Fiona’s interest in math has re-ignited the past few months. She is definitely thriving with Singapore Math. I’m already dreading the day she finishes it and we need to find something else. It’s just her style and just her pace. She loves the friendly unintimidating style of presentation, and the conceptual approach usually fits her to a tee. Not only that, but when she is muddled or confused by something, the sort of explanations that make sense to me work perfectly for her. It’s so easy guiding her through math learning!

Since November she’s completed a year and a half of the Singapore program. Every time she started a new semester I would look at the upcoming syllabus and think “Ah, here’s where she’s finally going to hit concepts that aren’t going to come easily.” But I’ve been wrong every time, so I don’t even bother thinking it any more.

Recently she began the book (4B) that covers decimals in depth. She has an awesome grasp of place value, which I credit partly to the way her mind organizes things, but partly also to the use we made of cuisenaire and base-ten manipulatives back when she was four. I thought that might be a good starting point as we began exploring place value on the other side of the decimal, so we got them out again. Shown in the photo are the large orange 1000-cube (back right), three orange 100-flats (middle left), five orange 10-rods (upper middle) and seven white 1-cubes, all from our cuisenaire and base-ten sets. 
The new fun came with the miniature and near-microscopic new manipulatives we created, shown to the right of the white 1-cubes. We got a piece of cardboard of the appropriate thickness and cut it into 1-cm squares. Stacked up, ten of them were just about exactly the size of a 1-cube, so these were our tenths. Fiona was very impressed. She thought it was hilarious when I started cutting one of the tenths into ten miniature rods. And when I then cut one of the mini-rods into practically microscopic 0.001 cubes that look more like grains of sand than math manipulatives, she thought I was crazy. 
But it was fun, and it worked. She could see that, just as we could (theoretically) combine 1000-cubes to make bigger and bigger manipulatives denoting 10,000 or 1,000,000, we could (theoretically) continue to slice and dice our sand-grain 0.001’s into smaller and smaller bits. And she had fun creating manipulative representations of numbers like 1425.174, and 20.32, and even 1000.001.
Once she has explored concepts concretely or symbolically, Fiona easily internalizes those ideas and rearranges them in her imagination, developing short-cuts and seeing patterns. The manipulatives will be put away now, possibly for good. But I don’t think we’ll bother saving the 0.001’s to pass onto another homeschooling family!
Micro-manipulatives

8 thoughts on “Micro-manipulatives

  • March 22, 2010 at 9:59 am
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    My son just asked for 'more math' recently, so we are on the hunt for a more in depth program that his engineering oriented mind will enjoy. I have heard great things from you on this, we may try it out.

  • March 26, 2010 at 2:05 am
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    OOh, that looks like fun. DS isn't into manipulatives, his Maths has always been done verbally in the car, so place value consisted of a conversation around the concept. But I recently got the base 10 set for DD, and she didn't just use it for building Roman camps, so it's possible that in a couple of years I will also be chopping cardboard into titchy bits. What a lovely idea.

  • March 26, 2010 at 10:01 am
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    We really like the Saxon math books for homeschoolers. Their explanations make sense, and the way they build upon each lesson works well for us.
    Blessings,
    Nikki

  • March 26, 2010 at 5:09 pm
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    Beccy, Fiona's definitely more of an oral math kid. I don't recall the last time (other than “playing the algebra board game”) that she's actually used manipulatives. But I do credit having a visual metaphor for place value as having been helpful for her in mastering those multi-digit algorithms for multiplication, division and the like. Just a one-session visual demonstration seemed to be enough, combined a with verbal explanation. The base-10 set went away after that. Which is just to say that I don't think manipulatives necessarily need to be used by the child to be helpful.

  • March 26, 2010 at 5:10 pm
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    Starcat, I'm glad Saxon works well for you. It definitely wouldn't work for us, but family and every kid is different.

  • March 31, 2010 at 3:22 am
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    I think my main issue with our base 10 set is that it cost an obscene amount of money. I'm glad I have 3 kids, to get some non Roman-camp-building use out of it. I got it for my eldest, and either our first session with it was the necessary once-off explanation, or I bought it too late (I suspect the latter). At least I remembered to bring it out for DD when she was still questioning concepts, and there is still the baby. 🙂

    I have to say, for nearly all my uses, duplo or lego bricks (or popcorn kernels in shot measures) have been enough. But DD does seem to *need* manipulatives. Maybe she is a different child, or just explaining subtraction and multiplication to a 4 year old require it.

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