## Monday, December 5, 2016

### Pattern Blocks for Older Kids: Symmetry and Similar Figures

I've been thinking, lately, about which of our math manipulatives have stood the test of time and which haven't, and working on creating even more valuable ways to use our current manipulatives with my now older children.

It's easy to use manipulatives (or anything, really) for counting and making basic patterns and calculating simple addition and subtraction and figuring out one half, but when you're able to use those same manipulatives to demonstrate long division or multiplying decimals or more sophisticated geometry--that's when you've got a manipulative that was worth its purchase price and its decade of inclusion on your shelves!

Pattern blocks are one manipulative that I sometimes struggle with. I *know* they're useful, and the kids love it whenever I bring them out, but I feel like I'm occasionally grasping for a non-babyish way to use them in our very non-babyish math these days. It's recently occurred to me, however, that their real value is as a two-dimensional geometry modeling tool--whenever our math turns to geometry, it seems that there's always an opening to genuinely include pattern blocks in a way that adds value to the lesson.

If you want to test whether your kid *really* understands symmetry, for instance, challenge her to create a symmetrical design using as many pattern blocks as possible:

 This piece is no longer perfectly symmetrical, as the Roomba tried to eat it. I had to fish a few green triangles out of its belly!
Bigger kids like bigger projects, so using as many blocks as possible makes it more fun for them. It also gives you a chance to delve more deeply into conversations about what is meant by symmetry. With this figure alone, we discussed whether the definition of symmetry would allow the rotating line of symmetry present in the hexagons formed by two trapezoids, and the differing shades of the green triangles.

That makes a fun review, but symmetry should be pretty old news to a bigger kid. Similar figures, however, are likely new news!

It can be tricky for an upper elementary or middle school kid to draw similar figures; it's easy for human error to measure out the ratio incorrectly, so a kid who understands similar figures and how they work could easily draw a figure that didn't look correct, but she wouldn't know what she did wrong. That's good in some ways, of course, because it's self-correcting--she knows she did *something* wrong, so she has to figure it out--but it's not good for reinforcing in a kid that intrinsic knowledge of similar figures.

Pattern blocks, however are perfect, because when they're right, they look exactly right, and when they're wrong, they look very wrong. There's no getting your measurement off by 2 cm and thinking that it doesn't look quite right but just going with it because your ruler says it's pretty close.

To make similar figures with pattern blocks, you simply choose one pattern block, then try to build it larger:

This is a great way to reinforce what a kid truly understands about similar figures. For instance, in the image below, Will's trapezoid is NOT correct. She made *a* trapezoid, yes, but she did not make a trapezoid similar to the single pattern bock trapezoid, because her ratios are off. The ratio of the single pattern block trapezoid is 1:1 base:height, but her large trapezoid construction is 7:8.

Do you see how it's so much easier to explain what's wrong with that trapezoid with these pattern block models? The models make it perfectly clear.

Here's a better similar figure!

Here's the construction of a similar equilateral triangle:

Again, you can easily check and measure it by comparing those three trapezoids at the base to the other two sides: will three trapezoids also line up the same way?

Here's one good parallelogram:

And here's the creation of another!

At this point, the kids started to get a little punchy with the fun of sitting on the carpet and playing with blocks like toddlers.

One might say that they even started to behave like toddlers...
 No, no, Will! Don't eat the pattern block!

 Sigh...
And I don't even really know what was going on here, just that I had pretty much lost control of the proceedings (assuming that I had some in the first place, which I probably didn't):

And yet, even after that, these similar hexagons were created!

Notice how both children chose to make their similar hexagons symmetrical?

And boom! We're back to symmetry!

I love the interconnectedness of everything.