Friday, May 8, 2020

April Favorites: Hot Air Balloons, Tony Award Nominees, and Dinosaurs

Will has been reading a lot of these in April!
I really miss our public library! It's probably a big clue that our family checks out too many books, since the library has been closed for over seven weeks and I STILL haven't run out of library books to read, but to be honest, most of the books still on my to-read shelf are ones that I'd have flipped through the day before their due date, thought, "Eh," and returned them.

I did find a couple of winners, though. I stole this graphic novel adaptation from Will's library shelves--



--and it is GORGEOUS!!! Children's novels often make terrific graphic novel adaptations because they're shorter so you have to exclude less, and frankly, I might have liked this graphic novel adaptation better than I liked the original novel.

I like to read a lot of nonfiction books, even though many nonfiction books seem to strive to make themselves deliberately unlikable (I am currently slogging through a biography of the man who essentially invented the study of geology, and although I really want the information, the author is making it VERY difficult for me!). Honestly, this book on the history of hot air balloons was another slog--



--even though I am absolutely obsessed with the content! You guys, hot air balloons are CRAZY, and the people who flew them did SO MANY CRAZY THINGS and DIED IN SO MANY CRAZY WAYS.

Alas that there were so many intrepid balloon explorers based out of the UK! It's, you know, an island, so some balloonist would figure out a new way to balloon, like maybe a bigger balloon with a different kind of valve and a different style of rope, and then that balloonist would launch their maiden flight to show off their new tech...

...and then that balloon and balloonist would basically float straight out to sea, never to be heard from again.

It's just so interesting to read about the whole history of people trying to master how to navigate perfectly in a hot air balloon, knowing that we still can't do it! Pilots raise and lower the balloon to catch different air currents, but there's no worldwide atmospheric infrastructure in place to exactly note where all these different currents are, so it's still a lot of guesswork. How cool and weird is it to know that, as a species, we have that much ignorance about our own atmosphere!

You might think, then, that since navigating a hot air balloon depends on knowing the speed and direction of various wind currents that you pretty much have to already be familiar with, hot air ballooning would be particularly unsuitable for exploration.

And you would be right, which does not mean that people have not tried it. The book devotes its final chapter to retelling the story of an 1897 attempt to REACH THE NORTH POLE BY HOT AIR BALLOON, and the story is utterly horrifying and I think about it probably every day. I won't tell you the whole thing, because I think you should read about it for yourself, but I will tell you that at one point the explorers attempt to walk back to civilization from the Arctic Circle, and they walk tons of miles every day, only to eventually figure out that they're making literally no progress because the ice that they're walking on is flowing north faster than they're walking south.

I'm also super into this garbled pseudo-historical (but VERY good) movie about hot air balloon exploration:



They've kind of stolen some characters (the heroine is clearly supposed to be Sophie Blanchard, who did not do the things in this movie but did stuff just as crazy, and eventually died when her balloon crashed on a rooftop in Paris, and she partly fell out of it and broke her leg and got caught in the ropes and was just dangling there, screaming while onlookers watched in horror, until she finally fell out of the ropes and to her death on the street), but as long as you remember that it's fiction with some stolen historical characters and events it's SUPER good and exciting and you'll want to read more about the history of hot air ballooning afterwards.

Okay, here's what else I read in April:



Will is also down to the dregs of her library selections, so much so that she has actually been griping all month that we do not have a better selection of books in our home library. This from the child who NEVER reads books from our home library, and rarely re-reads books at all. She's probably the only hyper-lexic child on the planet who doesn't receive a stack of new books for every gift-giving occasion, because there's no point.

I'm sure as heck going to remedy that for her birthday! Can you believe that the child shamed me for not owning a copy of Dracula? The LIBRARY owns our copy of Dracula! It's not my fault that the library won't let us come and get it right now! Sigh...

It was nice to see, though, that now that Will has deigned to read some books from our home library, some of those books were her favorites from the month:



Jurassic Park was especially fun, because the science is just as hilariously dicey as it is in the films. I knew whenever she'd picked it up because the outraged corrections and protestations of bunkumness would commence via hollering from whatever room she was in to whatever room I was in.

Here are Will's other favorites from April:



I'm going to add those Rivers of London books to my own must-read list, because they sound awesome!

Here's what else Will found to read in April:



That's a little more than half of the books that she usually reads in any given month. From what I can tell, she's spending the remainder of the time she'd normally spend reading binge-watching TV shows. I mean, Leverage is kind of educational-ish, I guess?

I have been doing a LOT of anxiety-related deep cleaning in April, and I've really been enjoying this podcast while I slog away endlessly:



I normally like narrative podcasts a lot better than panel discussion ones, but this one has the perfect format: there are two writers, and every episode they take turns so that one of them has researched the subject and can do the whole deep dive, and the other is the straight man who asks the type of questions that anybody just listening to the story for the first time would ask. It's almost always about some super popular thing that you've definitely heard of but actually know very little about, like the Duke lacrosse rape allegations, or shaken baby syndrome, and it turns out that whatever you think you know, YOU ACTUALLY KNOW NOTHING.

So this other random thing that I've been doing is watching old Tony Awards productions, essentially just so I can fast-forward through them to watch all of the performances from the best musical nominees. It's interesting to see what shows were out in any given year, and how their performances have gotten a LOT splashier over the decades!

Pro tip: the musical that you recognize is usually the one that won in any given year!



Except for the year with the Will Rogers Follies. Just... no.

I'm actually really looking forward to May! I'm trying to focus less on the huge disappointments, such as Syd's birthday AND her ballet recital being cancelled, and more on how I'll be able to focus on gardening all summer for once (no mid-summer vacation and coming back to half-dead, deer-eaten, weedy veggies), and lots of home and yard projects (I spent more of my stimulus check than was reasonable on a giant geodesic climbing dome for the backyard...).

Although if the library doesn't open back up this month, next month's reading list is going to be all... I don't know, lawnmower repair manuals and cereal boxes?

What are YOU reading this month?

Wednesday, May 6, 2020

Hawaii Unity Study: Make a Corrugated Cardboard Topographic Map of the Big Island



I know it's taken us almost a year to complete this unit study of Hawaii (including when we actually WENT to Hawaii in June 2019!), but this study has actually been a pretty comfortable one to keep on the back burner, just dipping into it every now and then when we've got a free hour or so in our school day.

It was easy, then, to look at my massive stash of corrugated cardboard Girl Scout cookie cases this winter, and think, "Hey! This would be a great time to talk about mapmaking and Hawaii!"

Our specific lesson was on contour maps, the circumstances under which you'd want to make or read one, and how to interpret the information--not super high-level stuff, but useful, practical knowledge for kids who have vastly more experience looking at hyper-real digital maps than they do black and white paper maps.

There are a lot of resources online for learning the basics of contour maps. This lesson specifically connects the study of contour maps to Hawaii, so was perfect for our purposes. This graphic shows common contour map topography linked to their elevation profiles. This USGS mapping system lets you dial down all the way to your neighborhood, seeing increasing layers of detail in the contour map as you go. Here's the USGS map legend so you can interpret what you see.

We also read a little bit from this book that I happened to have on hand. It isn't terribly rigorous but IS very clear!



Mostly just for fun, but also to make sure the kids internalized the connection between the 2D map and the 3D topography, I had them translate a 2D map into a 3D one, using this contour map of the Big Island of Hawaii as their template.

The process is dead simple: print that contour map of the Big Island as big as you'd like, then let the kids cut it up, trace the contour lines onto corrugated cardboard, cut the layers out--


--and hot glue them in place.

The result is a quite accurate and good-looking 3D representation!


I like the way that this overhead shot matches the 2D map:


To make the project more rigorous, you could require a higher level of craftsmanship by having the kid paint each layer, or label various features with toothpick flags. It would be especially interesting to map the Big Island's towns onto this, so you can see how elevation affects where people choose to live, or river and volcano features, so you can see how they affect topography, or even just the special and iconic tourist sites.

If you're including this in a deeper study of geology, you could even add the underwater elevations to your island--the Big Island would be massive if you mapped it from its true base!

If you've got a few kids or are in the mood for a super big project, you could even take the giant map of Hawaii project that we did here and translate the whole thing into a 3D contour map!

If you're not studying Hawaii specifically, you can give a kid much more ownership of the project by allowing her to choose what she'd like to map, and this would also make the project more rigorous as she'd have to figure out what to choose and how to source that contour map for reference. Or you could give the project a theme, and ask kids to build and compare different volcanoes, or different mountains.

I also like this project, which first has a kid build a model mountain, then slice it into elevations to draw the contour map. It would be fun to do this if you're reading a book that contains interesting and important topography--how cool would a map of Mordor be?!?

*wanders off to make a corrugated cardboard topographic map of Mordor*

Friday, May 1, 2020

Tales from the Top Bunk: Earning the Girl Scout Senior Room Makeover Badge



The Girl Scout Senior Room Makeover badge is so fun, and so worthwhile. I mean, doesn't it make a lot of sense that in a lot of cases, a kid who is now fourteen will want to change some things about her bedroom, or bathroom, or playroom, or any other personal space? I know that there are families who've moved, giving a kid an all-new space to decorate, or who regularly redecorate, anyway, but surely my kids are not the only kids who are still living in the exact same room that we moved them into eight years ago, sleeping on the exact same bunk beds.

Heck, I don't think the kids have even switched bunks in at least seven years!

At the same time, though, this badge seems like a challenging one to earn as a troop. Every kid's personal space is so... personal! Any project that you do as a group, whether it's canvas art or a mosaic picture frame or a throw pillow, isn't necessarily going to fit every kid's idea of what she wants in her own space, and learning to take ownership over choosing what goes in one's space--and therefore the responsibility of care and maintenance--over one's own space seems like the overarching point of the badge.

Nevertheless, for an individual kid--for MY individual kid, in particular--this Room Makeover badge was a perfect fit. I pulled it out last summer, actually (I pulled it up on my phone, even, crammed into the back seat of our little car with both Syd and Will, on the way to the airport to send them both off to Camp Grandma for a week), when Syd suggested that maybe she wanted some new things for her bedroom, and following the badge over the course of almost an entire year turned out to be a great way to guide Syd through the process of redecorating her personal space.

For Syd, the process of earning the Room Makeover badge was also different than is written in the badge book. The badge book has a specific skill set that it wants a kid to learn during the makeover process--she should be able to paint, sew, repurpose, and build, with a level of craftsmanship that makes her products attractive and usable. Well, Syd is my crafty kid, and she can already do all of that, and so instead of rehearsing every single skill and requiring her to create something that she didn't really want in her space, we focused on self-expression and, again, building that ownership over her space that also includes its care and maintenance.

Step 1: Gather ideas and inspiration.

Syd came to the table with some ideas about what she wanted in her top bunk personal space, and for everything else of course there's Pinterest, but for this particular step, I also wanted her to take a comparative, global view of what a teenager's personal space can consist of. Fortunately, there are several projects that accomplish exactly this and that are easily available to view. My favorite is this James Mollison book:


But if you can get by without the captions that contextualize every image, you can also see them here. This is a great book because not only do you see examples of shocking wealth, but you also see examples of shocking poverty, all through the lens of what that tends to look like when reflected by a child's sleeping space.

To get the same global perspective of older young adults' bedrooms, here's another good photo essay.

I also wanted an inter-generational perspective, so I found this epic set of photos of teenagers' bedrooms in the 1980s. For a funny look at complete unreality, here's another set of images of teenagers' bedrooms taken from teen films of the early 2000s, and another set from the 1990s--everyone had so much room!

And obviously, we couldn't finish up this topic without requiring that Matt tell Syd all about his own childhood bedroom (LEGOs for days! A Nintendo he bought with his own money!). As for me, I still have the rock-n-roll kitty cat poster that was the star of my bedroom for my entire childhood. It is my precious, and I will never consent to be parted from it.

Step 2: Paint something.


Nothing got painted. Not that I don't think that the space couldn't have used some freshening up, but Syd wasn't into the idea, so I let her focus on the plenty of projects that she WAS interested in.

Step 3: Sew or glue something.

So, indeed, nothing got painted, but Syd did a LOT of work on this step. The way that the kids' bunk beds are built (they're your bog-standard IKEA Kura set up upside-down, with a wooden sleeping platform built by Matt on the bottom solely so that Will can't grow up and tell everyone that her parents made her spend her entire childhood sleeping on a mattress on the literal floor), the top of the top bunk is basically at adult eye level, and so it's no wonder that someone whose sleeping space is at eye level would long for a nice curtain around her bed.

I gave Syd a pretty generous (for me, lol!) budget for her room makeover, mostly because it'd been so long since she'd had anything new for her room, but also because if taking ownership over her own space DOES lead her to take responsibility for its care and maintenance, then I am all for that! So I let Syd pick out a really lovely gauze, told her to research how wide the curtain should be (here's the answer to that!), and purchased the yardage that she told me to.

Syd and Matt scavenged a curtain rod from the garage (why do we have a curtain rod in the garage? Where did it come from? When did I have curtains that I do not now have?), and Syd measured its circumference to get the measurement of the channel she'd need to sew in her fabric to accommodate it. We went back and forth about tabs and grommets and clips and other reasonable ways to hang curtains (can you tell what team I was on?), but Syd was adamant that she wanted her curtain mounted the way that she wanted it mounted, so I settled for making sure she knew what the other options were, and then left her to it.

I DID win the "Do I really need to pre-wash my fabric?" battle, though. To the claim of "I don't need to make sure the curtain is pre-shrunk because I'm never going to ever wash it," I countered with "Oh yes you WILL wash it!"

To be fair, though, I don't think the child has ever seen me wash a curtain before...

Syd's other dream curtain attribute was twinkle lights. I mean, if you're going to have a gauzy curtain, you practically require twinkle lights, yes?

Unfortunately, it's never Christmas when you need it to be, so we had to rely on Amazon for twinkle lights, and I don't know if we just had bad luck, or if there really is some kind of national twinkle light racket going on, but the first two sets of twinkle lights that Syd picked out were absolute trash and had to be returned. Eventually, we seem to have scored with these sound-activated twinkle lights. They work for a change (even though Syd has already had to repair the wiring after her murderbrat got ahold of them...), they're just the length, size, and color that she wanted (because apparently warm white and cool white are different whites and this difference is important), and they blink in time to her music. I would have sold my mother to have had something like that at her age!


And actually, Syd did help Matt build a wall bracket for one end of the curtain rod--oh, and she painted it, too! She DID paint something!--and she helped him install it, so I guess she technically completed other parts of the badge that I didn't even count because I'm mean.

Step 4: Redo something. 

We played around with some ideas for this step, but ultimately, nothing stuck out as something Syd definitely wanted to do to her space.

Step 5: Build something.

The other thing that Syd really wanted to DIY for her space was a light-up photo wall. She found another super long set of twinkle lights that she could drape back and forth across the wall next to her bed--


--and it even came with adorable teeny clothespins for photos.

If only she had a bunch of teeny photos!

Matt showed Syd how to upload the photos from her ipod to a graphic design program and tile them onto a canvas, and Syd made me several 4" x 6" prints' worth of teeny photos that I printed for her.

When the photos arrived, Syd cut them out and pinned them up, and I think they look so cheerful and adorable in her space:



Because I can't even tell you when the last time I'd bought my kids new bedding was, and one of the things that Syd wanted in her room WAS new bedding to match her decor, it's a good thing she'd already earned the Girl Scout Cadette Comparison Shopping badge, and was quite capable of setting up her own criteria and searching for the best sheets for her price point. I was less enthusiastic about letting her also pick out a blanket, because OMG we already have so many blankets, and I feel like I do nothing but make more quilts every year, but apparently we do not have any blankets, nor any quilts, in Syd's specific top bunk color scheme, and fine, I might as well make up for eight years of never buying the kid a thing for her room all in one go.

And also a pillow that cost more than I thought it should. How much do y'all think is a reasonable amount of money to spend on a pillow? Is it thirty dollars?

Story time: When I was a teenager, I got a job pretty much as soon as I could drive, and a lot of the reason was so that I could have ownership over my own possessions, especially my clothes. I was both a fat kid and raised by my grandparents, and I spent my entire childhood either being stuffed into whatever hand-me-downs from my older cousin that I could be stuffed into or wearing clothes that my grandmother picked out or sewed for me. From the former, there were a lot of itchy dresses and corduroy pants (fun fact: fat kids HATE corduroy pants!). From the latter, there were things like polyester granny panties exactly the same as the ones my own grandmother wore, and one-size denim jumpers, the pattern for which started off as the pattern to make my junior high choir concert uniform but Mamma thought it was cute and should be immortalized in denim.

It wasn't cute, and it shouldn't have been immortalized in denim.

ANYWAY, even when I had my own money I wasn't a big spender. I mostly bought stuff like cotton panties and concert T-shirts from concerts I didn't go to (I STILL have my Pink Floyd concert T-shirt from Russia; it's as soft as butter and thin as tissue paper, and I'll probably be buried in it one day). I never felt like I spent any kind of big money, and yet every time I came home with a shopping bag my grandfather, who was, to be fair, himself raised during the Great Depression, absolutely grilled me about what I'd bought and how much it cost. And no matter what it was or how much I'd spent, when I told him the number he'd always suck in his breath and be disappointed at my excess.

Like, after a while I started lying, even, just saying some ridiculously low number that you couldn't possibly buy a pair of jeans or whatever for, even at Wal-mart, and he'd still do it. For him, it was more the principle of the thing--he didn't want me to spend my hard-earned money frivolously (or, possibly, at all...). For me, though, it started to feel like maybe I didn't deserve a $12 Russian concert T-shirt, or a $16 pair of jeans, or a $4 pack of cotton panties. Which is not something that Pappa would have ever believed, himself, but I feel like kids internalize stuff that you bitch about, even if you're not bitching at them, necessarily. And maybe, you know, I don't want Syd to feel like she doesn't deserve a $30 memory foam pillow just because her parents sleep on pillows so old I don't even know how long we've had them.

Actually, our pillows kind of suck. Maybe I deserve a $30 memory foam pillow, too! Unless that's a ridiculous amount to spend on a pillow? Which brings me back to my original point, which is that I have no idea how much is appropriate to spend on a pillow, and $30 feels like a lot, but I can afford it and therefore I'm not going to bitch about it to Syd. Instead, I'll just bitch about it for six paragraphs to you, because you're my safe space for bitching about stuff.

So even though this Senior Room Makeover badge didn't come together quite the way it does in the badge book, I think Syd (and I!) got a lot out of it. Syd got a chance to really think about what she wants her space to look like now that she's a teenager, and she learned how to make that vision a reality for herself. She got some nice, new bedding that she was definitely in need, of, anyway, and it was good timing for developing a routine for the care and maintenance of her belongings.

Please let me know for future reference how much is appropriate to spend on a pillow.

Wednesday, April 29, 2020

A DIY Binomial Cube/Trinomial Cube Manipulative



If you've figured out that you can make a manipulative to literally represent (a + b + c)^2, then it's not a big stretch to figure out that you can also make a manipulative to literally represent (a + b + c)^3.

One is a literal square. The other is a literal cube!

I made this DIY trinomial cube to match faces with my DIY trinomial square. This means that it's also set to a 1" standard, NOT a 1 cm standard as are most of my other DIY math manipulatives. But since it was soooooo much easier to find 1", 1.5", and 2" blocks than it was to find 1 cm, 1.5 cm, and 2 cm blocks, it also means that I could take some major shortcuts on this build and save myself a lot of time gluing teeny-tiny wooden blocks together.

I'll take the shortcut every time!

The math isn't exactly tricky on this, but there's a lot of it, and a lot of moving parts, so bear with me.

The trinomial cube has three layers. Layer A is a trinomial square in which every prism has Height a. For my project, a = 1".

Layer B is a trinomial square in which every prism has Height b. For my project, b = 1.5".

Layer C is a trinomial square in which every prism has Height c. For my project, c = 2".

The base block for each layer is a wooden cube that I purchased from Casey's Wood Products:

From left to right, that's a 2" cube, a 1.5" cube, and a 1" cube.

Let's go back to Layer A. We already know that every prism in Layer A will have a height of 1". The cube in Layer A is a^3, with a measurement of 1" x 1" x 1". This is nothing but a 1" wooden block, with no extra pieces added to it. As part of this layer you're also going to have a piece that's b^2, and a piece that's c^2, each with a height of 1", and the prisms that combine the measurements of ab, ac, and bc, each with a height of 1"

For every prism in this layer, you can start with a 1" wooden block, and glue on either .5" wooden blocks or 1" wooden blocks to make the correct sizes.

Here are all the prisms for Layer A:
  • a^3 (1" x 1" x 1"). This is a 1" wooden block.
  • ab^2 (1.5" x 1.5" x 1"). This is a 1" wooden block plus 10 .5" wooden blocks.
You need one ab^2 for Layer A and two ab^2 for Layer B.
  • ac^2 (2" x 2" x 1"). This is four 1" wooden blocks.
You need one ac^2 for Layer A and two ac^2 for Layer C.
  • two copies of  ba^2 (1.5" x 1" x 1"). This is a 1" wooden block plus four .5" wooden blocks.
  • two copies of ca^2 (2" x 1" x 1"). This is two 1" wooden blocks.
  • two copies of abc (1" x 1.5" x 2"). This is two 1" wooden blocks plus eight .5" wooden blocks.
You need two copies of abc for every layer, so six in total.

Every prism in Layer B will have a height of 1.5". The cube in Layer B is b^3, with a measurement of 1.5" x 1.5" x 1.5". This is nothing but a 1.5" wooden block, with no extra pieces added to it. As part of this layer you're also going to have a piece that's a^2, and a piece that's c^2, each with a height of 1.5", and the prisms that combine the measurements of ab, ac, and bc, each with a height of 1.5".

Here are all the prisms for Layer B:
  • ba^2 (1.5" x 1" x 1"). This is a 1" wooden block plus four .5" wooden blocks.
You need two ba^2 for Layer A and one ba^2 for Layer B.
  • b^3 (1.5" x 1.5" x 1.5"). This is a 1.5" wooden block.
  • bc^2 (1.5" x 2" x 2"). This is a 1.5" wooden block plus twenty-one .5" wooden blocks.
You need one bc^2 in Layer B and two bc^2 in Layer C.
  • two copies of ab^2 (1.5" x 1.5" x 1"). This is a 1" wooden block plus 10 .5" wooden blocks.
  • two copies of abc (1" x 1.5" x 2"). This is two 1" wooden blocks plus eight .5" wooden blocks.
  • two copies of cb^2 (2" x 1.5" x 1.5"). This is a 1.5" wooden block plus nine .5" wooden blocks.
You need two cb^2 for Layer B and one cb^2 for Layer C.

Every prism in Layer C will have a height of 2". The cube in Layer C is c^3, with a measurement of 2" x 2" x 2". This is nothing but a 2" wooden block, with no extra pieces added to it. As part of this layer you're also going to have a piece that's a^2, and a piece that's b^2, each with a height of 2", and the prisms that combine the measurements of ab, ac, and bc, each with a height of 2".

Here are all the prisms for Layer C:
  • ca^2 (2" x 1" x 1"). This is two 1" wooden blocks.
You need two ca^2 for Layer A and one ca^2 for Layer B.
  • cb^2 (2" x 1.5" x 1.5"). This is a 1.5" wooden block plus nine .5" wooden blocks.
  • c^3 (2" x 2" x 2"). This is a 2" wooden block.
  • two copies of abc (1" x 1.5" x 2"). This is two 1" wooden blocks plus eight .5" wooden blocks.
  • two copies of ac^2 (1" x 2" x 2"). This is four 1" wooden blocks.
  • two copies of bc^2 (1.5" x 2" x 2"). This is a 1.5" wooden block plus twenty-one .5" wooden blocks.
I painted these prisms the same way I painted the trinomial square prisms, except for the cube, every face will be painted. All the 1"^2 faces are yellow, the 1"x1.5" faces are green--



--the 1.5"^2 faces are blue--



--the 1"x 2" faces are orange, the 1.5" x 2" faces are purple, and the 2"^2 faces are red:



Some prisms in different layers are identical, so here are the total number of prisms by type that I needed:
  • one a^3 (1" x 1" x 1"). This is a 1" wooden block.
  • one b^3 (1.5" x 1.5" x 1.5"). This is a 1.5" wooden block.
  • one c^3 (2" x 2" x 2"). This is a 2" wooden block.
Here's a^3, b^3, and c^3.
  • three ba^2 (1.5" x 1" x 1"). This is a 1" wooden block plus four .5" wooden blocks.
  • three ca^2 (2" x 1" x 1"). This is two 1" wooden blocks.
  • three ab^2 (1.5" x 1.5" x 1"). This is a 1" wooden block plus 10 .5" wooden blocks.
You need one ab^2 for Layer A and two ab^2 for Layer B.
  • six abc (1" x 1.5" x 2"). This is two 1" wooden blocks plus eight .5" wooden blocks.
you need two abc prisms for each layer.
There are a lot of abc blocks, so thankfully Spots was willing to help me photograph them!




  • three cb^2 (2" x 1.5" x 1.5"). This is a 1.5" wooden block plus nine .5" wooden blocks.
three cb^2
  • three ac^2 (1" x 2" x 2"). This is four 1" wooden blocks.
three ac^2
  • three bc^2 (1.5" x 2" x 2"). This is a 1.5" wooden block plus twenty-one .5" wooden blocks.
three bc^2
 Spots is sorry that she knocked over my blocks, so here's a blep to make up for it:


And also a boop for good measure:


 And here's what it looks like when it's all finished!

LAYER A




LAYER B



LAYER C


Spots is still not helping...


The kids wandered over as I was finishing photographing the cube (meaning that now I had two teenagers AND a cat helping me...), so I told them this was a puzzle that I'd just finished building and invited them to see if they could put it together:



They didn't notice that it was a pattern, at first, and so made some unworkable choices:



Eventually, though, a light bulb came on...




And behold! It's laid out unusually, but it's our trinomial cube!


Here's the Montessori setup for the binomial and trinomial cubes. They're normally given to small children to work as a puzzle, which is a great way to make that higher level math familiar and not scary at all when they come to it later.

And here are a couple more references, if you want to plan a lesson around the binomial or trinomial cube:

Want to see what other mischief we (and the cats) manage to get up to with our brand-new DIY trinomial cube? Check out my Craft Knife Facebook page for updates!