  9. Teacher234

    Teacher234 Cohort

    Joined:
    Jan 21, 2018
    Messages:
    615
    Likes Received:
    160

    Sep 15, 2018

    When I start teaching long division, I love beginning with a quick review of finding the remainders. I use fruit snacks. I also provide a visual anchor chart and model with my students the problems.
     
  10. futuremathsprof

    futuremathsprof Phenom

    Joined:
    Jun 27, 2014
    Messages:
    4,398
    Likes Received:
    1,304

    Sep 15, 2018

    Beautiful advice.
     
  11. futuremathsprof

    futuremathsprof Phenom

    Joined:
    Jun 27, 2014
    Messages:
    4,398
    Likes Received:
    1,304

    Sep 15, 2018

    I’m curious, what do you do with the fruit snacks specifically?
     
  12. TrademarkTer

    TrademarkTer Groupie

    Joined:
    Jul 28, 2017
    Messages:
    1,485
    Likes Received:
    1,027

    Sep 15, 2018

    Please just say "eat 'em", please just say "eat em"!!!
     
  13. Ms.Holyoke

    Ms.Holyoke Connoisseur

    Joined:
    May 14, 2012
    Messages:
    1,915
    Likes Received:
    690

    Sep 15, 2018

    I am going to start with partial quotients and I am not sure if I need a day on just reviewing partial quotients. I'm also not sure how to connect the two methods though. What type of model are you talking about?

    I think this is the way to go for this topic. I have looked at some of the more inquiry based curriculum and the way that they teach long division seems ridiculous. For example, the open up curriculum just showed an entire long division calculation and wanted the students to justify/explain each step of the problem the first time they saw it. I know my college would frown upon this, but this is one of the units where I will be a "traditional teacher." :)

    That said, does anyone have activities for long division? I will probably be teaching this for over a week (especially including decimals.) I will do worksheets but I would also love some ways to make it less boring. I was thinking of group task cards at some point this week and my homeroom kiddos can help me prep them.
     
    Last edited: Sep 15, 2018
  14. Teacher234

    Teacher234 Cohort

    Joined:
    Jan 21, 2018
    Messages:
    615
    Likes Received:
    160

    Sep 15, 2018

    The fruit snacks are used as counters.
    For example:
    34/7
    I have my students make groups of 7 until they get to 34.
    7 fruit snacks 7 fruit snacks 7 fruit snacks 7 fruit snacks 7 fruit snacks
    After they get to 34, the students should realize that a 5th group can not be made. So, they count the equal groups and the unequal group is the remainder. Then they eat the fruit snacks.
     
    futuremathsprof likes this.
  15. gr3teacher

    gr3teacher Phenom

    Joined:
    Sep 13, 2013
    Messages:
    4,307
    Likes Received:
    887

    Sep 15, 2018

    When I did long division with third graders, I always used the family model as a mnemonic... Dad, Mom, Sister, Brother, Cat (Divide, Multiply, Subtract, Bring down, Check)
     
  16. Ms.Holyoke

    Ms.Holyoke Connoisseur

    Joined:
    May 14, 2012
    Messages:
    1,915
    Likes Received:
    690

    Sep 15, 2018

    Kind of makes me sad that my 6th graders don't know it when your 3rd graders did :(
     
  17. gr3teacher

    gr3teacher Phenom

    Joined:
    Sep 13, 2013
    Messages:
    4,307
    Likes Received:
    887

    Sep 15, 2018

    To be honest, I never really bought into teaching the partial quotients method. I know where kids are going when they hit middle school and high school and they really just need to know the long division process.
     
  18. Ms.Holyoke

    Ms.Holyoke Connoisseur

    Joined:
    May 14, 2012
    Messages:
    1,915
    Likes Received:
    690

    Sep 15, 2018

    There needs to be more communication between elementary and middle school teachers. I find it crazy that some of my students seem to have never seen the traditional algorithm for multiplying. Thankfully, this is a small minority of my students but they are struggling. However, I only have about 5 students who know the standard algorithm for division.
     
    futuremathsprof likes this.
  19. gr3teacher

    gr3teacher Phenom

    Joined:
    Sep 13, 2013
    Messages:
    4,307
    Likes Received:
    887

    Sep 15, 2018

    From my experience, the biggest problem is that too many elementary teachers can't really do math, so they rely on teaching tricks instead of helping students understand why something works (and why the most common methods for computation BECAME the most common methods of computation).
     
  20. Pi-R-Squared

    Pi-R-Squared Connoisseur

    Joined:
    Jun 23, 2013
    Messages:
    1,520
    Likes Received:
    353

    Sep 15, 2018

    The following conditional statement has applied through and through.

    “If you know how to divide, then you know how to multiply.”

    So if you don’t know how to multiply, then you don’t know how to divide.

    Your quick learners will know their times tables. Believe me.
     
    Leaborb192 and futuremathsprof like this.
  21. TeacherGroupie

    TeacherGroupie Moderator

    Joined:
    May 13, 2005
    Messages:
    29,807
    Likes Received:
    1,172

    Sep 15, 2018

    A silly little thing that may help, to begin with: have them work long division problems on notepaper rotated 90 degrees so that the lines make columns. A digit brought down must stay in its column, because that column represents its place value AND accounts for the placement of the next digit in the quotient.
     
    Leaborb192, a2z and futuremathsprof like this.
  22. futuremathsprof

    futuremathsprof Phenom

    Joined:
    Jun 27, 2014
    Messages:
    4,398
    Likes Received:
    1,304

    Sep 15, 2018

    :yeahthat:
     
  23. futuremathsprof

    futuremathsprof Phenom

    Joined:
    Jun 27, 2014
    Messages:
    4,398
    Likes Received:
    1,304

    Sep 15, 2018

    This is perhaps one of the most brilliant ideas I’ve read on here. It’s so simple, yet so elegant. I’m actually envious I didn’t think of this before... I’m adding this to my notebook of teacher tips!

    Thank you! :)
     
  24. futuremathsprof

    futuremathsprof Phenom

    Joined:
    Jun 27, 2014
    Messages:
    4,398
    Likes Received:
    1,304

    Sep 15, 2018

    This is incredibly helpful. Thank you! I may just borrow this idea for when I private tutor groups of elementary kids. Of course, I will still teach the concepts rigorously, but sometimes the lower-performing students need examples like these to conceptualize/visualize the math.
     
  25. Ms.Holyoke

    Ms.Holyoke Connoisseur

    Joined:
    May 14, 2012
    Messages:
    1,915
    Likes Received:
    690

    Sep 15, 2018

    Great idea!!!
     
    futuremathsprof likes this.
  26. Pi-R-Squared

    Pi-R-Squared Connoisseur

    Joined:
    Jun 23, 2013
    Messages:
    1,520
    Likes Received:
    353

    Sep 15, 2018

    The slow ones won’t know their multiplication facts so those students will write out the multiples of whatever divisor you’re using.
     
  27. Ms.Holyoke

    Ms.Holyoke Connoisseur

    Joined:
    May 14, 2012
    Messages:
    1,915
    Likes Received:
    690

    Sep 16, 2018

    I recently learned that I have many kids who do not know their multiplication facts...after being almost done with my multiplication unit! I’ve given them all multiplication tables as the other math teacher has done.
     
  28. a2z

    a2z Virtuoso

    Joined:
    Sep 16, 2010
    Messages:
    6,363
    Likes Received:
    2,238

    Sep 16, 2018

    If you teach them to use their fingers to say and trace the facts when they use the table, and they use the table consistently for a while they will start remembering the facts because there will be no guessing. Practice does not make perfect accurate practice makes perfect. Doing something wrong over and over (like guessing at math facts) only serves to make recall harder.

    Explain how using the chart and saying it will help them come to remember the facts. They will start to rely on it less and less when they know them. I do believe that most kids want to be successful, but they don't know how to fix some problems when they have tried other ways and it doesn't work.
     
  29. a2z

    a2z Virtuoso

    Joined:
    Sep 16, 2010
    Messages:
    6,363
    Likes Received:
    2,238

    Sep 16, 2018

    You are right. With multi-digit division, they do have to repeated addition to determine each division. Couple that with the multiplication chart and helping them make the connection (number sense), the learning of facts can come about slowly. It may take most of the year and continual practice problems throughout the year, but it can work.
     
  30. Leaborb192

    Leaborb192 Enthusiast

    Joined:
    Jun 18, 2016
    Messages:
    2,407
    Likes Received:
    1,180

    Sep 16, 2018

    .
     
    Last edited: Feb 3, 2019
  31. Leaborb192

    Leaborb192 Enthusiast

    Joined:
    Jun 18, 2016
    Messages:
    2,407
    Likes Received:
    1,180

    Sep 16, 2018

    .
     
    Last edited: Feb 3, 2019
  32. Leaborb192

    Leaborb192 Enthusiast

    Joined:
    Jun 18, 2016
    Messages:
    2,407
    Likes Received:
    1,180

    Sep 16, 2018

    .
     
    Last edited: Feb 3, 2019
  33. a2z

    a2z Virtuoso

    Joined:
    Sep 16, 2010
    Messages:
    6,363
    Likes Received:
    2,238

    Sep 16, 2018

    This is not what I see. Our kids never get multiplication charts. They are taught "what multiplication is" and then given flash cards to memorize facts. Multiplication charts used properly can be filled with accurate reinforcement for the students rather than guessing, but it has to be used with intent. They must be saying the facts while looking up the fact to cement the correct answer.

    Honestly, I think kids don't know facts because repetition has been removed from the classrooms, and as you said, many don't teach math.
     
    futuremathsprof likes this.
  34. a2z

    a2z Virtuoso

    Joined:
    Sep 16, 2010
    Messages:
    6,363
    Likes Received:
    2,238

    Sep 16, 2018

    Now that just confused the heck out of me.
     
    otterpop likes this.
  35. Leaborb192

    Leaborb192 Enthusiast

    Joined:
    Jun 18, 2016
    Messages:
    2,407
    Likes Received:
    1,180

    Sep 16, 2018

    .
     
    Last edited: Feb 3, 2019
    futuremathsprof and a2z like this.
  36. Leaborb192

    Leaborb192 Enthusiast

    Joined:
    Jun 18, 2016
    Messages:
    2,407
    Likes Received:
    1,180

    Sep 16, 2018

    .
     
    Last edited: Feb 3, 2019
  37. Ms.Holyoke

    Ms.Holyoke Connoisseur

    Joined:
    May 14, 2012
    Messages:
    1,915
    Likes Received:
    690

    Sep 16, 2018

    I actually think this might be more confusing because we want kids to see that we are trying to figure out what the hundreds digit is, which is why we write it on top of the 9.
     
  38. Leaborb192

    Leaborb192 Enthusiast

    Joined:
    Jun 18, 2016
    Messages:
    2,407
    Likes Received:
    1,180

    Sep 16, 2018

    .
     
    Last edited: Feb 3, 2019
    futuremathsprof likes this.
  39. futuremathsprof

    futuremathsprof Phenom

    Joined:
    Jun 27, 2014
    Messages:
    4,398
    Likes Received:
    1,304

    Sep 16, 2018

    This. I always show my students many different ways to solve a problem. I don’t think it’s acceptable to teach students only one method or algorithm. I’ll even present it to them like this:

    Method 1: ...

    Method 2: ...

    Method 3: ...

    I don’t just show students one method and say do this as there are always multiple ways to solve math problems. For example, a student may solve an integral by using Partial Fraction Decomposition or by doing a trigonometric substitution or long division or a myriad of other ways, just like a student may use the Rational Root Theorem paired with synthetic division or long division to find the solution set for an unfactorable polynomial. It depends on the student.

    The trick is that I require students to do one of each on their formal assessments.

    To further demonstrate, when my geometry students learn about points of concurrency, specifically, finding the centroid or center of mass of triangles of various types (so right, acute, and obtuse), I show them the standard algorithm and then derive the shortcut, which is to just average the x- and y-components of all the given ordered pairs. This looks like [ (x1+x2+x3)/3 , (y1+y2+y3)/3 ]. I do this because once students understand why the standard algorithm works and are comfortable with it, I just allow them to use the formula on the homework after a while of doing the other because an employer in the real world would just want you to use the most efficient method to get the job done. On my tests, they have to know how to do both because I expect them to know both. Both methods are equally valid, except one gets you there faster.

    In a like manner, elementary students should be taught how to solve problems in multiple ways so thy can use a method that they feel most comfortable with, IMO.
     
    Last edited: Sep 16, 2018
    Leaborb192 likes this.
  40. Leaborb192

    Leaborb192 Enthusiast

    Joined:
    Jun 18, 2016
    Messages:
    2,407
    Likes Received:
    1,180

    Sep 16, 2018

    .
     
    Last edited: Feb 3, 2019
    a2z and futuremathsprof like this.
  41. Ms.Holyoke

    Ms.Holyoke Connoisseur

    Joined:
    May 14, 2012
    Messages:
    1,915
    Likes Received:
    690

    Sep 16, 2018

    So what do you think of this activity for the end of the week?

    Your job is to create a division problem with a divisor of 7 and a dividend of at least 3 digits. Create a mini-poster explaining how to solve the division problem to a 4th grader.

    I had the kids do group posters for multiplication but it was not a good activity because not everyone was participating. I like the idea of kids showing their thinking though so it might work as an individual assignment?
     

Share This Page

Members Online Now

  1. stargirl
Total: 228 (members: 4, guests: 210, robots: 14)
test