Micro-manipulatives

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!