Long Division

Mushroom actually made this long division problem for himself because he was enjoying doing these so much.
Mushroom actually made this long division problem for himself because he was enjoying doing these so much.

I wrote about math lately at the Rowhouse, but since long division is the heart of fourth grade math woes, I wanted to post what we’ve done because I’m feeling in a good place about it.

I felt a real frustration that there didn’t seem to be any books specifically about long division for kids.  I looked and looked, but everything I found was little more than practice, not a full book about division.  That really surprised me since I know this is a topic that a lot of kids need a second stab at.  We did like reading the section on division in the Murderous Maths book Awesome Arithmetricks, but I wished there was a book of conceptual problems that would build up understanding of division of larger numbers.  Or even a single living math story book that would present some of the concepts.

Up until recently, the only division the boys had done were division drills, division with zeros, and partial sums.  In the partial sums method, you break the dividend into two or more parts that are easy to divide.  For example, in 287 ÷ 7, you would make it (280 ÷ 7) + (7 ÷ 7).  This is a nice lead in to traditional long division and in some ways is harder since there’s not a step by step algorithm.  This way is introduced in the final books of Miquon really clearly.  I felt like the kids were reasonably proficient with the drills and the partial sums, but that left the dreaded columns of long division.

To introduce the long division algorithm, we turned to the our old friends the Cuisenaire rods.  While we won’t get rid of them any time too soon, I realized this is one of the last major topics we can cover with them.  I feel a bit teary just thinking about it actually.  We have loved these rods so much and used them for so many things.  It’s not that they have been out on the table every day for the last five years, but they have played a role in every major math topic we’ve covered since kindergarten.

Over at Education Unboxed, one of the best free resources for elementary math there is, there are several great videos about doing long division with Cuisenaire rods.  I had to borrow a few extra tens from a friend to help make as many exchanges as we needed in order to illustrate these ideas.  Basically, you think of multiplication as the area of a rectangle, so the divisor and the quotient are the two measurements of the side of the rectangle.

After using this method for a few days, we have gotten into a pretty good place with long division.  The kids feel like they can tackle any problem without the rods.  When they get tripped up, such as Mushroom did with a problem that didn’t have any tens in the quotient, we can go back to the rods and model the problem and clearly see the mistake.

Here’s hoping that this good streak with math holds.

One thought on “Long Division

  1. Thank you for this and all of your other posts. So good to know that I am not the only one who gets teary over things like cuisenaire rods. For us, it was saying goodbye to the abacus we’ve loved since my daughter’s preschool days. Go Mushroom and Ballet Boy! Glad to hear the division is going swimmingly.

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