Want a super-fun hands-on geometry and spatial reasoning activity for multiple ages of kids?
Make geometry nets!
Unfortunately, almost all of the geometry net kits and models that you'll see are pre-made to form a specific net, and all the kid gets to do is fold and unfold them.
It's better than nothing, sure, and it's still fun to physically manipulate a model, and to guess what three-dimensional shape a particular net will form, but other than that there's not a lot to do there.
It's definitely not the problem-solving practice and spatial reasoning challenge that a kid gets when tasked to use open-ended building toys to make their own geometry nets.
Like these!
Forgive the poor quality of these photos. We both have inadequate indoor lighting AND homeschool even when it's gloomy outside!
This nifty little set is Googolplex, a vintage building toy that I checked out of our local university's library.
It's too bad that it's no longer manufactured, because it really is perfect for this project. Each line segment had a hinge attached to it, so that you really could fold the planes together and explore what 3D shape they made.
You could also add wheels!
I mostly made boring basic shapes, but Syd enjoyed the problem-solving involved in creating more interesting shapes and then making them move:
Her spatial reasoning game has always been pretty fly.
If you're interested in even more older kid exploration with polyhedra, check out these projects:
giant cardboard house. I LOVE this house idea! I should have saved the 753 corrugated cardboard Girl Scout cookie cases that have come through my house so far this year to make this with the kids, and I really had been trying to save all those boxes to upcycle, but I hit the wall on Saturday and had Matt take them to the recycling center. Perhaps next year!
geodesic dome with straws. I don't usually craft with single-use plastic like this, BUT the kids have it on our ultimate wish list to build ourselves a giant PVC pipe geodesic dome in our backyard. We may have to practice our designs with these!
gross-motor geometric solids. With this Bernoulli windbags, kids can make larger-than-life geometric solids that are as light as a feather. It's really fun!
paper polyhedra. These are just models to cut out and assemble, but it's a good gross motor activity, good for memorization, and they're pretty!
tetrahedron wall art. The STEAM skill here is in using pleasing colors and patterns to make art with different sizes of tetrahedra.
Zometool geometry. This super sophisticated building toy is perfect for complex geometric structures. The antiprism broke my brain!
Will is taking an online geometry course this year, and so I'm always on the lookout for even more interesting and complex hands-on geometry activities. Let me know in the Comments below if you spy something she or Syd would like!
I must tell you that my child has turned into one of those teenaged YouTubers. She has a channel on which she posts cartoons that she makes, usually music videos or memes.
Here's my favorite of her little skit-thingies:
Anyway, basically what I'm saying is that the kid has her animation hobby well in hand, and there is no technical instruction that I could usefully provide her on this subject.
But technical instruction is rarely my role, anyway. What I do is contextualize. Historicize. Enrich and embellish. Strew, if you will.
So on a typical Thursday afternoon, after lunch and before everyone starts getting ready for evening extracurriculars, you contextualize and historize a teen's YouTube animation hobby by talking about the earliest history of animation together, and then you make and play with a zoetrope!
I'm obsessed with everything Crash Course, so you won't be surprised that to get started, we watch the first episode of Crash Course: Film History. In it, the host talks about the zoetrope and the persistence of vision, a fun little optical trick that we've played with off and on over the years, although usually with a thaumotrope instead of a zoetrope:
To make our own zoetrope, Syd and I used a DIY zoetrope kit that I had squirreled away (for too many years to be proud of...), but it looks like to make something similar, you'd have to consult something like this book, because all the other DIY kits that I'm seeing now have too much plastic:
Like, I think that you're going to have fun with your zoetrope, but I don't think that you're going to love it so much that you're going to be glad that it's made of sturdy, keep-it-forever plastic and not nearly as sturdy, recycle-it-when-you're-done cardboard.
Anyway, the fun part, at least for Syd, isn't so much constructing the actual zoetrope. It's creating the animations!
If you can get it to rotate quickly and at a consistent speed, it works quite well!
We kept ourselves entertained with that thing for a looooooong time...
Syd and I also watched a video of this, the COOLEST ZOETROPE EVER CREATED:
I love that the 3D zoetrope represents such an intense intersection with art and hands-on craft. There's still place for old-school DIY used with tech-savvy techniques, is the take-away that I'm hoping that my little artist/tech-savvy creator took away from our project.
P.S. Here are a couple of other DIY zoetrope builds that you could utilize:
Cover your ears, Friends, because this is me saying it again louder for the people in the back:
MATH MANIPULATIVES ARE NOT JUST FOR LITTLE KIDS.
I mean, everybody knows this if they think about it. Everybody likes a good graph or chart or 3D model or virtual model or LEGO model or hand-drawn diagram or Google map. Everybody likes to see visual representations of information, and to fiddle with stuff to figure it out.
It drives me bonkers, then, that math manipulatives very rarely make their way out of the early elementary classrooms, especially when they're so useful for exploring and explaining a wide variety of more sophisticated concepts.
Ask me sometime about my handmade, take-apart model of the binomial and trinomial theorems!
In her intro to algebra curriculum, Syd is currently learning more about rates and proportions (handy timing, as that's what I use to allocate sales to my Scouts who work Girl Scout cookie booths--guess who's going to do all my cookie booth math for me this weekend?). In order to focus on problem-solving with rates and proportions, one should already have a competent working knowledge of calculating fractions.
Here, by the way, is one of those places where a kid can get lost in math for life. Math builds upon itself, and a curriculum that's currently teaching a kid how to graph proportional relationships is not going to hyperlink a review of every type of calculation that she should have mastered in order to solve the problem.
It should, but that's a different gripe.
So if graphing a set of proportional relationships requires a kid to divide fractions and she doesn't remember how, she's not going to be able to graph that set of proportional relationships. And then the next set that she's asked to graph, she still won't be able to do it, because she didn't learn how during the previous set, because she couldn't do the necessary calculations.
And then when the class moves on to scaling figures, if any of that work assumes that the kid can graph proportional relationships, then, well, she's not going to learn how to scale figures, either. And so on and so on until she gratefully taps out of math completely after Algebra 2 and spends the rest of her life telling people she's bad at math.
She's not bad at math, Friends. YOU'RE not bad at math, even if you think you are. You just got lost somewhere and nobody helped you pick yourself back up.
So when Syd was doing unit rates the other day, and for a moment she couldn't remember how to turn an improper fraction into a mixed fraction, even though she looked at the fraction for a second and then was all, "Oh, right, I've got to divide," I said, "Do you know why you have to do that?"
She said, "Because that's how you do it."
When a kid says that, it's because they don't KNOW why a certain algorithm works, and if they don't know WHY the algorithm works, then they haven't mastered the concept behind the algorithm. A kid who hasn't mastered the concept behind the algorithm that's really just a calculation shortcut is on shaky ground, mathematically, because memorizing algorithms isn't math, or at least it's not what math ought to be.
When I'm in charge of making sure people understand math, I make sure they understand the actual math, so that they can apply it to new situations, incorporate it into patterns, problem-solve using it, think creatively about it.
The best way that I've found to that level of understanding is seeing it and touching it. And that's how I found myself bringing out the fraction circle manipulatives and Cuisenaire rods and reviewing some fraction models with my eighth-grader.
First up: that tricky little improper fraction to mixed fraction conversion! You need to do this a LOT in algebra, and forgetting the algorithm or being unsure that what you're doing is correct will distract you from the algebraic concept you're trying to master, or just cause you to get the wrong answer so that you can't master the concept at all.
This model is an easy reminder of what you're doing when you convert an improper fraction to a mixed fraction, and vice versa.
To model how to convert an improper fraction to a mixed fraction, give your kid a pile of the same fraction from a set of fraction circle manipulatives, and ask her how many she has. Let's say she has 7 1/4s. She can write that as the improper fraction, or she can go a step farther and write 1/4+1/4+1/4+1/4+1/4+1/4+1/4=7/4.
Then, ask her to assemble the fraction manipulatives, seeing how many wholes she can make. She'll be able to assemble one whole, with another partial circle next to it. Write the new fraction, which is 1 3/4.
Walk through that in reverse, and you're instead modeling how to convert a mixed fraction to an improper fraction. Remind them of the algorithm, and have THEM show YOU how the algorithm matches the model at each step.
If they need some drill to cement the algorithm, here's a worksheet builder.
Here's another example, still with unit rates (I tell you, algebra has a LOT of fractions in it!): Syd missed a problem because she multiplied a fraction when she was supposed to divide it. When I pointed out to her that she'd multiplied instead of dividing, she of course knew that what she'd done had to be wrong, but she couldn't at first figure out what exactly was wrong about it, because she also correctly remembered that there WAS multiplication involved when you divided fractions.
After thinking for a bit, Syd remembered that you of course have to invert the divisor before you multiply it, but because that step didn't make any sense to her, it was easy for her to forget.
Time to get out the Cuisenaire rods for a review of dividing fractions!
Here's Syd doing the first step every time you work with Cuisenaire rods. Got to build the stairs to remind you which color represents which number!
Syd always likes doing this, too. Ahh, those number bonds for ten!
By the time we got out the Cuisenaire rods, Syd had remembered on her own how to work the algorithm for dividing fractions, so I had her work the algorithm first, then prove it using the Cuisenaire rods:
I think that the visuals here make the mathematical process so interesting. I'm fascinated at the way that the numerator of the divisor becomes the denominator of the quotient, and how elegant is the way that it becomes so.
And you'd never see it without these colorful math manipulatives in your hands!
Also, I DARE you to work with Cuisenaire rods for more than five seconds and not get distracted making fun patterns with them:
Speaking of multiplying fractions... that's also a good one to review models for, because doesn't it break your brain that multiplying fractions makes the product SMALLER?!?
Matt and I were actually watching Syd dance en pointe for us in our family room, but I turned to look at him and he was looking beautiful, too, so I snapped his photo. Only later did I notice the nonsensical number of books in the frame!
Girl Scout cookie season is upon us, you guys. As always, it's bonkers and ridiculous, organized by the skin of my teeth and the quiver of my chin, and it will take me until January next year to recover from it... just in time for it to start again.
There were many days in January when I didn't find time to sit down or eat actual food during the day, much less engage in happy pleasure reading, and yet I'm still a little embarrassed to tell you that I read only four books during the entire month.
No amount of stress inherent in helping thirteen children run their own not-so-insignificant part of the world's largest girl-led business can distract me from my pleasure in reading about the many wild adventures of Aubrey and Maturin. I love them, you guys.
I LOVE THEM.
And their adventures are SO WEIRD! You can never tell what's going to happen on the next page, much less the next chapter. You can never tell if someone you've gotten deeply invested in is going to die in a couple of minutes, or how our beloved heroes are going to get out of this next pickle, or where they're going to sail to next.
My Spanish instruction was long ago and far away, but isn't that ship named something like "hot shit?"
My other best book of January was an ethnography of dinosaurs:
The weirdest take-home from this is that there is a real sub-sub-sub-genre of literature entitled "dinosaur erotica." The second that I read this fact I had to announce it, and then Will and I spent waaaaay too long scrolling Amazon with our hands half-covering our eyes, giggling in horror at the titles.
Do you want to read Space Raptor Butt Invasion? Its reviews aren't that bad!
And yes, the rest of the family IS low-key helping me plot out some kind of super-weird erotica starring ever-more-unlikely pairings, because honestly, writing self-published megalodon erotica sounds WAY more fun than yet another novel that nobody but me is going to want to read.
Here's what else I managed to read in tiny snatches of time in January:
Even Will has been suffering from a dearth of free time; when she's not selling Girl Scout cookies or walking her dog or helping me out with all of my own scut work, she's busting her butt studying her AP subjects, poor kid.
Fortunately, she did still find some time to zone out with some good books!
Matt was excited to see this as one of Will's favorite books of January:
He's currently trying to get her to watch the Kevin Costner movie with him, but first she has to watch Watership Down with ME!
Here are Will's other favorite books from January:
Can you tell that Will took my advice to check out the sci-fi/fantasy shelves of the library? DOUBLE FIST PUMP!!!!!!!
More Will favorites:
Everyone in the family technically has this book on our January reading lists--
--because it was our latest family read-aloud, begun over winter break and finished just a couple of weeks ago. Will and Matt loved it, I liked it, and Syd loathed it so she gets to pick the next read-aloud.
Here's everything else Will read in January!
The good thing about doing a lot of tedious scut work, such as hauling cases of Girl Scout cookies here and anon, counting lots of dollar bills, calculating lots of percentages of sales and rate/time/distance formulas, and hauling around yet more Girl Scout cookies is that I've had plenty of time to listen to podcasts!
Mostly on the weekends, mostly while carrying cases of Girl Scout cookies from one end of my hall and back again, I listened to the entire first season of The Dream in January:
I don't have any skin in the pyramid scheme game, other than when I was a kid one of my second cousins once sent me a chain letter, AND when I was in college I was friendly with a guy in the fencing club who legit did Amway out of his dorm room.
But now I know ALL about pyramid schemes, and you guys, I don't think you should do those multi-level marketing business things. I mean, you can if you want, but you're not going to make any money from them, because you're not Betsy DeVos or Donald Trump.
And that 1970s trial that ruled that Amway is NOT a pyramid scheme was corrupt.
I am for sure going to listen to the second season of The Dream this month, because it's about the "wellness" industry, and I desperately need them to tell me all about Goop. Y'all remember about me and Goop, right?
Goop snark helps my sanity!
Want to know another AMAZING thing that I found?
Because not all heroes wear capes, there are people out there in the world, Friends, who make entire playlists of music that Aubrey (a violinist) and Maturin (a cellist) could have played onboard Aubrey's ship. And sometimes, they also include sea shanties!!!
These playlists are perfect for streaming while you read the series.
This one is my favorite:
It's an enchanting playlist even when you're not reading about the British Navy during the Napoleonic War, although if that's the case, the occasional sea shanty might be confusing.
The only time I've really had to watch YouTube this month is when I'm putting away laundry, but one morning while I was drinking coffee I randomly turned on the TV for a minute to distract myself from the anxiety ball already forming in the pit of my stomach (that day was a logistical nightmare of Girl Scout cookies needing to be picked up overlapping with Girl Scout cookies needing to be delivered to multiple parents at multiple overlapping times, Girl Scout cookie booths, also overlapping, to be prepped for and stocked, and a drive-thru cookie booth the next day that did not have anywhere NEAR enough signage made for it yet), and I found this completely off-the-hook video of a Carnivale parade in Rio.
It. Was. EPIC!!!
As soon as Will woke up, I made her come in and watch it with me, and then she was obsessed, too, so later we found another video and made Syd watch it with us, and when Matt got home that night and all my Girl Scout cookie nonsense was over we showed him another video, and then the next day he found yet another video, because obviously if you're not obsessed with the Carnivale parade in Rio then you don't even know what's good:
Seriously, there were a couple of guys flying around with honest-to-god rocket packs. And somebody got literally eaten by a giant dragon. And there was a guy on a boat, and a bunch of guys dancing around him dressed up like water, and they had hoses on their heads that SPRAYED WATER.
