Friday, December 9, 2016

Homeschool Math: Zometool Geometry

We've been using Will's recent geometry unit in Math Mammoth to do a lot of enrichment with Zometools, which are a practically perfect geometry modeling manipulative.

Although I loved geometry as a kid, the modeling of two-dimensional and three-dimensional figures is clearly a place where my own education was lacking, so I've been relying on other Zometool resources to mentor us all.

Zome Geometry gets very quickly out of our depth, as there's very little of the hand-holding that I've come to expect in most teacher's manuals (in fact, when paging through it I feel like young scholars of old must have felt upon being handed an edition of Euclid's geometry and told, "There you go! Read up!"), but the beginning units are well suitable for doing some interesting modeling of two- and three-dimensional figures.

So that's what we did!

We're first meant to make these stars and calculate the interior angles. After you've done a few of those, it's easy to create your own formula for calculating the interior angles of a circle.

Now we're trying to use the star models to make regular polygons. This only works for some of them, and for others, you have to delete some of the spokes.

Will got involved in her own extension activity.

It turned out really cool!

On another day, we were asked to use our polygons to construct both prisms--easy!--and antiprisms--SUPER hard, as we didn't have any hand-holding!

I struggled and struggled and struggled to construct an antiprism from my pentagon model. I found many interesting symmetrical constructions, but no antiprisms!

Will struggled and struggled and struggled as well, first to create antiprisms from her squares, and then, after she gave up on that, to contruct antiprisms from triangles.

She got really frustrated before she finished, but finally...

And this girl mostly did her own thing, but at least she was at the table with us! I have come to believe that the ten-year-old schoolwork stubborn streak is a REAL thing, now that my second kid has it, too.
We're playing around with Zometool geometry some more today, but now that Will has moved on in her Math Mammoth to integers and Syd to graphing, our math enrichment will look very different next week.

Life-sized Battleship, perhaps?

Wednesday, December 7, 2016

Christmas Craft: Paint-Filled Clear Ornaments

Last week, I wrote a round-up of clear ornament crafts for CAGW, primarily because I scored a couple dozen clear ornaments from a Joann's doorbuster and needed ideas for what to do with them.

My favorite, and the one that seemed the most kid-friendly (and the cheapest!), was the one that's all over Pinterest this year, with people everywhere filling their clear ornaments with acrylic paint, swirling it around, and then pouring out the excess.

It really is kid-friendly, super cheap (if you have some craft acrylics), and SUPER fun!

And it really is just that easy. You squeeze craft acrylic paint into a clear ornament--

--swirl and shake it around--

--and then set the ornament upside-down back on top of the paint bottle to drain back out:

I discovered in the process that I had some mostly-empty paints that I had bought more of but hadn't yet replaced. This is how you get out all the last dregs!

Oh, just making sure that I don't waste a single smidge of that almost-empty paint, even though I bought new ones...
Posted by Crafting a Green World on Tuesday, December 6, 2016

When Syd came to join us later (she'd been busy baking cherry bread with her grandmother), she did even more experimenting. She played around with our artist's acrylics, although she quickly discovered that it was too thick to work on its own. It did work better when she squeezed it in with a couple of colors of craft acrylics; the craft acrylics seemed to thin the artist's acrylics down enough to give it some flow, and that's how she got such lovely golds and silvers into her ornaments:

She even played with putting in glitter, and it worked great!

Although the results are gorgeous, this is actually a quite process-oriented work, and both kids (and I!) worked contentedly at it for a long time. It was very nice to swirl the colors around and watch them flow! 

We left the mixed-color ornaments to rest upside-down on top of the plastic carton that they'd come in, since of course we couldn't pour the paint back into the bottle all mixed up. After the excess had drained out, we did have to put a second coat into a couple of the ornaments, as too much paint had drained out and left empty streaks.

These ornaments also probably aren't suited to being hung in direct sunlight; the paint isn't uniformly thick, and although our ornaments all look great in our lit room, I noticed as I was taking photos that if I held them in direct sunlight, I could sort of see through some parts of some of them.

That being said, when hung on our tree they look fabulous, as if they're enameled:

Christmas colors annoy me, so I indulged myself by making several ornaments in black and grey and navy blue. You can't just go out and buy colors like that in the store!

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!

 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.

Friday, December 2, 2016

Homeschool Book Review: Three-Dimensional Art Adventures

You might have noticed that I don't often have art as a subject in our weekly lesson plans. Primarily, that's because Matt has an art degree and he gives the children an art lesson every weekend. I consider them to be private art lessons, thriftily outsourced!

I do like to do art with the kids, but I don't consider myself skilled enough to prepare my own lessons, so I really appreciate packaged lessons that include study of an artwork and a hands-on extension. I have several of those kinds of resources in my Homeschool: The Arts pinboard, my favorite of which is this site with leveled art history studies. I especially like to incorporate those lessons into our other studies--we used the lesson on Daniel French, for instance, in our study of the Lincoln Memorial.

The other way that I like to use art lessons, if I don't have an academic context to put them in, is as a fun weekend activity to do with the kids. We spend a ton of time together during the school week doing projects, so you'd think that the last thing that we'd want to do on a weekend is sit down for another project, but it seems new and different, somehow, when it's not also a task to be checked off of a work plan.

That *kind of* explains why I received Three-Dimensional Art Adventures for free from a publicist back in July, and I'm only just now ready to write about it. I made note of the most promising activities, then put the book in with my other resources, and when the time was right for a particular activity, there it was, ready and waiting for us!

I think the kids' favorite of the activities that we tried is the "trick hand." The lesson began with a study of From the Knees of My Nose to the Belly of My Toes, which the kids found fascinating, then guided us through the creation of our own "tricky" piece:

I can't tell which one, but underneath Will's drawing is for sure one of those LEGO books I was telling you about yesterday!

Does it annoy you to try to draw or write on a picnic table? We do it all summer, and it bugs the crap out of me! Painting boards are on my long-term to-do list.

This is when the magic happens!

Everyone's turned out really well, although we all figured out ways to make the effect even better next time (use a ruler to draw the straight lines, elaborate the curve on the curvy lines, make the lines as close together as we can, etc.), so it's still an activity that's repeatable.

Another week, during our shark unit, the kids became fascinated with the clean, streamlined silhouette of the shark, and so I took that opportunity to introduce the "Capturing Simplicity" lesson. It began with a study of a sculpture from Ancient Greece (and now I'm putting that down in my Greek mythology lesson plans to look at again when we study Hermes!), and continued with our own simple, sculpted silhouettes:
I don't know why I didn't photograph Will's, but she did her first initial. It looks really cool!

The tutorial calls for air-dry clay and paint, but we used Sculpey, and it worked perfectly.

I've often wanted to create some sort of cataloging and indexing system for myself, to use with my homeschooling resources. I have tons of print and digital resources, and when I create unit studies, I'm always flipping through every single thing, adding a reading from here and an activity from there. I mean, just in this book alone, the artwork studied ranges from Ancient Greece to modern, geographically circles the world, covers a huge variety of themes, and uses materials from nuts and bolts to pen and paper to fabric to floral wire.

Next on my to-do list from the book: the collage lesson, just because it's been ages since the kids and I have done collages together (and I have a bunch of random materials that I've been saving up and would love to get used up!), and the lesson on sculpting movement using floral wire as the medium.

Because Hermes!

Thursday, December 1, 2016

Our Favorite Kids' Books of 2016

As a family, we have read thousands of books this year. To be fair, Will, who reads several multi-chapter books every single day, has pulled most of the weight in getting us to this number, but the rest of us are no book-reading slouches, either!

That being said, I actually feel a lot more confident in giving out our favorite book recommendations for 2016. I mean, we played with a few toys in 2016, but we read a LOT of books.

We came to this late in the year--I'd read Wonder before, but the kids just read it last month for a library book club meeting. It was, however, a revelation for them, one of those instances when someone reads the perfect book at the perfect time. Will, who normally prefers books that take place in imaginary realms or at least star talking animals, even loved the book, and Syd listened to it once, read it once, listened to the Playaway of the Wonder stories SEVEN times, read pretty much all of Mr. Brown's Book of Precepts out loud, and recently requested the Wonder Playaway again so that she could listen to it some more. It's a beautiful book about a kid dealing with a really big difference, and all the other kids in his life who have to learn how to accept really big differences.

And if you read it, you MUST read the Wonder stories next. Julian's chapter touched me more than the entire first book.

Percy Jackson has been another absolute phenomenon this year, at least in Syd's world. Will and I have read them all, but Syd? Oh, my gosh, she LIVED in them. For months. Still does. She talks about Percy and Annabeth like they are friends who live in the next town over, and knows just as much about their god and goddess parents. This obsession was the inspiration for our current Greek mythology unit study, which has been just as big of a hit with both kids.

Syd likes Riordan's other series, as well, but that's nothing in comparison to how deeply she feels for Percy.

Normally, Will has a "love 'em and leave 'em" attitude towards the dozens of books that she blows through every week, but Skulduggery Pleasant has stuck with her. The books are witty, gothic but not spooky, and full of adventure and intrigue, She is smitten by the idea of "taken names," and is desperately into the intricate plot of the series of books.

We all really like these books of famous events and stories retold in LEGO, but Will especially loves them, and has discovered new genres of literature and new events in history. The assassinations book isn't completely kid-friendly (although... why would you assume a book about assassinations would be?), as one of the highlights of the story of Boston Corbett (the guy who killed John Wilkes Booth), is that he was a religious fanatic who castrated himself before dinner one evening because he was upset at having been tempted by some prostitutes during his walk home.

And yeah, there's a LEGO illustration for that. Anyway, Will was totally titillated by this tale, so much so that we conducted more research on Corbett, and even found some photos of the hole that he spent the latter part of his life in---yes, a hole. Will REALLY wants to make a pilgrimage there one day.

We read a LOT of comics and graphic novels in our family, but many of them aren't kid-friendly. Will can read whatever she wants, but Syd is my baby, so it's nice to have graphic novels that everyone can enjoy, but that she, especially really likes. Phoebe and Her Unicorn is super kid-friendly, but it's not baby-ish--the unicorn has an attitude, and the banter between the two is witty and engaging. Phoebe and Her Unicorn is actually a comic strip, and it's my dream that one day it will run in our newspaper, perhaps instead of For Better or For Worse, which I abhor.

 And speaking of graphic novels that Syd loves... she has spent the entire year worshiping Raina Telgemeier. First, she fell in love with her Babysitter's Club adaptations--and I even tried to give Syd the novels, but she didn't like them, just Telgemeier's graphic novels of them--then she discovered her original works, and has eagerly read all of them several times. I also really like her work, which has the kind of drama that many tweens like, but isn't schlocky. Her newest novel, Ghosts, has only been out for a couple of months, so it's still possible that you could happily surprise a kid who hasn't read it yet.

I've mentioned a few times before that we have a Family Read-Aloud. Now that the kids are older and their evening extracurriculars run later, we don't do this as often as we used to, but at least two or three nights a week, we come together as a family and Matt reads us the next chapter of our current book. The kids and I braid each other's hair, or color in our Tolkien coloring book, or just sit under a blanket and listen. For over a year now, it's been Tolkien, first The Hobbit, and now we're well into The Lord of the Rings--it'll probably take us another year, at least, to finish! I am very adamant that the kids do not see film adaptations of books until they've read the books, so although we've watched the Hobbit films as a family (with MUCH criticism), we're saving the wonderful Lord of the Rings movies until after we've finished the entire book. It's even better that way, as our world-building can take place entirely in our heads. We talk about it a lot, reference it to each other, the kids and I have been known to invent Lord of the Rings fanfiction, and basically it's just given us a very large common reference point in interests and conversation. I highly recommend it as a family read-aloud.

Syd recently re-introduced us to David Wiesner, when she brought home Mr. Wuffles and Matt and I basically snatched it out of her hands so that we could read it, too. If you have kids, you probably read him a lot when your kids were little, but then forgot about him when you stopped browsing the picture book aisles at every library visit. Well, he's still awesome, and still fun even for older kids and adults (I'd argue that he's even MORE fun for older kids and adults, because we get his sense of humor better).

Probably every kid in America has read the Warrior Cats series, which is fine, because they're awesome. They're another of the few books that Will still re-reads and still talks about after she's read them, so out of the thousands of books that she's read this year, you know they must be very, VERY good! This is also a good series if you've got a voracious reader, as not only are there a billion books in the series, but there are also manga and field guides, etc.

I could seriously give you dozens upon dozens more recommendations of books that we've read and enjoyed--I didn't even tell you about the Al Capone series that we love, or the Dark is Rising series that we're currently listening to in the car, or the more mature graphic novels that we let Will read with us--so feel free to comment if you want even more recommendations or something more specific. And also feel free to comment with your own and your kids' own favorites of the year, because we can ALWAYS use something new to read!


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