Homeschool Time Fillers That Aren't Busy Work (Even for High Schoolers!)

My high schooler would be horrified to know this, but I do sometimes assign her work that's more of a time-filler than it is a substantive assignment.

Sometimes, it's because she has a busy week and I want to keep her on schedule but not add to her stress.

Sometimes, it's because *I* have a busy week and I want to keep her on schedule but not add to *my* stress.

Sometimes we've finished up a big unit of study but it's not the perfect time to start the next one, or one of us isn't feeling 100%, or we've got an appointment or some other thing that would interrupt her flow, but I still want her learning that day.

Essentially, time fillers work well for all those times and gaps when you want your student doing something educational, but you also want it to be low-stakes for both of you. The student is using her mind but not wracking her brain, and YOU don't have to review, edit, correct, or evaluate!

Here's some of my favorites from my collection of high school-level time fillers that are educational but low-stakes:

Board Games

Sometimes teenagers just need a break from book work and screen work. Reading textbooks and solving problems and filling in answers is also just one limited, specific type of learning, so I don't like that to be all my high schooler does for school all day. 

We don't have a formal logic study currently, but logical thinking is an extremely beneficial skill, so I encourage a lot of logic games that I file as math enrichment. We play word games, association games, and creativity games for English credit, and historical games like Senet, Mancala, and Go for history/geography credit. Occasionally, I'll even find a game that we can play in my high schooler's target language.

Here are some of my favorites:

We've got some made-up games that we can play anywhere, as well, most notably the Wikipedia Game and Dictionary Definitions, and once in a blue moon I'll go to the trouble of downloading and printing an online-sourced game like Phylo, especially if it fits into a niche in a subject that we're studying. 

Documentaries

I already see the public library as my personal streaming service, so it doesn't feel like a big deal for me to do a quick catalog search whenever I'm planning the next few weeks' studies and just go ahead and request any documentaries that are on-topic and look interesting.

Documentaries about a topic of study build depth and context, and now that we're all such ipad babies, focusing on a piece of content for a whopping one hour really is something that we need to do every so often to stay in practice!

My immediate go-tos for documentaries are anything PBS, National Geographic, or BBC. Independent films and documentaries produced by news publications are also good, but I usually avoid anything else you might find on cable (TLC is most definitely NOT!) as being less in-depth than I want for a high schooler. The teenager and I are currently in the middle of a two-part PBS special on uranium, which I'm counting as enrichment for her Honors Chemistry study, but here are some other documentaries we've watched for high school:

Although they aren't quite documentaries, there are also a ton of lectures, presentations, and streams available on YouTube. Q&A sessions give me secondhand cringe, so we don't watch that part, meaning that the actual run-time is shorter than listed. This is also a good place to find performances that enhance liberal arts or language studies; my homeschoolers and I have watched lots of plays on YouTube, and lots of TV shows performed in whatever target language they're studying at that time:

Podcasts

We listen to a lot of audiobooks for the teenager's English credits, mostly while she works on her studio art and I do a handicraft and we chat. I don't want to give up that precious stitch-and-bitch time even when we're not burning through a 14-hour tome, though, so in between books I'll often fill in that space with a podcast. 

You can usually find a dozen different podcast episodes on any topic, so it's not hard to find something that fits into the teenager's current studies, but vetting new ones to see if they're good or if they're trash can take some time. We've also got favorite podcasts that are educational without necessarily being on-topic; here are a few:

 

Puzzles and Solitaire Games

We loooove our puzzles, with my teenager spending as much time working sudokus as my partner and I spend working crossword puzzles. Just in the last year or so the teenager seems to have mostly grown out of (or just mostly completed!) all of our in-house hands-on logic puzzles, but here are some of the favorites that she particularly enjoyed from childhood through the first couple of years of high school:

These days, if I want to assign her a short time-filler puzzle that's something fun, I'll have her do the daily Wordle, Murdle, or Set online. All three update daily, so there's always a new puzzle!

Process-Oriented Projects

I think that sensorial knowledge is still important to continue building, even into these older kid years. It's also important to continue building one's creativity and to remain comfortable with play, experimentation, and the concept of doing something simply to experience the process. 

To encourage my teenager to stay creative and experimental, I'll sometimes surprise her with an assignment like finding a new cookie recipe to bake, or creating a sticker design based on something we've been studying, or flipping through a stack of books I got from the library with her in mind, etc. Basically, I just want to stretch her out of her comfort zone of what she normally likes to bake or draw or read. Or maybe I'm just craving cookies but don't want to make them for myself! 

The art/math combo is my favorite focal point for building sensorial knowledge and experimenting with process. Over her high school years, the teenager has been compiling a portfolio of geometric art, and adding to it is a great way to bake some low-stakes math enrichment into the school week. Making things like mandalas, polyominoes, and tesselations put sensorial math knowledge into use, and build on geometry process that she's learned. 

Also, I'm obsessed with the spirograph!

In the lead-up to a holiday, there are all kinds of sneakily educational, mathematically sophisticated holiday crafts to create. There's a lot of beautiful math involved in wire-wrapping beads to make stars, or folding precisely symmetrical paper ornaments, or stitching felt mandalas or snowflakes. 

When there's not a holiday on the horizon, sometimes we'll just do something random like check out an origami or paper airplane book, or buy ourselves a DIY kit and decide to learn how to crochet. I'm currently low-key obsessed with a friendship bracelet loom that I made out of corrugated cardboard, so there's a lot of weaving going on around here.

As we move into the Spring semester of the teenager's Senior year, I can't decide if we're going to be doing more of these types of assignments, or less. On the one hand, I'm not opposed to ending one's high school career with a whimper rather than a bang, so as the teenager starts to finish her last units of study one-by-one, I don't want to necessarily replace them with equal amounts of puzzles and documentaries. But on the other hand, I do think that most of us need a goodly amount of productive work most days, so I definitely don't want a teenager to finish up all her learning and then sit around on my couch for several months actively not learning, ahem. 

Perhaps I'll see if there's a larger, more culminating-type project that the teenager would be interested in working on during those increasingly free school hours further into Spring? Or perhaps we'll get very, VERY good at crochet!

P.S. Want to follow along with my craft projects, books I'm reading, homeschool projects, road trips, and other various adventures on the daily? Find me on my Craft Knife Facebook page!

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!