A Visit to St. Nick, and the Christmas That I'm Enduring

I had a different kid a year ago. I had a kid who I bribed to do her schoolwork. Who took every instruction, whether it be "brush your hair" or "please pick up that piece of paper from the floor" as an invitation for a fight to the death.

Who refused to visit Santa.

This year, that same kid sits down and completes all of her schoolwork every day without prompting. She has her moments, but she's a genuine help most days. She even brushes her hair!

The other kid, mind you, hit her tweens the second that she turned ten, and she's now my kid who sneaks out of her schoolwork and wanders off to play when she's given a chore.

But she's still very much a kid at heart--they both are, really--and this year, hallelujah, I was able to get them both over to Santa's couch for a nice little visit:

It was a Christmas miracle.

Of course, you can't visit Santa at the Children's Museum without doing all the other stuff at the Children's Museum, too!

I didn't realize something until we were in the dino dig pit for the thousandth time in the children's lives and a friend whom we'd met there asked me how this set-up is different from the real dino dig site. I looked around us, blinked in surprise, and said, "Huh. Not much, actually!" The experience of digging, chipping off the matrix from the fossils, is pretty similar to what it's really like to expose fossils in the field. The walls around the pit contain a 360-degree panorama of what actually does seem to be our South Dakota dig site. And outside the dig pit is a wall with more fossils to chip out, and those fossils are embedded into a bank that is just about identical to the actual bank that we actually dug actual fossils out of!

Every Christmas, and again in February, the museum transforms its stairway into a slide!

Last year, one of these kids would NOT ice skate on the pond.

This year, however?

Yeah, she seemed to feel okay about letting loose.

 This one's always okay with letting loose!

I'm not going to lie--this Christmas is hard. I feel guilty every time I mention how hard this year as a whole has been for me, because there have also been so many amazing and wonderful things. I mean, how petty does someone have to be to call a year in which they went on a cruise to Alaska "hard"? It feels gross to call it such. Babies are dying in Aleppo. I'm lucky and I know it.

And yet... this year has been hard. This Christmas is hard. Not even a minute ago, in response to something casually cruel that Will said (despite her attitude change, she *is* still a tween...), I looked up from this computer and said to her, "I'm not going to tell you that you can't feel the way that you do, because you can, but I will tell you that you're feeling that way because you're immature. I would give so much to be able to see my grandparents again, and one day, when you're more mature and it's too late, you're going to feel the exact same way."

The last time that I saw my grandfather was last Christmas.

So I'm really not trying to make this "the best Christmas ever" or any of that other crap. I'm just trying to get through it. I'm putting on my game face as well as the holiday music. I'm faking it until I make it. I'm doing all of the other cliches that describe what you do when you need to make something great for your kids while you, yourself, are feeling deeply sad.

It's a fortunate thing, though, that when you deliberately try to give happiness to your kids, they have a tendency, the little ice skaters and Santa's lap sitters and pretend dino diggers, to give it right back to you.

Work Plans for the Week of December 19, 2016: Food Crafting, Lots of Science, and CHRISTMAS!!!

Yes, these work plans are late. We had a day trip on Monday to the Children's Museum of Indianapolis, and day trips always throws off my blogging schedule, as I can only find the time to write on my personal blog on the days that I'm not doing my paid writing for CAGW.

These work plans are also a bit of a repeat. School last week went okay, but I seriously underestimated how much a business trip of Matt's would affect us. It was quite an eye-opener to realize how much I depend on my partner to get that second load of dishes done and that second load of laundry and haul the kids around to their evening activities and supervise the completion of their last bits of school so I can veg out and even turn off the TV after I fall asleep. Nothing like waking up at 3:30 am because YouTube randomly switched from my livestream of the ISS to a video on the hollow Earth conspiracy theory, not being able to get back to sleep, and then spending the entire day either chauffeuring kids or madly scrambling to make party food that we need THAT DAY and etsy orders that have to be shipped THAT DAY and checking my email to confirm the address of Will's Pony Club party and discovering that not only does it start half an hour before I thought it did, but that there's a GIFT EXCHANGE!!!

I donated a publicist's review copy of a cookie decorating book and kit to the cause. Not only can the publicist apparently just hold her breath and wait for that review that now isn't coming, but dang it, it was also going to be a Santa gift for Syd!

AND I get there to drop Will off and a co-hostess expresses (maybe slightly passive-aggressive) surprise that I'm not staying, because apparently all the other parents are staying, even though there was nothing said in any of the emails about parents being expected to or even welcome to stay. And she's the first kid there, because maybe it really does start half an hour later but there was a mistake on the email? Or I'm just really prompt? I never figured that out. And then Syd and I get home so I can make a play dough etsy order real quick and find that the dog has pooped on the rug by the door, maybe because she wasn't feeling well or maybe because we'd been in and out of the damn house all damn day and hadn't had time to play with her. And then Syd and I spend all of Will's party time making and packaging my play dough order--

I couldn't have gotten it done without my play dough chef!

--then haul the dog into the car with us (because I'm sure as hell not leaving her alone again!) to run back to get Will 15 minutes early from her party so I can go in and pretend like I'm a good, attentive mom, only to find her alone with the hostess AGAIN because all the other guests and their good, attentive moms randomly left fifteen minutes before THAT.

We drive back, get the dog in the door, and are greeted by Matt, who FINALLY got home, after a delayed flight, from his trip. I am just a teeny bit ashamed to say that I walked straight into his arms and burst into tears.

And that, Friends, is why that Friday's schoolwork became Tuesday's schoolwork, completed on Tuesday without manic energy or fuss of any kind.

Memory Work this week is mostly spelling words, because I can't make Syd do her Wordly Wise at home so we're doing it in the car, where she can't get away, instead. Books of the Day are more books from the Banned Books list and some pre-reading for the Black History Month essay contests that the kids usually enter. Other daily work includes typing practice through Typing.com, keyboard with Hoffman Academy lessons, journaling or story prompts with me, Wordly Wise for Will and Word Ladders for Syd, their current events journal (it wasn't meant to be a long-term project, but I keep extending it because I'm so pleased with how it's going), and for Will, SAT prep through Khan Academy.

Tangent: If anyone is interested in our prep plans to get Will ready to take the SAT in the spring, as a seventh grader, just ask!

And here's the rest of our week!



MONDAY: We spent the day at the Children's Museum!

TUESDAY: Both kids are almost done with their respective semesters of Math Mammoth, with Syd finishing her final review next Monday (because yes, I am making the kids do math next week so that they can finish their respective semesters by year's end) and Will doubling up math lessons next week and finishing on Friday. They're both doing coordinate planes still, although Will's math adds in integer calculations and Syd's math adds in graphing with different types of graphs.

That's one reason why the coordinate grid foldable, although it's not as hands-on as I usually like my hands-on math to be, is so useful; the kids retain their calculating ability but often lose the terminology, so after they labeled this coordinate plane I had them put it in their school folders to keep as a reference tool.

The kids do one lesson a day in their Analytical Grammar (for Will)/Junior Analytical Grammar (for Syd); Will is currently studying adverbs, and Syd is studying prepositions. In February, after essay contest season and the National Mythology Exam, I'd like to start a packaged writing/literature unit with both kids (I'm a little embarrassed that I don't want to create my own curriculum, as that's exactly what I used to do for years as a freshman comp instructor at our local university... but I don't!), so hopefully we'll have reached a good pause point for Analytical Grammar by then.

There are so many fun activities to explore the difference between inherited and learned behavior, but we did just one more to cement the concept before moving on: the Animal Survival Scenario worksheets from this unit. I required the children to answer in complete sentences and to provide a video example to flesh out one of their claims. Will used this gorgeous video from Planet Earth to flesh out her claim that swimming is a learned behavior in polar bears.

Aphrodite and Ares are our subjects in Greek mythology this week; interestingly, D'Aulaire's Book of Greek Myths does not tell us the story of Aphrodite's origins, so Will helpfully read it to us from The Myths of Greece and Rome. We prefer Guerber's edition to the Bullfinch, just so you know. The trading cards are also coming along well, with the kids drawing thoughtful images on the front and writing relevant facts on the back of each.

I had thought that I would change our our literature activities by the week, but the kids are really enjoying reading and checking books off of their MENSA reading lists, so we're just going to keep running with it. I'm looking forward to graduating Will up to the next list, because she's been complaining lately that she's read everything in the children's department and most everything on the young adult shelves--and she has! I walk the adult fiction shelves with her and help her choose books sometimes, but of course mom recommendations are always suspect, so more reading lists with more books that she hasn't read are ALWAYS welcome!

WEDNESDAY: The current module in our Animal Behavior MOOC is animal communication, and after watching the introduction to the module, this day's assignment asks the kids to interact for ten minutes with a pet, then write an essay describing the animal's communication during that interaction.

Will has always been a reluctant writer, so I'm thrilled that Syd loves it so much. She's taken to the Junior Scribe badge activities with gusto, completing them all independently, although I do have vague plans to perhaps encourage her to illustrate her work and then get it printed and bound into a book... we'll see. Fortunately, Will seems surprisingly enthusiastic about earning her Leader in Action award, which requires leading an entire Girl Scout troop meeting--and if there was ever proof that Girl Scouts encourages kids to stretch themselves out of their comfort zones, this is it! She has several possibilities for activities related to the Brownie World of Water Journey, including making polymer clay raindrops, edible aquifers, seashell crabs, and terrariums, We'll be making everything except the terrariums (I forgot to buy activated charcoal) today, so that Will can evaluate each in regards to how difficult it is to make, how difficult it might be to teach, how consistent the results might be, and if it seems fun!

I continually wish that I was doing more with Story of Science, as one reading comprehension activity and one hands-on activity don't seem like enough to distill all of the interesting content from the chapters, but I also bought those Quest Books so that I could save myself the lesson prep time... Perhaps I'll sit down over our Christmas break and research more activities, or perhaps I'll learn to let it go. Regardless, we're sticking to the Quest Book for this week, so this day's activity is answering reading comprehension questions for chapters 6-7.

THURSDAY: This day's Animal Behavior MOOC videos are on signals and information and modes of communication. After watching the videos, the kids will explore the Animal Communication Project to learn more about various animals, and also research video examples that provide evidence of the claims made in the Animal Communication Project readings.

Our Story of Science demonstration on this day is changing the acidity of water, using bromothymol blue as an indicator. In order to do this demonstration, however, my good friend has to dig through all of her stuff to find her bromothymol blue that she's going to let me borrow (because doesn't everyone have lab chemicals in their pantry that they're willing to lend out like a cup of sugar?), so if it doesn't turn up, we'll put off the demonstration until it does.

My kids don't exactly realize that not everyone receives random craft kits in the mail like magic, so they're never quite as excited to review them as I am, but even they're pretty revved up about this Star Wars felt kit that we're going to test out and write about. I'm thinking we'll turn them into ornaments!

FRIDAY: As with all other instructors on the last day of school before Christmas, I don't expect to get much done today. If they can get their daily assignments and a trading card for Ares completed, then we're going to spend the rest of the day making gingerbread houses while drinking hot chocolate (mine with bourbon) and listening to Christmas music.

And then it will be Christmas!

Homeschool Math: Measuring Tall Objects Using Ratios of Similar Right Triangles

I know that sounds really complicated, but it's actually pretty simple.

Take two similar right triangles:

via Skwirk

For these triangles, angle A = angle D. Angle B = angle E. And angle C, obviously, = angle F. The sides that make these angles are proportional: AC:CB = DF:FE.

If the ratio of triangles ABC:DEF was 1:10, then you could multiply side AC times 10 to get side DF. You could multiply side BC times 10 to get side EF. Here's more information about how that works.

To measure something really tall, then, you're going to use that 1:10 ratio. Here's what you do!

1. Go find something really tall. Hmmm..... I wonder what is near us that is also really tall?

Found something!

2. Measure out 30 feet from the drive-in screen:

A couple of places for human error here are the fact that the ground has a slope and that the kids are measuring, so don't expect perfect accuracy.

3. Take two yardsticks. One goes straight on the ground, pointing toward the drive-in screen. Set the other up so that it makes an angle with the prone yardstick, then put your eye as close to the vertex as you can and sight up to the top of the drive-in screen. 

It was about 20 degrees, max, on this afternoon, by the way. This kid is a baller.

4. Get a partner to wrap the angle with duct tape so you can move it. Our yardsticks also came with holes in the ends, so a better method would be to buy a bolt, washer, and wingnut so that you could simply tighten the wingnut and hold the angle that way.

In a pinch, though, duct tape is fine:

5. You are now going to measure out your similar right triangle that's 1/10 of this size. So whereas you were 30 feet from the drive-in screen, you now need to be three feet from the drive-in screen:

6. Place the vertex of your angle at the three-foot location, get back down on the ground so that you're once again eye-level with the vertex, and sight back along that top yardstick again:

7. Verbally direct your partner to the point that your sight-line leads you to. Warning: your partner might be kind of acting like an asshole:



8. Measure the height from the ground to that point (side BC), and multiply by ten. Your answer is side EF, or the height of the drive-in screen!

When we did this, we got a measurement of 60 feet for the drive-in screen's height. I have no idea if this number is at all correct, particularly since I can pinpoint several instances of possible human error in our process. The next time that I happen to see the family who owns the drive-in, however, I plan to ask!

If you're doing this project with kids, you'll probably want to limit the large something that you measure to less than 90 feet, since 1/10 of that would be 9 feet, and even middle graders are going to have a hard time reaching up that high with a tape measure. I  also wouldn't use this for measurements of heights that you could easily measure by hand, since smaller numbers will just make the inaccuracy of the human error stick out more--even a miscalculation of five feet isn't such a big deal with a drive-in screen, but for a nine-foot deck, that same miscalculation would be pretty egregious.

And yes. This is one of the many reasons why I love math!

The Nutcracker 2016: Mommy's Little Soldier

Syd earned a promotion this year at her Nutcracker audition. No longer an angel, bringing light back to the world, this year she joined the ranks of the tin soldiers who fight in the Nutcracker Prince's army in the battle against the mice.

Not only did this mean more stage time, but it's also a more interesting role, with varied choreography and an actual plot to uphold and interaction with the adult dancers. It was a lot more responsibility, but a really fun role for a kid.

Never one to slack off in her preparation, Syd soon developed a background for her character, who she decided is a hardened veteran of many battles against the mice:



Just between us, the soldier's costume is also MUCH cuter than the angel costume, even with its wings and halo. Soldiers wear navy shirts, white pants with suspenders, black spandex leggings that they pull up over their pants to look like boots, navy jackets with gold details, and cardboard hats with straps under the chin and shiny silver starbursts on the front:

during the fitting in the costume shop

and in the dressing room, waiting for the call! I'm about to fix her leggings so they match.

I also took a more active role this year. Last year, there was a sexual assault case concerning the college student dancers and one of their dance instructors that occurred during Nutcracker rehearsals, and although it didn't go anywhere near the world of the child dancers, it opened my eyes to the vulnerable position of children in the performance industry, relinquished by their parents for hours at a time, weeks at a time, during rehearsals. Whatever else I know about myself, I know for sure that I can keep track of multiple kids for as long as I need to, and get them ready to go and where they need to be exactly when they need to be there, so whenever I wasn't at fencing or watching the show, myself, I volunteered backstage with the soldiers, knew where all of them were at all times, forced them all to go pee before their call time, hairsprayed all of their fly-aways into perfectly neat soldier buns, fixed all of their little jackets so that the gold stripes lined up just so, refused to let them sit down after they'd put on their white trousers, let the most nervous among them dry off her clammy hands on my T-shirt seconds before showtime, and, surprisingly, really, really, really enjoyed myself quite a lot. I have no desire to dance onstage, myself, but I can see why Syd likes it!

Will and I share fencing, so volunteering backstage is my chance to share Syd's world, and enjoy it with her.

Ballet dancers have a lot of crap! You've got your costume, your hair stuff, your street clothes, tons of food, a book or two, and card games. Lots of card games. There were MANY Uno and Spot It! tournaments during the long waits backstage, fulfilling the stereotype of soldiers and their card games.

Here Syd is, reading Wonder for the billionth time. This is also my only good photo of her soldier bun, which is just like the angel bun, only it has to be on the smack top of one's head.

 But what do you think the little dancers like doing most of all?

Watching the livestream of the show! It always began about 35 minutes before our own call time, and as soon as the curtain opened, all the soldiers would crowd around to watch. And yes, they danced along, because they're just that adorable.

 One of the cutest parts of the show, however--and there are MANY cute parts--is that during intermission, some of the costumed children are chosen to mill around the lobby for photo ops. I prepped my soldiers by telling them that it was going to be like being Mickey Mouse at Disney World, and it was seriously adorable to watch people mobbing them for photos:

Syd, of course, had a wonderful time, danced her heart out, enjoyed the hours of downtime spent with her friends, liked having me there, and got so much of value from the experience. And I have to say that I, too, had a wonderful time. I loved watching Syd dance her heart out from the darkness, just a few feet away (while keeping a weather eye out for that one curtain that had a lot of potential to clock a soldier in the top of the head as it fell). I took pleasure in watching her play around with her friends and eavesdropping on all of their kid conversations. I could not have been more thrilled to finally get to see her up close in her costume and take pictures to my heart's content, even if they were on my crappy camera phone. I came home absolutely exhausted from the stress and the human interaction and all the running around every single night, but that chance to spend time with Syd in her world?

Totally worth it.

Work Plans for the Week of December 12, 2016: Cooking and Christmas and Lots of Science!

After two weeks of a lighter schedule that helped get our little soldier through Nutcracker season, we are back for two more weeks of a full work load before we take another week off for the holidays. I kept the kids focused on the basics for the past couple of weeks--math, typing, keyboard, grammar, vocabulary, SAT prep for Will--and that turned out to be a good thing, in that the lighter schedule may have helped get Syd through the slacker phase that has made getting her to do her schoolwork just about impossible.

Let's see if it holds this week!

Interspersed with the lighter academics, I used our extra time last week to make the kids help me FINALLY put the garden to bed (newspaper covering the plant rows, an entire yard full of leaves raked and put on top of them), to go through their winter clothes (this year I finally remembered to have them do this BEFORE I take a look at their near-empty clothing bins and go panic shopping at Goodwill--they're full to bursting now!), and, of course, to do some Christmas crafting with them. Check out these beaded ornament hangers that we make every year because I'm too cheap to go buy any!

Super pretty, right? And all they're made of is stash jewelry wire and beads that I'm dying to get rid of, anyway.

Memory Work for the week will be a lot of review, as it wasn't a focus for the past two weeks. Books of the Day are mostly taken from the 2015-2016 Banned Books List (when this comes out every year, I immediately request them all from our public library, and suggest the purchase of the few that the library doesn't have), so Will is reading The Absolutely True Diary of a Part-Time Indian and This Book is Gay; I'm reading City of Thieves and Extremely Loud and Incredibly Close; Will and I are both reading Looking for Alaska, and both kids are reading the picture books I am Jazz, My Princess Boy, This Day in June, and King and King (plus its sequel). I'm also pre-reading Just One Day to see if it would be a good fit for Will.

Daily work for both kids this week includes Analytical Grammar for Will and Junior Analytical Grammar for Syd, Wordly Wise (or a word ladder for Syd; she loathes her Wordly Wise, and I'm not quite sure what I'm going to do about that yet), ten minutes a day of journaling or imaginative writing, typing practice, keyboard practice or a Hoffman Academy lesson, SAT prep on Khan Academy for Will, and the last week of their current events journal.

And here's the rest of our week!

MONDAY: We're not ready to start a new poem this week, and I don't have another literature unit that I'm ready to implement, so the kids can work on their MENSA reading lists some more. I try to keep several books from this list--in both written and audio formats--on our library shelves, so choosing the next selection should be easy.

Both kids are actually in just about the same subject in their Math Mammoth units, with Will studying positive and negative integers and applying that to the coordinate plane, and Syd learning how to graph on the coordinate plane and then moving into other types of graphs. This will play well into our later hands-on math enrichment!

The Animal Behavior MOOC is much more dry than the Sharks one, so I've been having trouble keeping Syd's attention on it. Fortunately, this week they're covering inherited vs. learned behaviors, and there are lots of hands-on activities to help cement those concepts. On this day, after watching videos on how animals learn, the kids will be challenged to make a puzzle toy for one of their pets, and then encouraged to observe the pet as it uses it. I think that Syd will really enjoy this one!

There's a lot that can be done with Story of Science, but I don't want to still be doing it into 2018, so I'm having to be a little more selective with the hands-on activities that we do than I've often been--this is why we've actually been finishing units of study this year! This week, we'll be covering chapters 4 and five, and the Quest Book activities are simple question-and-answer worksheets that will make sure the kids have a solid grasp of the content before we move into the fun activities.

I assigned Hephaestus a couple of weeks ago, but Syd was so busy with The Nutcracker that she didn't get to it, so this assignment is mainly for her. Will never finished her Hades trading card, however, so she, too, can do some catch-up during this time.

Syd is finished with ballet for the semester, and Will with Chinese, but Will and I have one last week of fencing, and she has one last week of ice skating, so we'll still be out and about with extracurriculars this week.

TUESDAY: I plan to blow the kids' minds on this day, by showing them how to measure the height of something really tall (in this case, the drive-in movie screen next door) using ratios. If we're not freezing our booties off, I'll then show them how to do it with trigonometry, and we can compare results.

This day's Animal Behavior MOOC video on inherited vs. learned behavior also lends itself to a couple of fun activities to illustrate how these traits affect us. The kids were supposed to have done self-portraits in their art lesson with Matt this weekend, and were then going to label them with their own inherited and learned behaviors, but I don't know what happened to Sunday, but it wasn't art! We'll table that to the weekend, I suppose.

Playgroup and fencing will take us through much of the rest of the day.

WEDNESDAY: Some of the rest of this week in the Animal Behavior MOOC is too difficult for Syd, so Will has some extra work to complete on this day. With her critical reading skills, she should be able to handle reading abstracts of scientific papers to evaluate their rigor. Both kids, however, should be able to handle the reading comprehension activity from this Understanding by Design curriculum. The curriculum is written for the fourth grade, but I've had no problem adapting it for my fifth- and seventh-graders this week. 

I've got a bit of cooking for others to do this week, so in true homeschooler style, I'm turning it into a Home Ec assignment and making the kids help me! On this day, I've volunteered us to contribute a meal to a family in our homeschool circle who've just had a new baby. I've (gratefully!) received one too many casserole/pasta bake in my time, so my own rule of thumb for a meal train is a large cheese pizza from our favorite local pizza shop, plus a homemade fruit salad and a home-baked treat. For this family, I think we'll bake brownies!

I need to set aside some time to focus on Syd's Girl Scout goals, since she'll be bridging next year, but for now, I'll let her pick a new badge to get started on while Will and I focus on her Cadette Breath Journey and the Leader in Action Award that she's hoping to earn. For this award, she has to lead a meeting for Brownie Girl Scouts--what a happy coincidence that we happen to be part of a multi-level troop and have our very own Brownies! There are going to be LOTS of valuable skills to be learned from leading a meeting for younger girls.

THURSDAY: I can't let a week in December go by without some sort of holiday craft, so we're going to be sneakily practicing symmetry and regular polygons by making large-scale popsicle stick snowflakes to hang from our high ceilings.

One more activity and the Module Exam for Will, and that's Module 2 of the Animal Behavior MOOC done and done! 

Just between us, I'm hoping that Will's horseback riding gets cancelled for cold temps, because I am ready to have this semester's extracurriculars also done and done!

FRIDAY: We are out and about for much of the day on this day, especially poor Will, the most introverted among us. We're attending a school matinee of the local theater's holiday show in the morning, and then the afternoon brings Will's last ice skating class of the session and a holiday party for her Pony Club. You'll never guess what I'm bringing to the party...

Fruit salad and dessert! I SUPER want to make these horse-themed cupcakes, so that's what the kids and I will do during our brief interval of at-home time. Hmmm.... perhaps we should make the cupcakes the night before.

The other work for the day should be independent and efficient--there's a coordinate grid foldable to cement the vocabulary, and a research project, again from that Understanding Design unit, that asks the kids to figure out what inherited and learned behaviors allow different animals to thrive in different habitats.

SATURDAY/SUNDAY: Gingerbread houses! The New Star Wars! Housecleaning! Yardwork!

And then one more week until Christmas break!

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?

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!

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.