Monday, June 11, 2018

Hands-On Fibonacci Sequence Explorations: Combining Logic, Math, and Art


I've realized that much of the hands-on math enrichment that I offer the kids is "number sense"--helping to develop their intrinsic understanding of numbers, their flexibility with them, their pattern recognition of number relationships. Whether it's fractions or geometry or exponents that we're studying, I always see space in their curriculum where free exploration can make kids wiser in what they're studying.

In algebra right now, the older kid is studying proportions and ratios, so what better time to spend some more time on the Golden Ratio?

I introduced the kids to the basic concept of the Fibonacci Sequence and how it's calculated, then asked them to use each number in the sequence as one side of a square. They were to draw those squares on 1cm graph paper, color them in, and cut them out. I told them that they should stop only when the next square would not fit onto a single piece of graph paper, although if we did this project again, I'd tape together larger sheets of graph paper ahead of time so that they could extend the sequence further.

Here's one of the sets that the kids came up with:



Apologies for the poor lighting in these photos, but school gets done on rainy days as well as sunny!

You can make lots of pretty patterns with just these squares. And yes, I DO think that Fibonacci Sequence stacking blocks would be AWESOME!

Next, I told the kids that these squares of the Fibonacci Sequence are also a puzzle, and I challenged them to use all of their squares to make a rectangle. They're familiar with this idea from the pentominoes that we've played with.

Here is the older kid's rectangle:


And here is the younger kid's!


The kids did not confer, so I think it's interesting that both built their rectangles the same way, and neither happened upon the "spiral." In fact, when I later rearranged the pieces to show the spiral, the younger kid still didn't really see it. This is where more and larger squares would have helped by extending the pattern.

I took away the larger squares, and had the kids solve the puzzle to make a rectangle with only the three smallest:


Then I added the next piece, and again asked them to solve the puzzle:



Do this again and again, and you see how the pattern can be formed:


Beautiful, isn't it?

In related news, we were at the US Space and Rocket Center last week for the older kid's Space Camp graduation (more on that another time!!!), and in their museum, look at the display that we found!


It was particularly terrific because it extended the pattern for us to see!


 I didn't look at any additional resources with the kids until after they'd worked the "puzzle," because I didn't want them to see a solution, but later in the day we watched these two YouTube videos from two of my favorite YouTube channels:



Here are some other great Fibonacci resources that we've been exploring:
And here are some more ways to explore the Fibonacci Sequence in logic, math, and art:
This project gave inspired me to come up with some more extension ideas just for me. I think it would be really cool to design a large-format squares of the Fibonacci Sequence, print it, and glue it to foam board the way that Matt and I did with the decanomial square. Imagine how many more interesting patterns you could come up with. I also deeply need to sew a Fibonacci sequence quilt.

As if I don't already have enough dream projects on my to-do list!

Thursday, June 7, 2018

Crafty Book Review: Drawing Wild Animals, and 8 More Art Activities for Biology

I've mentioned off and on for years now how much the kids enjoy how-to-draw books. Every now and then I'll check out a pile of them from the library, and every now and then a publicist will send us a free one to play with.

Our most recent review copy is Drawing Wild Animals, which is coming in super useful for our Honors Biology study. The animals are categorized by class, with examples of mammals, amphibians, and reptiles represented. Some of the animals that the book shows you how to draw, such as the frog, toad, and salamander, are animals that the kids can practice from the book, then draw again as we do nature studies. We can do the same drawing practice, but then visit the zoo to study and draw animals like the tiger, giraffe, rhinoceros, zebra, elephant, lemur, and rattlesnake.

And, of course, some of the animals we can just draw for fun! Here are some sketches that Will made from the book the other day:

Will doesn't consider herself to be a competent artist, which means that she's often reluctant to do art. I'm always thrilled, then, when a resource is so deliciously tempting that even she will happily partake! And, of course, it helps when it's user-friendly enough that she's pleased with what she creates--that's positive reinforcement for practicing art!

Syd does consider herself to be an artist--and oh, she's a wonderful, gifted artist, indeed. Here's what she drew:



I think the detailing on the antlers, and the hair on the... hare... are new techniques that she picked up from the book. Super useful to be able to draw antlers and bunny fur!

Syd has sometimes been less engaged in our extensive biology studies this past year, so I'm contemplating deliberately incorporating more art into our biology. Syd always likes to do art! Here are some of the ideas that I've been researching:
  1. I love these free, downloadable artist's study lessons. The first grade packet includes a close reading and extension activities for The Peaceable Kingdom; the second grade packet includes Tiger in a Tropical Storm; and fourth grade has an Audubon plate and The Horse Fair.
  2. The Endangered Species Art Contest takes place every year!
  3. There's also a National Fossil Day art contest!
  4. A magazine collage would be fun for younger kids to create.
  5. Look how beautiful these feather prints are!
  6. You can make a life cycle story board for for every unique life cycle that you study.
  7. This photo tutorial is for a papier mache dinosaur, but papier mache would work for any whole-body animal study, or even as a project on cells or organ systems.
  8. The Children's Museum of Indianapolis has an entire curriculum about paleo art. It's young for my two, but easily adaptable.
I feel like I'm on the right track with this, but I don't think I've yet hit on anything that would be a meaningful contribution to our study and would fill Syd with excitement. Let me know if you've got other suggestions for me!

Wednesday, June 6, 2018

When Your Kids Outgrow Their Building Blocks, Turn Them Into Art!

My kiddos are BUSY this summer, which means I've had a little more time on my hands than usual.

And when I have time on my hands, my hands tend to get messy!

After I've written lesson plans and finished all my freelancing for the week, I've found myself, more often than not, watching Downton Abbey and messing around with my stack of super-old and completely value-less vintage comics. I have decoupaged comic books onto some crazy things in my time, but lately I've been confining myself to the harmless obsession of making decoupaged building blocks using my vintage comics and the blocks that the kids don't play with anymore.

Some I am making entirely for myself. I would NEVER sell my now most treasured Captain America block, for instance!


Comic book shops often sell their "worthless" comics for small change, and that's where I find comic books to craft with. I collect only comics featuring characters whom I really like, of course, but then the danger to that is that I often can't part with what I've made with them.

But part of the deal that I make with myself is that when I make something FOR myself, I try to make some similar things for my Pumpkin+Bear etsy shop--gotta pay for those craft supplies somehow, don't you know! So even though I super love Thor, I've listed this block featuring his bromance with Iron Man in Pumpkin+Bear,sigh...


I'm keeping my GI Joe block, though, because Snake Eyes!


But, fine. I'm selling this Iron Man comic book block. I love Iron Man, but that Civil War movie still has me pissed off:


And here's Hulk!


Some of the comics that I'm crafting with are the really beat-up ones that I had as a kid. I LOVED this Tom and Jerry comic in which Jerry sneakily feeds Tom until he's too fat to chase him (which huh. I had a lot of food issues as a kid, and I STILL have them. This comic could not have helped with that...), but it's absolutely falling apart, so now it's a super cute decoupaged building block:


Nobody is tearing my brand-new Thor block out of my grasp, however!


But, yeah. You can have Archie:


But NOT Captain America!


Spider-man, though--I've got a couple of Spider-mans. You can buy him as a rectangular prism--


Or a delightful cube:



But you just can't have my Captain America!


Or my Thor:


Here are another couple of comics that I owned as a kid. I clearly didn't have enough comics, because I have this old Richie Rich one memorized, and also worn down to a nub except for what I salvaged to make this decoupaged block:


Here's my weirdest block, though. I don't know who on earth bought me an Adventures of Kool-Aid Man comic, but did you know that it was published by Marvel? Kool-Aid Man could be an Avenger!

For now, though, he's just a very, very, VERY weird comic book block:





This will likely be my last Pumpkin+Bear update for a bit. I want to try to sneak into my studio to make some comic book magnets using upcycled Scrabble Tiles as a base, but I'm also road tripping and camping with the kids, packing them for camp (and making 100,000 trips to the store for everything on the packing list that I don't own), sewing them some summer clothes, planning some fun unit studies for them, and helping Will finish up her Girl Scout Silver Award project. 

Of course, making Scrabble tile and comic book magnets while watching Downton Abbey would be a nice, relaxing break from my to-do list...

Monday, June 4, 2018

Here's Every National Park Junior Ranger Badge You Can Earn By Mail (Updated August 2024)


August 2024: I corrected some links, marked through some sites that no longer allow mail-in badges, and added some new mail-in badges to my list.

July 2023: I crossed out several Junior Ranger badges that are no longer available to earn by mail, but fortunately I also added a few new ones, too, and I updated my map with new Junior Ranger badges that kids can earn on-site.

It's been four years since the kids first discovered the Junior Ranger program at Badlands National Park, and thus began their obsession. I'm never one to let an educational experience go, so since that first thrilling day, I have deliberately organized ALL of our US vacations to include as many Junior Ranger programs as possible, and I've included all of the Junior Ranger programs that it's possible to earn by mail into our homeschool plans.

"How did you figure out where all of the Junior Ranger programs are?" you ask.

Friends, I made a giant freaking map:



Yes, that is EVERY SINGLE NATIONAL PARK SITE WITH A JUNIOR RANGER PROGRAM. I put them all in by hand. I went to every single national park's website, searched for its Junior Ranger program, and if it had one I put it on my map.

When I plan road trips, I check my map for all the national park sites with Junior Ranger programs that we could detour to, and then we detour to them. During our upcoming road trip, for instance, we're visiting Saint Croix Island and Acadia National Park, primarily for their Junior Ranger programs.

But the kids' enthusiasm for earning Junior Ranger badges is unceasing, and yet we cannot spend our entire year traveling to various national parks. If only!

So I went back through every one of those websites, and I noted every park that permits children to earn their Junior Ranger badge by mail. Most of these parks provide the badge book as a downloadable pdf for kids to complete using internet or book research (often the park's own website, but we've also found useful park videos on YouTube). They mail their completed badge books to the park, and in return, the park rangers mail them back their badges and certificates.

It's always, eternally thrilling.

The kids have been doing this for years now, and still have tons of Junior Ranger badges left to earn by mail. They've learned geography, history, and several sciences in the process, experienced the breadth and depth of the national experience in ways they haven't had the opportunity to do in person, and have an intense appreciation for the variety of cultural, historical, and geographic artifacts and monuments that must be explored, preserved, and protected.

Not every national park, or even most national parks, allow their Junior Ranger badges to be earned by mail, mind you. You'll know if one does, because it will say so on its website or on the book, and it will have the book available as a downloadable pdf and include a mailing address for the completed book to be sent to. Many parks will state, kind of pissily in my opinion, that they do NOT allow badges to be earned by mail, and that's their right, but I think everyone loses when they do that--why stifle a kid's desire to learn? Why refuse an opportunity to grow someone's knowledge and love of your national park?

Before you get your kid all revved up on earning these badges by mail, you should know that since you've got to mail the completed badge books to each park, you'll be paying a few bucks for postage and manila envelopes each time. If you're conserving resources, check out the online badges that I've noted in my list--those let kids either do or submit their work online, so you don't have to pay for either supplies or postage.

Fortunately, MANY national parks are happy to have more kids interested in them and working to learn more about them! Here are all the national park Junior Ranger badges that you can earn by mail:

NOTE: I do NOT include Junior Ranger badges in which the badge book is offered as a pdf from the national park site, but kids cannot mail them in or submit them online to earn the badge without a visit to the site. Lots of national park sites offer their badge books as pdfs so that kids can get a head start on the book (which is a great idea!), and some sites even allow kids to mail in their badge books later if they didn't have time to complete them at the park, but this is is solely for badges that kids can earn entirely from home.

I'm also not including any of the newer "virtual Junior Ranger programs," which let kids complete some web activities and then print an image of the Junior Ranger badge. Those can be fun, but this list is solely for physical badges that kid can earn from home.

AND I'm also not including Junior Ranger badges that officially aren't available by mail, but that people have anecdotally or allegedly sent in, regardless. It's cool that it works for some people, and you're always welcome to contact a national park site and ask for an exception, but this particular list is hopefully just for the safe bets.


This is one of my absolute favorite activities that we do in our homeschool, but it's partly so wonderful because it's so adaptable. Sure, it can be your entire geography curriculum, or just an enrichment to another spine. You can include it in your history studies, or in the natural or earth sciences. Even if you don't homeschool, these Junior Ranger books are so fun that kids can simply DO them for fun. My kids do, and they think it's a nifty trick that I also let them count them for school!

If your kids love earning Junior Ranger badges, then they'd likely be interested in learning about the national park system as a whole--there's so much to explore there, from history and culture to geology and the sciences. Here are some of our favorite resources for learning about and exploring the national park system:
P.S. Want more obsessively-compiled lists of resources and activities for kiddos and the people who want to keep them happy and engaged? Check out my Craft Knife Facebook page!