How to Homeschool Math: Our Curricula, Resources, and Activities for Middle School and High School (So Far!)

In a lot of ways, middle school and high school are GREAT years to homeschool math. Homeschool math curricula are written to the student in these grades, so most of your mentor time is simply keeping them on track and making sure they're completing their work correctly. 

This, though, seems to be when a lot of parents lose confidence. Yes, you can teach your kid how to multiply multi-digit numbers with your eyes closed (I hope! If not, just look it up--it's easy to re-learn). But if your kid needs help with quadratics, you might be at a loss, because you don't remember that nonsense AT ALL, and now you're back to thinking that you're terrible at math, you don't like it anyway, and you probably shouldn't be teaching your kid, anyway.

I'm not going to tell you whether or not you should be teaching your kid, but I AM going to tell you that middle school math and high school math are NOT beyond you. The only reason you think they are is that your kid's independence has meant that you've stopped following along with them in their math curriculum, and of course you're going to be lost when they ask you to help with some random skill that you haven't reviewed the background for. 

So keep following along in your kid's math, even if they can follow it themselves these days. And even when they don't need your help, keep doing enrichment with them. All those fun games and activities and craft projects and puzzles that inspired them to love math in the elementary years are still fun and inspirational, and being older and knowing more skills just means that they can be exposed to even cooler games and activities and craft projects and puzzles! Sometimes math is going to be a real slog for them, because some of those skills ARE hard and DO take a lot of grit to master, and while that grit is also a very important lesson, kids also need to be reminded that math is fun and exciting. 

That's what YOU'RE for!

The kids' curriculum for middle school math was the same as for elementary school math, Math Mammoth's Light Blue Series. After a kid finishes level 7, she's ready for Algebra!

For part of middle school, we also used this text as a combined math/science/history study:

This is Will's curriculum for high school math:

• Art of Problem Solving Introduction to Algebra: This was Will's Algebra 1 curriculum, which we spread out for all of eighth and ninth grades. We used the textbook alone for the first half, until I got sick to my bones of Will turning my corrections into a power struggle and switched her to their AOPS online classes. They're spendy as hell, and if we couldn't afford them I'd still be teaching her, myself, but it's quite the relief to no longer be the object of math-related ire!
• Here are extra resources for AOPS Introduction to Algebra Chapter 1.
• Art of Problem Solving Introduction to Geometry: After Algebra 1 comes geometry!
• Art of Problem Solving Intermediate Algebra. Will is going to start this class later in August. After that, I'm confident that AOPS precalculus and calculus will see her through to graduation!

Here are some other textbook, reading, and viewing resources that we used:

Depending on your kid's interest and attention span, middle and high school open you up to the whole range of books and documentaries geared to a general audience. You are going to be shocked at how many really fun non-fiction books on mathematical topics there are! There are histories, biographies of mathematicians, cool things that people have done using math--seriously, do a catalog search at your library! It's going to be awesome! There are also tons of documentary series and high-quality feature films--think about the first time you watched something like Primer or The Astronaut, and how inspired you were. Now imagine that you're a teenager with a billion opportunities in front of you. It's really exciting!

I don't have a list of must-have manipulatives and enrichment resources for these grades, because there aren't really any "must-haves." That doesn't mean that middle and high school kids DON'T need manipulatives, however--just the opposite! Middle and high school kids have the sophistication to use anything in the real world that interests them, or any high-quality tools and supplies that might help them engage in their passions or inspire them to try something new. Here are some of the super random things that my kids have enjoyed and that have given them a deeper understanding of mathematical concepts:



Here are some of the other exciting stuff that we've done in middle and high school math. Just like with elementary math, some of these projects were inspired by what the kids were currently studying or their interests at the moment, and some were cool projects that I presented to them or that we did as a family. I like both ways--if the kids are studying geometry, for instance, that's the perfect time to introduce some really wild and fun geometry activity, but it's also the perfect time to introduce some really wild and fun very much NOT geometry activity, too. Get those brains ranging deep and wide!

• Archimedes' Method of Exhaustion to Calculate Pi. We're kind of collectively obsessed with pi in our homeschool. I'm also a huge history nerd, so I was all about showing the kids how Archimedes approximated pi by calculating the perimeters of of inscribed and circumscribed regular polygons on a circle... and then I had the kids try it!
• Level this down to a challenging elementary activity by simply showing a kid how to draw circumscribed and inscribed regular polygons on a circle.
• This activity also works as-is for high school.
• Map Coloring. Using the greedy algorithm makes map coloring surprisingly systematical (and fun!), but it's still a tricky little challenge.
• Mathematical map coloring can be used as-is as a challenging elementary activity.
• Mathematical map coloring can be incorporated into geography and history studies at the high school level. There are always maps to color!

• Model Algebraic Equations with a Decanomial Square. This is a terrific introductory exploration of how to write and solve algebraic equations. 
• Level this down to a challenging elementary activity by using it as an extension after a kid learns how to calculate area.
• Level this up to high school by asking the kid to simplify the equations they create.

• Perfect Squares Hiding Inside Area Models. Practice spotting perfect squares, or use these area models to help you build equations that use the Order of Operations, especially exponents.

• Model the Pythagorean Theorem with the Decanomial Square. The decanomial square is endlessly useful! Here, you can use some of the square pieces and some centimeter graph paper to model and test the Pythagorean theorem.

• DIY Binomial Square/Trinomial Square Manipulative. This manipulative is related to the binomial cube/trinomial cube, below. Your kid might encounter binomial squares in their math curriculum, but even if they don't, I am a BIG fan of introducing it here. It's great practice in modeling formulas that might seem abstract (and therefore scary), and it's fun!
• Level the binomial square/trinomial square manipulative down to a challenging elementary activity by playing with it after the decanomial square.

• Binomial Square from a Decanomial Square. I love to present the same concept several different ways and at lots of different times. This activity uses the decanomial square to build a binomial square, and then explore creating an equation that represents that configuration. I like it even better than the manipulative, above, because there are so many more choices a kid can make.

• Area Models to Square Binomials and Trinomials. Before (or while) you teach the FOIL method to square a binomial, let kids actually see what they're doing! THIS is how FOIL makes sense!
• Level the area models to square binomials and trinomials down to a challenging elementary activity by exploring it without connecting it to the FOIL method.

• Fibonacci Sequence. Middle school is a great time to explore the Fibonacci Sequence for fun! Kids can create their own Fibonacci Sequence models, and then play with pattern creating using them. 
• Level Fibonacci Sequence exploration down to elementary by providing the models as manipulatives, and letting kids concentrate on the pattern creating.
• Level Fibonacci Sequence exploration up to high school by including more reading/viewing resources that discuss extensions and applications.

• Fraction Division with Cuisenaire Rods. If all you know about dividing fractions is to invert the divisor and then multiply, you don't *really* understand dividing fractions. Model it with Cuisenaire rods, and you can see what you're actually doing!
• Level this to high school by using it as a review when a kid can't immediately recall the correct algorithm.

• Fraction Multiplication Model Sun Catchers. Here's a really fun project that's as much art as it is math. As long as you choose your sample problems correctly, you'll make a model that will both demonstrate exactly what you're doing when you multiply fractions, AND you'll have a beautiful sun catcher!
• Level this down to a challenging elementary activity by pre-printing the model blanks and encouraging more open exploration of the ways that one can combine two colors rather than specifically making multiplication models.
• Geometry Nets with Building Toys. Convert a kid's building toys into polyhedra models, either challenging kids to come up with specific polyhedra or encouraging open exploration to see what polyhedra are possible. Here are some building toy sets that work well with this activity:

 

• Level this activity down to elementary by introducing the concept of geometry nets during free play, and encouraging kids to create the nets for some of the Platonic solids.

• Graph Candy. Here's a delicious way to review fractions, decimals, percents, and ratios, as well as how to make graphs and pie charts. 

• Graph the digits of pi. Don't believe that pi goes on forever? You will after you've graphed it as far as you can stand! This also makes a beautiful art project, even a permanent installation. It can be a fun activity to do over several days, eventually taking over an entire wall or spreading out across the whole house.
• Level graphing the digits of pi down to elementary by introducing it after learning the concept of graphing. Use Cuisenaire rods as the graph pieces!

• Mark Circles in the Snow. A fresh snowfall is the perfect time to take math outdoors! Here, the kids practice their geometry knowledge by marking a giant circle in the snow. Grab a meter stick or tape measure to take some measurements, and head inside, or snuggle up to a bonfire, to calculate the radius, diameter, and circumference.

• Measure Tall Objects using Ratios of Similar Right Triangles. Get outside and measure something tall!
• This activity works as-is for high school, as well.

• Zometool Crystallizations. The sky's the limit when you figure out how to tile a basic shape in both two and three dimensions. This is a surprisingly tricky logic puzzle, and it's terrific for building patterning intuition.
• You can use this activity as-is in both elementary and high school.
• Tangrams. I first introduced tangrams to the kids when they were very small and we were studying China, but tangrams are such a sophisticated manipulative that you can easily challenge yourself with them no matter how old you are.
• Definitely use tangrams as-in in high school!

• DIY Binomial Cube/Trinomial Cube Manipulative: This is a visual, tangible model of the binomial cube and trinomial cube. Kids can help build it, or simply manipulate it after it's built. You can create pattern cards or work through it verbally. You can use it as a bridge to teach kids the formula or let them figure out a workable formula through their own experimentation.
• Level the binomial cube/trinomial cube manipulative down to a challenging middle school activity by calling it a "puzzle," the object of which is to create a perfect cube.
• Level the binomial cube/trinomial cube manipulative down to an elementary activity by offering it as free play.

I don't blog about every single thing that I do with the kids, so here are some of the Pinboards where I collect even more middle and high school math resources. Some I've done, some I haven't, but I think they all look pretty cool!

• Homeschool Math: Fractions
• Homeschool Math: Geometry
• Homeschool Math: Algebra
• Homeschool: Logic
• Homeschool: Physics

I often tell people that I LOVED homeschooling the early years--I mean, who wouldn't? The picture books! The mud puddles! The field trips to the fire station! But the thing about me that you've probably sussed out is that I need a LOT of mental stimulation--like... a LOT--and homeschooling those little kids didn't always provide it to me. There was a whole summer when I think I fell asleep every single afternoon while reading Syd whatever Rainbow Fairy book she'd presented to me that day. Anyway, homeschooling big kids isn't like that. They can do puzzles and work projects and try activities that genuinely grown-up humans think are cool, too, and don't have all the answers for. That Zometool crystallization activity, for instance? I STILL think about the crystal that I created, and I still kinda think that I accidentally found the cure for cancer or unlocked another dimension with it...

...until, you know, I took it apart so that we could do something else cool with the pieces.

P.S. Want to see what else we do that's cool? I share resources, works in progress, and more updates on our adventures daily over at my Craft Knife Facebook page.

How to Homeschool Math: Our Curricula, Resources, and Activities for Elementary

Yes, you CAN homeschool math.

Do not give me that sulky face, and don't you dare tell me that you clearly cannot homeschool your child because you obviously don't remember how to divide fractions.

Of course you don't remember some math stuff! You learned all that a zillion years ago! But you know what?

You are a grown-up adult. You can pick it back up. It's really not that big of a deal.

Also, remember that time that you tried to learn some math thing back in school and it was too hard and you got mad at yourself and said that you hated math and you're not good at it?

You were NOT a grown-up adult back then. You were a child.

How fun, then, not to pass that same negative mentality on to your own kids?

Elementary math can be so much fun for kids! Elementary math is fun manipulatives. It's fun games. It's jumping and screaming and singing. It's drawing and painting. It's measuring and pouring. It's reading books together, and doing puzzles, and figuring out interesting problems. It's some of my happiest memories with my kids.

ELEMENTARY MATH

Both my kiddos studied math informally until second grade, then began in Math Mammoth's Light Blue Series at either Level 2 or Level 4, depending on the kid. Math Mammoth took them both all the way through elementary and middle school math.

For part of elementary and middle school, we also used this text as a combined math/science/history study:



Here are some other textbook, reading, and viewing resources that we used:

Almost all of these came from the library, and most consist of fun picture books that I found for us to read together--even older elementary kids (and even high schoolers!) love great picture books!

And here are our most important manipulatives:



There are tons more manipulatives that I created myself or Googled, downloaded, and printed. I'm a BIG proponent of DIYing as much as possible!

Below, I've listed tons of the enrichment activities, extra reading/viewing resources, and fun stuff, that I did when my kiddos were elementary ages. They're not listed in any particular order, because they don't have to be done in any particular order! I liked to have the kids doing some kind of hands-on math activity every day, and if it wasn't inspired by them wanting to bake or build or draw or read together, then I invented a fun invitation or set up a game or suggested a project or offered up a puzzle.

I also set up enrichment and hands-on activities to support skills that the kids were struggling with, or to expand on skills that they were blazing through. Seriously, ask me how many hands-on activities I know for teaching rounding!

So scroll through my list of fun enrichment activities, and definitely set them up to support something specific, but also feel free to engage in them at random. I mean, most of what we did in elementary was totally random, and those were some of the best years of my life!

• Building Big Numbers with Base Ten Blocks. This is the BEST math activity that my younger elementary kids ever did. It's endlessly repeatable when they're little, and builds that crucial number sense that they need to make everything else make sense!
• Clock Cake. Clock reading is a skill taught in elementary math, but it's ever more abstract these days, as every device has a digital clock and analogue clocks are becoming more of a rarity. The solution? Bake and decorate your own clock!
• Roll the Time. To get even more clock-reading practice, write minutes onto a blank die, combine it with a twelve-sided die, and have a kid roll the time. She can tell you the answer and draw it onto a blank clock face.

• Demonstrating the Commutative Property of Addition using Cuisenaire Rods. Cuisenaire rods are superb at demonstrating equivalent equations.
• Pascal's Triangle. You can find the blanks for these online, and seconds later, you've got an in-depth addition review!

• Roll to a Hundred. I'd completely forgotten how many of those printable hundred charts we used in the early elementary years! There are endless amounts of games you can make using them, all of which reinforce numeracy and computational skills.

• Add Multi-Digit Numbers using an Abacus. Just as when the kids were learning to read I wanted them to see all kinds of letters in all kinds of fonts and all kinds of sizes and made of all kinds of textures, I liked the kids to practice counting and adding and subtracting in all kinds of ways, with all kinds of manipulatives. If you've never used an abacus, it's well worth learning how to work it properly!
• Write a Googol. Big numbers are so fun for little kids!
• Build Decimal Numbers using Base Ten Blocks. Just as you can build whole numbers with Base Ten blocks, you can also build decimal numbers--it's all Base Ten!
• Subtraction with Borrowing across Zeroes using Base Ten Blocks. If you can do it in Base Ten, you can generally model it with Base Ten blocks.

• Metric Conversions in Grams using Rice Models. If you have a balance scale and some rice, kids can make their own metric conversion models, using a LOT of problem-solving and practical life skills in the process. And even in high school, we STILL pull out those rice models whenever a kid needs a metric conversion refresher!

• Metric Conversions in Liters using Water. You can't keep this metric model forever, but you can use it to cool you off on a hot day!

• Hands-on Rounding. For some reason, Syd really struggled to master this concept, and so now I have a zillion concrete, physical, hands-on ways to teach rounding.
• Decanomial Square. You're going to see me refer to this a lot, as it's one of our most-used math manipulatives. It's well worth DIYing or buying one, because your kids will still be using it in high school!

• Skip Count with Coins on the Hundred Grid. It's good to practice skip counting a lot, and in a lot of different formats. This version also reinforces coin values.
• Multiplication Touch. It's quite the project to build the roll-up hundred mat and the number tiles from scratch, but Multiplication Touch is well worth it! It's surprisingly fun to play, so works great not just for memorizing the facts, but also for reviewing them for years.

• Multi-Digit Multiplication using Area Models. Centimeter graph paper, Base Ten blocks, and Cuisenaire rods are your best friends in elementary!

• Model Long Division with Base Ten Blocks and Cuisenaire Rods. You can cover a LOT of mathematical ground with just those two types of math manipulatives! By the time a kid hits long division, she's already starting to get math instruction that's more focused on teaching her how to plug numbers into an algorithm than it is on understanding what she's doing, and that's not cool with me. When I teach long division, I like to drag out all the blocks and show a kid exactly--and I mean EXACTLY!--what is physically happening to the literal numbers that she's dividing.
• Literally Walk through Long Division. The beauty of homeschooling is that nobody--not you, and definitely not the kids!--are trapped at a desk. Get the wiggles out and bring whole body learning into your math study by drawing a GIANT long-division problem on your driveway and then having your kids solve it. Who knew there was so much walking, crawling, and skipping in math?

• Compose Fractions with Rice Krispy Treat Models. Because number sense is delicious!
• Model Converting Mixed Fractions to Improper Fractions. You need circle fraction manipulatives for this activity, but the good news is that it makes converting between mixed fractions and improper fractions as clear as a bell and as easy as pie! Here are the circle fraction manipulatives that we own:

• Level these fraction models up to middle school and high school by bringing them out whenever kids need a review. They WILL randomly forget how to convert between mixed and improper fractions, but going back to the manipulatives will quickly remind them, and every time they re-learn it, they'll cement it into their brains even better!

• Montessori Pink Tower. Playing with the Pink Tower can be soooooo satisfying for the pattern-loving child, and it's great for their hand-eye coordination and number sense.
• Montessori Pink Tower and Cuisenaire Rod Patterns. If you're loving the idea of open-ended exploration of math manipulatives for young learners, then you should really check out Montessori math! These kid-built, elaborate patterns are satisfying to create and look at, and since they're built on a Base Ten system at a centimeter scale, they're terrific for building a kid's number sense. Here's the Montessori Pink Tower:

• Level pattern-building using the Montessori Pink Tower and Cuisenaire rods to middle school by having kids create their own diagrams or pattern cards from their creations. Perhaps they want to share them with a younger learner, or even publish them!

• Blow Bubbles with Geometric Figures. What happens inside a prism when you dunk it into bubble solution? More fascinating geometrical models! Here are our Zometools:

• Find the Area of Irregular Polygons using Graph Paper. Everything is more fun when it's on graph paper! For even more reinforcement, use centimeter graph paper and fill in the polygons with Base Ten hundreds, tens, and ones, and Cuisenaire rods.

• Make Mandalas with a Compass and Protractor. Here's a fun art activity that happens to teach compass and protractor use while also offering a lot of scope for creativity and process-oriented art. 
• Level this activity up for middle and high school by encouraging even more elaborate, thoughtful creations.
• Origami. This is one of the best geometry activities that your kids won't even recognize as math work! Start with SUPER simple builds so that they don't get frustrated with the fine motor requirements, but no matter what they make, they're building an intrinsic knowledge of angles and shapes and how they work together in two- and three-dimensional spaces.
• Level this up to middle school and high school by working through ever-more-challenging how-to books.

• Pentominoes. Allowing kids free exploration of mathematical models and manipulatives and interesting shape puzzles is one of the best things that you can do with them in elementary, whether or not you're officially homeschooling. Pentominoes are especially fun for older elementary kids who enjoy stretching themselves with challenging puzzles.
• Level pentominoes up to middle school and high school by working through ever-more-challenging puzzles, and calculating the number of possible solutions to puzzles.
• Ink Blot Prints that Show Bilateral Symmetry. Get really messy in order to get really symmetrical!

• Symmetry and Similar Figures with Pattern Blocks. This is a more challenging activity for older elementary, but you get to drag out ALL the pattern blocks and it makes the kinda abstract concept of similar figures crystal clear!
• Tangrams. This is another math manipulative that's endlessly entertaining, even onto middle school and high school. Heck, *I* still love to play with tangrams!

• Zometool Stellations. To stellate a polygon is to extend its line segments. It always makes something beautiful, and it encourages kids to stretch their imaginations and become more mathematically creative thinkers.
• To level this to middle school, have the kids measure the angles both inside and outside their polygons.

I don't blog about every single thing that I do with the kids, so here are some of the Pinboards where I collect even more elementary-level math resources. Some I've done, some I haven't, but I think they all look pretty cool!

• Homeschool Math: Addition and Subtraction
• Homeschool Math: Base Ten
• Homeschool Math: Fractions
• Homeschool Math: Geometry
• Homeschool Math: Measurement
• Homeschool Math: Money Math
• Homeschool Math: Multiplication and Division
• Homeschool Math: Telling Time

I LOVED doing math with the kids in elementary. I loved exploring open-ended activities with them--activities that I, too, thought were fun! I loved reading math poems and picture book biographies of mathematicians together. I loved every single time a kid was happy while doing math, every single time she felt confident, every single time she took a risk, every single time she struggled and struggled and finally understood. 

It's exactly what learning should be, and it was my privilege to give that to my kids.

Turn an Old Blender into a Planter

I originally published this tutorial on Crafting a Green World.

Yes, that's a super-expensive Vitamix blender pitcher that finally cracked (it's too embarrassing to tell you why, but I assure you it was because of Reasons).

No, I could not stand to simply toss it away, even after it spit something like a half-gallon of hot tomato soup onto the counter before I figured out it was broken.

Instead, I did what I do with every single even vaguely container-shaped piece of junk that needs a second life around here--I turned it into a planter!

The process is so easy that yes, you, too, should be turning every single even vaguely container-shaped piece of junk into a planter. Think about how much sturdier your piece of junk is than a chippy terra cotta pot, and how much more eco-friendly than a brand-new plastic pot.

And think about how roomy that beautiful broken blender pitcher is. So much space for strawberries!

Tools and Supplies

Here's what you need to plant strawberries or anything else that delights you, in your own broken blender pitcher:

• old jar lid (optional: see Step #1 to see if you'll need one)
• gravel
• potting mix
• plant

Directions

1. Prepare the blender to be water-tight.

Blender pitchers have their blade attachment at the bottom. Generally, this won't be a problem, and in fact, it's even easier to turn your blender pitcher into a planter if you keep the blades installed.

However, this is my super-expensive Vitamix blender pitcher that we're talking about here. I saved up a LONG time to buy that baby, and I sure ain't dropping a ton more money for another entire brand-new pitcher! Instead, my partner removed the blade attachment from this broken pitcher and installed it in the new pitcher that I bought to replace it. It was still pricey as heck, but way less expensive than buying the complete replacement pitcher with the blades included.

So if you, too, have removed the blade attachment from your blender pitcher, making the pitcher water-tight again is as easy as scavenging an old jar lid that is larger than the hole but smaller than the bottom of your blender. Set the lid over the hole and you're done. If you want to be perfectly safe, use epoxy glue to adhere the lid in place, but since the next step is going to be filling something like half this pitcher with rocks, all that weight will also keep the lid in place.

2. Add a layer of rocks.

This depends on the plant, of course, but it's likely that your blender pitcher is far deeper than necessary. Instead of wasting a LOT of potting soil in that space, fill up what you don't need with rocks.

Some really cute options would be river rocks, broken pottery pieces, shells, even aquarium gravel if you've got it, but I am flat out of cute rocks and such and so honestly, I just scooped up some of the gravel off of my driveway.

Whatever. Pretend like it was a thoughtful aesthetic choice.

3. And then you plant!

I'm so in love with the transparency of this planter. Look at what pretty layers the rocks and potting soil make--even prettier if you add that aquarium gravel or shells or pottery shards! I'm also loving the fact that it's got a handle, making it easy for me to move around; add just the right bracket, and you could also hang it or mount it somewhere fun.

And that's how you might find me deliberately thrifting old blender pitchers this year--because now I'm all about the idea of a planter with a handle!