Friday, January 13, 2017

Manipulatives That Stand the Test of Time

I've had the idea for this post in my head for quite a while, as my kids get older (upper elementary and middle school--yikes!) and I see that although we've used some manipulatives just a time or two, or a month or two, or even a year or two, other manipulatives have been part of our regular rotation since the children were in preschool.

There are even a couple of manipulatives that I never purchased or spent the time making, thinking they'd be used only sporadically, and have simply wished that I owned several times a year since the kids were young. Silly me!

You probably know by now that these and Base Ten blocks are my FAVORITE math manipulatives. We have used them endlessly. The kids have less patience for them now that they know that whenever I whip them out, there's generally a much quicker algorithm waiting for them as soon as I'm done, but nevertheless, they're vastly useful when a kid is having trouble understanding a concept. Two days ago I used them to help Syd understand decimal multiplication--let the ten bar equal one, and you've got several decimal options available to model. And seven years ago, I used them to help Syd understand addition within 5!

Here are some other ways that we've used them over the years:
As with most of the other manipulatives that I'll show you, I've occasionally expanded our collection over the years, as we've needed them for more and more advanced work. In a perfect world, I'd have enough to build an entire decanomial square from them, but we're at the point now where we have enough to do most of what we want to do.

This is the other math manipulative that I do not know what I would do without. I consider them indispensable, and again, I have expanded our collection several times, especially with more thousand cubes. These blocks, which consist of a 1cm cube, a 10 cm bar, a 100 cm flat, and a 1,000 cm cube, are brilliant for leading a kid into an intrinsic, whole-body understanding of the Base Ten system. You have to have them to understand what you're truly doing when you add or subtract multi-digit numbers. You have to have them simply to model numbers. We use Base Ten blocks and Cuisenaire rods as a single tool, with the Base Ten blocks representing all the powers of ten and the Cuisenaire rods often (although not always--for borrowing and carrying, you should only use Base Ten blocks) to represent all the numbers in between.

Here's some of what we do with them:

Decanomial Square

We came to the game a little late on this one, as it took me literally years to decide that I wasn't going to find exactly the decanomial square that I wanted. Instead, I had Matt make one for me. 

Anyway, you can start using this one as soon as your kid starts learning the multiplication table (or before, of course, as a puzzle or to model repeat addition as area), because it works quite well as a visual multiplication table of area models. However, it's also great for all kinds of area and perimeter studies, as well as how to form equations, and is an easy demonstration of the Pythagorean theorem.

You can use the decanomial square with Base Ten blocks and Cuisenaire rods, and I am constantly in search of a cheap Montessori-style pink tower so that I can also use it to demonstrate cubes.

These are the priciest of our manipulatives, a cost that I absorbed by making this the kids' big combined Christmas present one year when I'd had a good winter in my pumpkin+bear etsy shop. Although we started using these just for free play to build for fun--which we still do!--these building materials should see the kids through high school, and they're used in universities, and even grad programs, to model some amazingly sophisticated concepts.

Here's some of what we've done with them:

Hundred Grid and Number Tiles

This, on the other hand, is easily handmade (here's how to make the grid, and here's how to make the tiles), although we do have a set of number tiles made for an overhead projector that we use on our light table. You can use the hundred grid and number tiles from the time a kid is wee, simply for naming numbers, ordering them, and counting on. You can use them for skip counting. You can use them for multiplying. If you make a second set of number tiles to match a multiplication table, you can use them for memorizing the table and for playing various multiplication games. 

Here's some of what we've done with them:

We haven't used the hundred grid lately, although I won't rule out finding another use for it in a later unit. Even if we don't, though, using it from the age of three through the fifth grade is a good amount of use!

Pattern Blocks

We used pattern blocks a ton in preschool and lower elementary, but it's actually only recently that it's occurred to me how useful they can be in upper elementary and the middle grades. We recently used them in Will's lesson on congruent and similar figures, and considering the fact that they've been using these same simple shapes since they were wee, that's a pretty darn good run!

Here's some of what we've done with them:

Here are some outside links to activities that we've done but that I haven't blogged about, myself:

If you, too, are really into hands-on work for older kids, I'd love to know what manipulatives you use and how you use them.

And if you see a Montessori-style pink tower going for cheap, let me know immediately!

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