How to Teach Hands-On Long Division

Frustrated teaching long division? Monopoly money to the rescue! You’ll learn how to teach your child both HOW to do long division and WHY it works.

When I was an elementary school teacher, I always knew when it was long division week in the fourth grade. My normally positive and energetic colleagues would come to the staff room slumped over and exhausted, commiserating and complaining about the drudgery and frustrations of teaching so many children this complicated process. I particularly recall a day when one teacher, normally very reserved and quiet, demonstrated the “long division dance” that she’d created out of desperation to help her students learn the steps!

long division

Even though long division can strike fear into the heart of even veteran teachers, I have two pieces of good news for you:

  • As homeschool moms, we only have to teach long division to one child at a time. (Well, maybe two if you have twins. But not 25.)
  • With a hands-on approach, children can not only learn how to do long division, but also why it works. This saves a lot of time in the long run, because they can more readily remember the steps, find their own mistakes, and deal with more complex long division situations.

In the video below, I demonstrate how to teach long division so that your child will learn both the how and the why of long division. (Or, if you want to get a little jargon-y, so that your child will develop both procedural fluency and conceptual understanding.) All you’ll need is a sheet of graph paper (for keeping the digits lined up) and some play money with 1s, 10s, and 100s.

(Sorry that some of the money is off-screen. My production equipment consists of our very basic camera on a tripod, and I didn’t zoom out quite enough!)

Happy Math!

19 thoughts on “How to Teach Hands-On Long Division”

  1. Kate,
    Thank you so much for posting this! It is exactly what I was looking for. I am currently doing my field experience and am working with a student who has a hard time getting motivated. I think this will help tremendously. I have a question about how you might assess them after teaching them this lesson. I hate the “work sheet” approach and was wondering if I could pick your brain about any other ideas you might have. Thank you again,

  2. Glad it was helpful, Haley! You might try using a small whiteboard rather than worksheets–kids often find it less intimidating to work one problem at a time with a whiteboard rather than facing down a whole page of them.

  3. Two-digit divisors are hard! If he’s struggling with the concept of it, I’d go back to 1-digit to review the overall process and then show him how the 2-digit divisor process has the same steps but just with more difficult calculations.

    But for most kids, it’s the calculations that are the problem. Usually, it’s the estimations. My main advice is to always round the divisor up to the next multiple of 10 to make the estimations easier. So, for example, if you’re dividing 837 by 46, round the 46 up to 50. Then, after he multiplies and subtracts, if he finds that his estimate was too low, have him adjust the number in the quotient and subtract out another group (rather than erasing all the work.) This is hard to explain in words, but I hope it makes sense.

    And my last suggestion is graph paper, or lined paper turned sideways so that the lines help line up all the columns. This makes a huge difference for many kids. Hope this helps!

  4. Do you have any tips for helping kiddos memorize the multiplication facts? We are
    Working on it, but having trouble with memorizing them. Thanks!

    • I usually teach counting by 2, 3, 5 and 10. This makes it easy to figure out these facts. I would get a chart and fill in the ones you child knows . Start with basic rules of zero and 1. Fill in chart. Then as long as your child knows addition doubles 2+2 7+7 times 2 is easy. Think 3*2 is 3+3. I would teach 5 and 10 next. Also explain it doesn’t matter which way they go 2*3. Is same as 3*2. Now your chart is pretty full of known facts. The 3s are easy if your child can count by 3. Then teach doubles and this is memorizing. 2*2 , 3*3 done already. 4*4. A four by four is a mean machine I will get one when I am 16 therefore 4*4=16
      5*5 is 25: 2 Fives is 2. 5 or 25. See chart getting filled in …
      8*8 I are and I ate til I was sick on the floor 8*8=64
      The rest is really memorization. Except the 9 times table. You can use you finger I am sure there’s a you tube video. Hope this gives you some ideas. Instead of flash cards there is War card game instead of turning over 1 card you put down 2 and multiple, rolling dice and keeping track of score adding together

      • thank you I also do that I do write a pice of paper and made it into a card I put 5*2 or 4*9 on a card and shaved them into an envelop shack it pick out the one on front of it .

  5. This is amazing! My daughter is a kinesthetic learner and I can already she her grasping this concept through this activity! God Bless you and Thank you!

  6. Regarding the question on how to teach multiplication facts, and Kate’s ‘Facts That Stick’ books: these books are worth every penny! My daughter and I have used all four of these books (addition, subtraction, multiplication, and division) with my granddaughters. They went from taking 10-15 min. to complete a 100 problem drill sheet to 4-5 minutes to completion. We will use them with the seven year old as soon as she is a bit older, to eliminate a lot of time and frustration. My suggestion is to buy the PDF so that you can print out as many worksheets as you need, especially if you plan to use them with more than one child.

  7. What a simple, great way to explain long division hands on! I would have loved that as a child, but instead I just memorized steps.

  8. Do kids really need to learn how to do long division with a 2 digit divisor? This is one instance where using a calculator makes a lot of sense. I think:
    -Single-digit long division is useful. It helps one to understand the idea of leftover units and exchanging them with lower units as you showed.
    -Estimating long division with 2 digit divisor might be useful as well
    – Learning/memorizing multiplication tables, single-digit add/subtract are useful.
    But I don’t see the use of spending too much time on long division with 2 digit divisor. More important things to work on are: Algebraic thinking, word problems, order of magnitude, estimation

    • Hi Ozdal,

      I agree that it’s not worth a lot of teaching time, for exactly the reasons you mention. It’s worth it for kids to understand the concept and solve some problems, but not worth cranking through pages and pages of tedious problems.

      Happy Math!

  9. thank you I also do that I do write a pice of paper and made it into a card I put 5*2 or 4*9 on a card and shaved them into an envelop shack it pick out the one on front of it .

  10. I just stumbled across this article tonight. A math teacher and recently a 4th grade one.
    Came home to day feeling defeated on teaching this skill.
    The heavens above were smiling on me. This is such an easy way to do this small group.
    Thank you for enlightening my fire , I am taking this and going adapt it to my students.
    Much appreciated!


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