DIY Upcycled Cardboard Polyominoes

 

This tutorial was originally posted on Crafting a Green World.

Polyominoes are a super fun educational toy. When made from upcycled cardboard food packaging, they’re also super eco-friendly!

If you’ve ever played Tetris, you know what polyominoes are, AND you know how fun they are!

Without getting too mathy, because I know that scares some of y’all, polyominoes are shapes that you can draw on a piece of graph paper using the same number of squares.

You know dominoes, right? Those are polyominoes made of two units.

Tetrominoes are made of four units. When you play Tetris, you’re playing with tetrominoes!

Pentominoes, pieces made from five units, are my personal favorite.

There are infinite really interesting math problems–many of which have never been completely solved!–that utilize polyominoes. But even for us non-professional mathematicians, polyominoes remain very fun. You can build cool patterns with them. You can create puzzles from them, then try to solve them! And, if you have a kid around, they’re a sneaky way to build their logical reasoning skills and to teach concepts of area, perimeter, patterning, and other even more abstract, sophisticated geometry and measurement concepts.

Also, I’m just going to say it one more time–they’re really fun!

You don’t need another set of plastic game pieces kicking around your home, though. Instead, here’s how to make any set of polyominoes that you want from sturdy, upcycled, recyclable cardboard.

To make your own set of upcycled cardboard polyominoes, you will need:

• upcycled cardboard. Cardboard food packaging is perfect for this project–for this tutorial, I’m making all my polyominoes from Girl Scout cookie boxes! It would be VERY fun, though, to make “life-sized” or giant polyominoes from corrugated cardboard.
• graph paper. Once upon a time, I scored the rest of someone’s stash of 1″ graph paper at a yard sale, but the internet exists now, and so you can just print graph paper at any size. Or if you, like all the other cool kids these days, don’t own a printer, you can buy it commercially.
• measuring and cutting supplies. I made all these polyominoes with a pen and a pair of scissors.
• double-sided tape (optional). All polyominoes other than Tetris pieces are meant to be able to be flipped over, and if you get into doing polyomino puzzles, solutions will often require it. For that reason, I make most of my own polyomino pieces double-sided. But if the difference between the front and back of a polyomino piece doesn’t bother you, then don’t bother with this extra step!

Step 1: Create the polyomino patterns.

This first step is my favorite!

On graph paper, sketch out the outlines of your polyominoes. You can easily Google patterns for various polyomino sets, but kids, especially, find it VERY fun to create their own polyominoes from scratch.

Cut out your polyominoes, and you’re ready to apply them to the cardboard.

Step 2: Use the paper templates to make cardboard polyominoes.

Trace around the polyominoes and cut them out of the upcycled cardboard.

Using upcycled cardboard food packaging gives you a lot of scope for creativity! If you’ve got a variety of colors, like I do with my Girl Scout cookie boxes, it can be fun to make each type of polyomino a different colors. Or, decide that the plain cardboard side will be front-facing, and decorate the pieces with markers.

Step 3 (optional): Make the polyominoes double-sided.

Tetris gets away with not letting you flip pieces by making the flipped side a completely separate piece. For every other use, though, you’ll generally want to be able to flip your pieces over. If you’re using cardboard that’s roughly the same on the front and back, that’s not a problem, but with this cardboard food packaging that has a printed side and a plain side, I’ve discovered that many people, and especially kids, find it non-intuitive to have to flip pieces. We’re just not used to working with both the “front” and “back” of a puzzle!

To solve that problem, make your polyominoes double-sided.

Just cut out a second piece (flip the pattern over if the piece isn’t symmetrical!), then attach the two with double-sided tape. Now both of your sides look cute, and it’s easy to realize that you can flip them!

There are so many ways to extend the fun of polyominoes while exercising your brain and developing numeracy and logical reasoning skills. A mini set taped onto a magnet sheet and put into an Altoids tin is a terrific little travel game; for even more fun, hand-draw or print puzzle templates on plain paper and cut them out to fit in the tin, too. A larger set of tetrominoes and a few pieces of grid paper taped together make a fun two-player, analog Tetris game; for more fun, add more magnets and place on a wall-mounted metal sheet.

P.S. Want to follow along with my craft projects, books I'm reading, dog-walking mishaps, encounters with Chainsaw Helicopters, and other various adventures on the daily? Find me on my Craft Knife Facebook page!

DIY Corrugated Cardboard Tower of Hanoi

 

This tutorial was originally published on Crafting a Green World.

Tower of Hanoi is a super simple, surprisingly fun logic game suitable for early elementary through adults.

I have a weakness for solitaire games, especially logic puzzles. I’ve built up a respectable collection thanks to thrift stores and yard sales, but there’s always room for one more puzzle in my life, especially one that’s NOT made from plastic!

This Tower of Hanoi is NOT made from plastic! Instead, it’s made from that likely-looking piece of corrugated cardboard hanging out there in your recycling bin. Cut it up, add some decorations, and you’ll have yourself a brand-new version of a 140-year-old logic game.

Here’s everything that you’ll need to DIY your own Tower of Hanoi:

• corrugated cardboard. Since the pieces are manipulatives, I prefer the thicker, sturdier corrugated cardboard over the thinner kind for this project.
• measuring and cutting tools. You’ll need circles of varying diameters to use as templates for your Tower of Hanoi pieces. Look around, and I bet you can scavenge these circles from your existing bottles, cups, caps, etc.
• embellishment supplies (optional). You don’t *need* to embellish the pieces, but since when did that stop anyone from making something pretty?

Step 1: Measure and cut the pieces.

You can play Tower of Hanoi with three or more pieces, but I think seven or eight pieces are a good total number to have. You can always subtract pieces from a larger set to make a round easier!

To make the complete puzzle look like a lovely tower, select circle templates with different diameters, ideally ones that will give a nice graduated look from smallest to largest when you stack them. As you can see from the above photo, you should be able to find all of these circle templates around your house. My smallest circle template is an eensy SodaStream flavoring bottle cap, and my largest is the top of a plastic drink cup from my favorite pizza place–I also used the bottom of the cup to make a different circle!

Trace all the circles onto corrugated cardboard, then cut them out by hand with sturdy scissors.

If you like the way the undecorated Tower of Hanoi looks, you’re done! However, I think the game looks a LOT cuter with some embellishment…

Step 2: Decorate the pieces.

With seven pieces to my puzzle, how could I NOT make a rainbow?

One of the many amazing things about corrugated cardboard is that it takes all kinds of embellishment like an absolute dream. I painted these circles with Liquitex acrylics, but Sharpies or even Crayola markers all show up well. Use Mod Podge to decoupage scrapbook paper, or paint plus paint pens to make more detailed artworks on these tiny canvases.

Step 3: Play!

The rules of Tower of Hanoi are simple:

1. Start with the tower stacked with the circles in descending order, smallest to largest.
2. You have three total spaces in which you can work, and you start with the stacked tower sitting on one space. Younger players might benefit from having a play mat on which you’ve drawn out three spaces for them, but it’s unnecessary for older players.
3. The objective of the game is to reassemble the tower on another space. The reassembled tower must again be stacked with the circles in descending order, smallest to largest.
4. You may move one circle at a time between any of the three spaces.
5. You may NOT stack a circle on top of a circle that is smaller than it. Circles can only be put on empty spaces or stacked on top of circles that are larger than them.

The above photos illustrate a few different moves in the game. I don’t want to give you too many moves so that I don’t spoil your fun, but you can see from the photos the three working spaces, and the circles that are placed on a space or on top of a larger circle.

Remember that you can’t move an entire stack of circles at once–you can move only one circle at a time!

If you want to see the game in action, check out this online playable version.

If you’re a mathy kind of person, there IS a mathematical solution, and a pattern, to this puzzle. Figuring out how to record your moves is also a great introduction to analog coding, for those of you interested in STEM enrichment.

Want to give someone you love a sneakily educational gift? A beautifully embellished Tower of Hanoi inside a lovely little carrying case is just the thing!

Know a kid who’s high-energy and always seems to need more gross motor activity? Upscale this to a giant 3D version that they have to use their whole bodies to stack! Exercising their brain will make them just as tired as exercising their body, so you might even get a full night’s sleep!

P.S. Want to follow along with my craft projects, books I'm reading, dog-walking mishaps, encounters with Chainsaw Helicopters, and other various adventures on the daily? Find me on my Craft Knife Facebook page!

The Sieve of Eratosthenes as an Aid to the Memorization of Prime Numbers

Just as memorizing sight words can help a kid read better and more confidently, there are tons of math facts that, if memorized, will make a kid's calculation work quicker and more confident. 

Our culture is well used to having kids memorize the multiplication tables through at least 10 (through 12 is better!), and certain formulas like the quadratic formula or the Pythagorean theorem, but it's so helpful to just know, when you're busy doing your algebra, say, if a number is a perfect square or a Pythagorean triple, etc. It builds confidence when a student is learning advanced math concepts, and it increases their speed and fluency, which they will VERY much appreciate whether they're working through a page-long proof or an SAT problem set!

When my kids were pretty little, we dedicated the first ten minutes of the first car trip of the day to memory work, and they memorized a lot of advanced concepts by rote then (most famously, the first 25 digits of Pi, a party trick that they still both often pull out over a decade later, lol!), but it's a better aid to learning and to memorization to have them, whenever possible, create for themselves the anchor chart that contains the information I want them to memorize.

So when I realized recently that my teenager has lost most of the prime numbers to 100, I pulled back out the same activity that she used to create her Prime number chart back when the kids memorized the primes to 100 the first time around back in 2016.

It's the Sieve of Eratosthenes!

Creating the Sieve of Eratosthenes is simple. All you need are a hundred chart and some colored pencils or crayons. This hundred chart has the numbers by rows, and this hundred chart has the numbers by columns. This hundred chart is blank, for some sneaky real-world handwriting practice writing the numbers to 100. 

To create the sieve, you simply start with the first Prime number, 2. Don't color it, but color all of its multiples. Bonus points if you unlock the pattern and color it that way! The next uncolored number is your next Prime number, 3, so leave it blank but color all its multiples. It makes a pretty pattern, too!

Carry on through 7, and by the time you've colored the last multiple of 7, you'll have colored every composite number through 100, and every uncolored number is a Prime. Your grid will look like this:

photo credit: Wikipedia

I think the patterns that it makes are beautiful and fascinating!

While you're working, it's best if you have a Ginger Gentleman supervise you:

While you're working, you also might notice that you have a sudden, inexplicable swarm of Asian lady beetles inside your home. Would the Ginger Gentleman like to meet one?

He very much would!

Please note: no Asian lady beetles were harmed in *that* particular encounter. When Matt got home and found the swarm and went for the vacuum cleaner, though, well...

The Sieve of Eratosthenes is a quick, enjoyable, non-rigorous enrichment activity for an older kid, best used for a review of Prime numbers or to construct a memory aid/anchor chart. However, you can actually also do this activity with quite young kids, since multiplication is the only skill required. It's fun and hands-on, the patterns are pleasing, and it gives kids a really interesting math concept to explore.

Here are some good books to use with younger kids in partnership with this activity:

To extend the fun, younger kids can play Prime Number Slapjack or color in a Prime path maze. If kids are a bit older and are ready to properly learn about Primes, composites, factor trees, and the factorization of Primes, this lesson and this lesson are excellent jumping-off points. 

We have a lot of wall space in our home, and my kids have always enjoyed making large-format posters, maps, and charts to put on our walls. A large-format hundred chart mounted on a wall lets kids have a different experience coloring it in mural-style, and would also allow room for kids to write each composite number's factors into those squares. Alternately, extend the hundred chart to 1,000 and keep sieving, although I wouldn't blame you for eventually pulling out the calculator!

Here are some books that older kids and adults would enjoy; completing a reading assignment (and perhaps even a response essay!) builds context and adds rigor to an otherwise simple activity, and is a good way to facilitate different ages/abilities working on the same project:

Here are some other math facts that a student could aid fluency by memorizing:

• fraction/decimal conversions
• PEMDAS
• Quadratic formula
• squares
• square roots (perfect square factors and simplified square roots to 100)
• Pi to several digits
• Pythagorean theorem
• Pythagorean triples
• triangle identities
• SOH CAH TOA

P.S. Want to follow along with my craft projects, books I'm reading, dog-walking mishaps, encounters with Chainsaw Helicopters, and other various adventures on the daily? Find me on my Craft Knife Facebook page!

How to Make the Easiest Upcycled Cardboard Building Set

 

This tutorial was originally published on Crafting a Green World.

This upcycled cardboard building set is a terrific open-ended toy that won’t cost you a cent!

If you’ve ever seen a kid with a handful of LEGOs, you know how wonderful open-ended building toys are. They let kids exercise their creativity, build their problem-solving skills, strengthen math and physics concepts–and keep themselves entertained for ages, too! Open-ended toys have a lot more extended play-value than toys that have a single purpose (and a lot LOT more play-value than noisy, light-up toys!).

This particular upcycled cardboard building set is as open-ended as they come. You can create the pieces in any shape you can imagine, connect them in a myriad of ways, and even paint or decorate them however you’d like. And the best part is that as long as you have a piece of corrugated cardboard in your recycling bin, you can expand on your building set forever.! Tbh, creating the set is as fun as building with it!

Here’s how to make the quickest, easiest, and SUPER fun upcycled cardboard building set:

To make this building set: you will need:

• corrugated cardboard. Thin cardboard won’t work for this project, but pretty much any corrugated cardboard will. If you’re short on corrugated cardboard, check your local recycling center or ask around your friend group for shipping boxes.
• scissors. Cutting corrugated cardboard does take hand muscles, but larger scissors make it easier. If you’re making this project with younger kids, let them draw the pieces they want onto the cardboard, and then you can do the tough job of cutting them out. If kids are a little older, though, give them a go at cutting the cardboard themselves–it’s tough, sure, but it builds the hand muscles they need for writing by hand and other fine motor activities.
• tools for embellishment (optional). I really like the look of these plain, but with paint, markers, or stickers, you can add variety and creative inspiration. Googly eyes are always fun, as are pieces painted in a rainbow of colors. Use your imagination to make the cardboard building set of your dreams!

Step 1: Draw templates (optional), and cut the cardboard into shapes.

I’m a little obsessed with geometric shapes, but you can cut your corrugated cardboard pieces however you like. If you’re making a basic set for a kid, a variety of geometric shapes, along with some free-formed, more abstract pieces, will give them a good starting place.

If you’re making a set WITH a kid, however, my favorite technique is to encourage the kid to draw or cut any fun shape their heart desires, modeling a few ideas for them, perhaps, to give them the idea. While they’re being creative, I’ll cut out those same boring geometric shapes (I’m obsessed!) so that they’ve got some basic pieces to work with, as well.

Step 2: Cut notches in the cardboard pieces.

Cut a thin notches in the cardboard pieces wherever you’d like them to connect. Longer notches will hold the connections more firmly, but you don’t need the notches to go more than 1/4 or 1/3 of the way through the piece.

Cutting notches is a little easier than cutting out the pieces, so if you’ve got a kid who’s on the cusp of being able to cut the corrugated cardboard, this is a doable activity to help build their hand strength.

This is also a great place to add to the interest of the set. Finding unusual places to cut notches encourages kids to make more creative connections.

To play with this toy, simply connect the notches and start building!

I think kids have the best time when they can follow their own interests and imaginations, but you can sneak in some STEM problem-solving by offering up challenges. What is the tallest tower you can build? What is the longest bridge you can build between two chair backs? Can you build a square shape using only circle pieces? Try building a cat!

Cheap, accessible toys like these are especially important to have out in the world, because they build equity. The local underfunded childcare center probably doesn’t have fancy Magna-Tiles, and heck, even Duplos are ridiculously expensive these days, but anyone can make and donate a huge set of the most beautiful cardboard building toys with some time and patience.

And homemade toys like that are important for every kid to have, even if their parents can afford the bougie stuff. Maybe it’s the pre-Christmas anti-consumerist crankiness starting in me already, but I think it’s crucial for every kid to learn that some of the best toys are both handmade and free. I mean, I love all those fancy, expensive natural wood toys as much as the next crunchy mom (ask me about my Waldorf toy obsession anytime!), but you know what’s nearly as natural, and even more free, than that?

CARDBOARD, that’s what!

DIY Cat Scratcher from Upcycled Corrugated Cardboard Boxes

This tutorial was originally posted on Crafting a Green World.

This upcycled cardboard cat scratcher is a great way to use up all your corrugated cardboard boxes. Cats love it, and it's a useful donation to your local animal shelter.

There comes a time in every person's life when they find themselves simply awash with cardboard. Maybe you just finished unpacking from your latest move. Maybe you went a little too ham on the most recent gift-giving holiday. Maybe your Girl Scout troop sold 2,000 boxes of Girl Scout cookies and now you have 250 empty cookie cases to show for it.

Whatever the situation that has left you with too much corrugated cardboard, I have the perfect solution: an upcycled cardboard cat scratcher!

Cats LOVE this style of cat scratcher, and it's a great one to make for them because it's eco-friendly on both ends: use upcycled cardboard to make it, and recycle it when you're done with it. Make a few of these cat scratchers and tuck them around your space so your cat never has an excuse to sharpen their claws on your furniture. If you don't have cats, make these cat scratchers anyway and donate them to your local animal shelter. My local animal shelter specifically requests this style, and my Girl Scout troop enjoys making and donating them.

This cat scratcher is an improved version of the two types that I made back in 2020. In the years since, I've refined my style to what my own cats and the animal shelter prefer, and redesigned the scratcher to be sturdier and more easily recyclable. My own cats do still really like that round one from the 2020 tutorial, and that's a great style if you've got a lot of room to devote to a nice, big cat scratcher. This version here, though, has a more inconspicuous profile, transports better, and my local animal shelter says it works better in their cat enclosures.

To make this upcycled cardboard cat scratcher, you will need:

• lots of corrugated cardboard. If you're using Girl Scout cookie cases, you'll need about five per cat scratcher. Otherwise, prepare to cut up more cardboard than you thought you'd need--this cat scratcher uses a LOT!
• measuring and cutting tools. At the minimum, you need a ruler and a pair of sturdy scissors. The work will go quicker with a quilting ruler, self-healing cutting mat, and craft knife.
• hot glue gun and hot glue. You're not going to use much, but this is still an essential component.

Step 1: Cut the bottom off of a box.

Choose a cardboard box whose area at the bottom has the dimensions that you're looking for in a cat scratcher.

Measure 2" up from the bottom of the box all the way around, then cut. Reserve the rest of the box for Step 2.

The bottom of this box will be the base for your cat scratcher.

If necessary, reinforce the bottom box flaps with hot glue.

Step 2: Cut corrugated cardboard into strips.

Flatten and/or disassemble a corrugated cardboard box, then examine it to see which way to cut. You want to cut across the corrugations, not parallel to them. When you cut, the cut edge of the box should show a cross-section of the corrugations--that's what the kitties love to dig their claws into!

Use a ruler and craft knife to cut a 2" wide strip down the cardboard, then repeat until you've cut up the entire box. Recycle or repurpose any leftover cardboard.

Measure the length of your box bottom, and cut the cardboard strips to this length. Recycle/repurpose any end pieces that don't reach the correct length.

Continue cutting cardboard into strips until you have enough strips to completely fill the box bottom. If you're making these from Girl Scout cookie cases, it takes about five cases, including the one you cut the box bottom from, to make this cat scratcher.

Step 3: Insert strips into the box bottom, gluing as you go.

After you've got enough strips, dump them all out of the box bottom and set up the hot glue gun. Lightly glue the strips together as you reinsert them.

This is my biggest improvement over the 2020 version of this cat scratcher; when the strips weren't glued together, I found that occasionally my cats would snag their claws into one and pull it out of the box! THIS cat scratcher keeps all its strips nice and snug inside for ultimate cat scratching perfection.

Step 4 (optional): Glue the cat scratcher to the base.

If you want to make the cat scratcher REALLY sturdy, then after all the strips are glued together, carefully pry the whole thing out of the box bottom, then use hot glue to lightly glue it back in. This will keep even the most enthusiastic cat from pulling the entire cat scratcher out of its base.

Either way, the added beauty of this corrugated cardboard cat scratcher is that it's DOUBLE-SIDED! When a cat has worn one side of the scratcher down, carefully pry it out of the base (the hot glue should peel away fairly easily, if you weren't too enthusiastic when you glued it), flip it over, and reinsert it, re-gluing it as necessary.

The model for this tutorial is Dill, one of the three-week-old kittens plus mama cat (also in some pics) that I'm currently fostering for my local animal shelter. I'll keep them safe and happy here with me until the kittens weigh at least two pounds and are at least eight weeks old, and then I'll bring everyone back to be speutered and adopted. Kittens this young don't do well in a shelter setting, and foster families are crucial to their survival, well-being, and proper socialization. If you've got space in your living area and your heart, please reach out to your local shelter and ask about their foster programs

This is one of my all-time favorite upcycling projects. It's a nearly-waste-free way to turn trash into treasure, it fills an incredibly useful niche in cat gear that you'd otherwise have to buy new, and it's a simple, cheap donation project that directly benefits the most innocent creatures in your local community.

I challenge you (and me!) to make every unwanted corrugated cardboard box that comes into our lives into a cat scratcher for use or donation.