Craft Knife: homeschool middle school

Showing posts with label homeschool middle school. Show all posts

Tuesday, October 31, 2023

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!

Monday, February 1, 2021

Every National Park Junior Ranger Badge You Can Earn from Home

My updated map of all the national park Junior Ranger badges that you can earn on-site, and my list of all the Junior Ranger badges you can earn from home by mail or email, lives right here!

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!

Wednesday, November 11, 2020

I Turn Quizlet Flash Cards into Physical Flash Cards because I Am Stubborn and Ridiculous

And because the kid already has quite enough screen time without also studying her French vocabulary on one.

I am SUPER old-school to be so weirded out by this, I've learned. Syd doesn't even have a single physical, paper textbook in any of her public high school classes--actually, she only has a textbook at all in two of her classes! The other three classes just have... teacher-created lessons. And YouTube video links. Worksheets of unknown provenance.

Don't tell her textbook-less algebra teacher, but I checked out a high school algebra textbook (and teacher's manual!) from our local university's library, and I've been referring to it quite a lot as I help Syd with her work.

I also print out most of her biology and French readings from the digital textbooks, which I know is the most appalling misuse of my personal resources, but you know what? The print-outs don't crap out in the middle of a timed open-book test, or refuse to load when an exhausted kid is coming up on a deadline, or lag when three other members of the household are in simultaneous but separate online meetings.

Flash cards, of course, don't have nearly that level of urgency, but I like having them physical. I like having them portable, so I can torment the children with them in the car, and I like having them readily available, so I can pester the kids with a couple whenever they randomly walk by.

So here's what I do to make my kids' lives more annoying. I take a Quizlet (you can often find Quizlets already made for whatever you're studying, even for specific chapters of specific textbooks)--

--tell it that I want to print it--

--and then set it up as 3"x5" index cards that print 16 to a page:

I use a guillotine paper cutter to cut the flash cards into rows, then cut each row in half, leaving each French/English word pair connected. To finish each flash card I fold it in half and glue it with a glue stick. It becomes the perfect, pocket-sized, double-sided flash card!

So yes, super old-school and resource heavy, but to be fair, I've been happily using flash cards with the kids since they were preschoolers. Here are just some of the things that we've done with them from preschool on up:

Laminate them and trace words with dry-erase markers.
Print two copies and match them or play Memory with them.
Print them tiny, add a pin, and use them with pin flag maps.
Print them full-page and let the kids color the line art.
Print them full-page and use them as display posters.
Leave them in the car and declare the first ten minutes of the first car ride of every day "memory" time--we did this for several years!

Here are some of my favorite flash cards that we've used:

addition, subtraction, and multiplication drill. I absolutely used these with the kid when they were memorizing their math facts. Yep, they LOATHED them, but you know what? Review only took a couple of minutes every school day, and it 100% helped seal the facts into their little-kid brains.
Chinese vocabulary flash cards. For a couple of years, the kids took a Saturday morning Chinese language class. The next week, I'd find flash cards for the vocabulary that they were studying so that we could review for just a couple of minutes daily.
European countries and capitals. We used these a couple of years ago when Will was studying AP European History and Syd was studying European Geography. Now that Will is studying AP Human Geography, I'll probably bring them back out!
French alphabet flash cards. These are pretty enough to print full-page and display on a wall--which is what we do!
sharks of the world. We used these a few years ago when we did a summer shark study, and since then I've brought them out a couple of times for Girl Scout badgework.
Story of the World timeline cards. Unfortunately, the original source for these no longer exists, but you can still find bootleg copies (ahem). We used the SNOT out of these when the kids were elementary years! We glued them to our big basement timeline, as well as laminating a set to use as memory drill. Once upon a time I even found a bootleg set of all the comprehension questions from the Story of the World books set up as flash cards, and we used the snot out of those, too!
zoo fact cards. I made these during the couple of years when Will's obsession led us to nearly every zoo in the land. It would be extra useful to make a set for a zoo or aquarium that you went to often.
insect flash cards. We used these steadily for several summers in a row when the kids were younger, and I still pull them out at some point most summers, because we always end up swinging around to entomology.
sight word caterpillar. Syd has fond memories of the caterpillar that took over our walls and taught her the dolch sight words!

Saturday, October 31, 2020

How to Make Clear Slime

I originally published this tutorial on Crafting a Green World.

Slime is a wonderful sensory experience, and I'm thrilled that so many young people are embracing the joy of exploring interesting textures (there are no interesting textures on their phones!). Making slime is also a terrifically educational activity, with problem-solving and reading and following instructions combined with quite a lot of chemistry and not a little bit of physics, as well.

To make clear slime, I consulted my own resident slime-making expert. She's put in hundreds of hours making slime, and is here with us today to teach you how to make clear slime, the Holy Grail of slimes. Syd's clear slime isn't your ordinary, everyday "clear" slime that's actually milky or white, she tells me. When she says that her slime is clear, she means it is CLEAR.

As in crystal!

So read along as the world's slimiest kid takes the task of making clear slime and breaks it down so simply that even the average non-slimer adult can follow it.

To make clear slime, you will need:

Clear Elmer's glue. I used to be able to buy this by the gallon, but lately, I've only found smaller containers for sale. I sure hope the gallon size comes back soon!
Hot water. The water should be hot, but still, a comfortable temperature for a kid to touch. For mobile slime-making (yes, this is something that she does...), Syd boils a kettle of water, then pours it into a thermos for transport.
Contact lens solution. Buy the cheapest on the market for this project, making sure that it contains boric acid.
Baking soda.
Two mixing bowls, a spoon, and a resealable container for storage.

1. Pour 1/2 cup of clear glue into a bowl. Remember that kids do this, so don't worry about trying to make your measurements too fussy. The important thing is that you're using CLEAR glue, not white. You can use white glue for other slimes, but then your slime won't be clear!

2. Mix in 1 tbsp of saline solution. This is also known as contact lens solution.

So here's a thing that I want to tell you about: we're going to talk about borax. When slime-making first got big, there was an actual backlash as people started FREAKING OUT that their kids were touching borax. As alternatives, people started posting slime recipes that don't use borax. Some of those recipes are great, some are not, and lots of them use contact lens solution as their substitute for borax.

Y'all, contact lens solution and borax both come from boron! They're pretty much the same, just that one is in powder form and the other is dissolved into a solution.

Not that I think that you should even force your kids to avoid borax, because I don't think that at all. Heck, my kids were making laundry soap from borax with their bare hands at the age of eight (they probably should have been wearing gloves, but still). Borax is FINE, Friends. Sure, if they bathe in it every day for a month it'll irritate their skin, but so will pool water.

3. In a separate container, dissolve 1/2 tsp of baking soda into 1/2 cup of hot water. Stir it well and make sure that it dissolves completely.

4. Once the baking soda is completely dissolved, pour it into the glue mixture. Try to pour it over the entire surface of the glue mixture.

5. Wait approximately a minute, then stir. Knead if necessary.

At first, the mixture will be a goopy mess but continue stirring and you'll be able to see when the slime activates because it will start to ball up. It will still be sticky when you start to knead it but keep working it and it will become ever more elastic and non-Newtonian until it's the perfect slime.

You will have some of your baking soda and water solution left in the bowl, and that's perfectly fine and normal.

One thing that your slime will not start out as is perfectly clear, for the simple fact that you just kneaded a ton of bubbles into it.

If you really want perfectly clear slime, then pop it into an airtight container and let it sit for a day. The next day, it will be clear!

Note that as soon as you start playing with it, though, you'll start kneading bubbles back into it. This picture is of the clear slime that Syd has played with for a while, and you can see the bubbles:

Pro Tip: Syd stores her slime in small plastic deli containers to keep it fresh--and off of my carpet! She tells me that this particular slime will lose its bounce after several days, but it's easy to reactivate it. To reactive this clear slime, dissolve 1/2 tsp baking soda in 1/2 cup hot water. Pour the older slime mixture into this solution, stir, and then knead it when it becomes firmer. Keep the reactivated slime and discard the excess water.

Thursday, September 3, 2020

Homeschool Math: Perfect Squares Hiding inside Area Models

Syd was simplifying radicals the other day, and not having a fun time of it. She was struggling to link the concept of factoring the radicand to simplifying, and I was trying, as usual, to think of hands-on manipulatives that might clarify the process.

I did NOT find a way to model simplifying radicals using manipulatives, alas, but while I was playing around with the decanomial square I DID find a hands-on enrichment that kids who are first learning the concept of perfect squares might enjoy.

I like this little activity because it connects the mathematical definition of the perfect square with the Montessori-style sensorial skill of eyeballing it, or even measuring it by feel. Although you're technically not allowed to eyeball stuff as mathematical proof, pattern recognition via the senses is very important. That's how kids learn to read, for one thing, and it's how IQ tests are built, for another.

Use this activity with a kid who's first learning, or reviewing, the concept of the perfect square. You can do it with paper area models that a kid can draw and color on, or you can do it, as I've done here, with the decanomial square model, which is extra fun because it has pieces you can manipulate. Kids could try to find the largest perfect square(s) that would fit inside the area model, or just find any perfect squares that would--whatever they find fun and you find helpful! Here are some models that show examples:

These first two are when I was still thinking I might figure out a way to model simplifying radicals. I LOVE combining manipulatives with a dry-erase board to help kids connect the model to the algorithm it represents.

For all these examples, I've pulled an area model from our decanomial square, and we're arranging the perfect squares on top of it, leaving, of course, a remainder since the area models aren't themselves perfect squares.