Tag Archives: cuisenaire rods

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.

Three Math Programs at Once

This is Mushroom using Cuisenaire rods and Hands-on-Equations pieces to work variables puzzles in Beast Academy.  He was supremely happy as he did it.  It made the puzzles easier, but once he had done them this way, doing them without the manipulatives was a breeze.

variables

If anyone out there is interested in the Hands on Equations program, I highly recommend it.  Both the boys enjoyed it and, as you can see, it occasionally comes out as a visual reminder of the principles they learned.  As well, I highly recommend sticking Cuisenaire rods and base ten blocks in there to use, which allows for bigger numbers and more complexity as well as a more clear visual representation of the numbers.

Math Forks in the Road

Mushroom is rapidly nearing the end of Miquon.  I predict he’ll be finished with Purple within the month and that’s if we draw it out.  BalletBoy has recently finished Math Mammoth 3.  In the meantime, we’ve been trying out Beast Academy.  BalletBoy likes the graphic novel textbook, but the workbook isn’t right for him.  Everything in it is either too easy or too hard.  I haven’t felt like he’s gotten a lot out of it, so I don’t think he’ll be continuing other than to read the textbook for fun.  If you’re not familiar with Beast Academy, Tinderbox has an excellent review of it here.  Essentially, through a graphic novel about monsters, it introduces math in a very conceptual way and the more difficult practice problems often practically invite frustration.  They want you to try and fail and try again and have an epiphany.  Shockingly, it has been working for Mushroom, which is re-emphasizing the realization I’ve been having lately that he is actually pretty good at conceptual math thinking, even if his calculation skills lag behind.

The other day, we were covering the triangle inequality in Beast Academy and Mushroom wasn’t getting it, so I pulled out our constant friends the Cuisenaire rods.  See how the triangle on the left works because the sum of the two shorter sides are longer than the long side?  But the triangle on the right can never work.

photo (98)

For a split second, when I didn’t see this activity on Education Unboxed to link it, I thought I had made up a new use for the rods, but nah, I found it somewhere else.  Sometimes I think the rods are pure magic.  They really can be used to teach nearly any math.

What’s next for math at the Rowhouse?  I don’t totally know.  Mushroom will continue Beast Academy, but he needs the ability to switch away when he gets frustrated.  The spiral, jumpy, non-threatening nature of Miquon worked so well for him that we have to find a way to recreate some part of it.  We have several books like this one which should help us use the rods, but we need something else.  I know that Singapore, Math Mammoth and MEP aren’t right for him and it seems silly to begin Right Start only to have it run out on us soon thereafter.  What we do is still a bit up in the air.  For BalletBoy, after a lot of discussion between him and myself, we’ve decided he needs more practice with third grade concepts so he’s going to do MEP 3b, which will be a lot of review and a few new things, alongside the Singapore Challenging Word Problems 3, which we’ve done a little in, but not much.

I feel very unsure about math right now and am worried we’re playing hopscotch with programs a little too much.  I’m trying to be mindful of the need to stick with a sequence to help us keep gaps at bay.  On the other hand, I feel like when we do stick too closely with a single program, both boys have trouble honing their math thinking, not to mention that they get bored and frustrated.  It’s definitely a time of some self-doubt here.

Miquon and Cuisenaire Love

After using a hodgepodge of half a dozen things for math this year, Mushroom has settled into a regimen of mostly Miquon with the other resources, including Singapore Challenging Word Problems, Math Mammoth, MEP, and Right Start games, taking a clear supporting role.  After dallying for so long to find his stride and taking some diversions for other topics, he’s just now starting Miquon Green, which is essentially the second half the second grade curriculum.  But no worries.  I’d rather go slow and feel like he gets it than rush ahead.

I feel like I’ve really hit the Miquon stride with him.  It’s so very different from the mastery approach I take with BalletBoy’s Math Mammoth.  Instead of covering a topic from head to toe, not releasing until a child can recite it in their sleep, Miquon gives you little pieces of the puzzle in digestible chunks.  A child doesn’t have to master multiplication by fractions.  Instead, Miquon allows them to become confident with the easiest problems first.  I can really see the ways in which this ought to help Mushroom down the line see his way to solving math problems with mental math and common sense instead of by pulling out paper and pencil to do a complicated algorithm (or, heavens forbid, a calculator).

I’ve also found a good balance of really using the Annotations to build supporting activities for the lab sheets using the Cuisenaire rods and a white board.

Speaking of those terrific C-rods, a poster on the Well-Trained Mind Forum has created an invaluable set of user friendly videos about how to use the rods to teach, well, nearly everything.  Whether you’re a Miquon user or just Cuisenaire curious, please go check it out here at Education Unboxed on Vimeo.  It’s an amazing free resource, one of those things that makes me feel like the homeschool community is so generous and cool.  Here, this one on square numbers sums up what’s so nifty about using C-rods and Miquon with kids to teach concepts used reserved for older kids: