Tag Archives: math

Current Homeschooling Materials — Math

I was a total math geek in school. I was on the math team in middle school and went to math summer camp. On purpose. For fun. And I liked it!

My kids don’t seem to have the same passion for math that I did. The oldest is actually really good at intuitive math and abstract math concepts, but tends to get a little bored at actual computation. My middle kid is a perfectionist. My youngest might actually end up really being my math kid…

This is the first post in a weekly series of posts about the materials we use. Homeschoolers just love to know what other people use and how they use it. My family tends to bounce around a lot — we can never use the same thing for too long before someone gets bored of it and starts fighting me, so I switch it up a lot.

For math, I really have to pull from a lot of places. My kids never just go through a workbook and do it all methodically… I totally would have (and did!), so I have no idea where they get this from.

The boy (12) — Introducing algebra and such through games and trying to solidify his basics before we plunge forward into harder math. Don’t bore him. Lots of skills practice, applying it to things and games:

The Girl (9) — great at math except her perfectionist tendencies tend to make her stress out a lot. She doesn’t like struggling for answers. Ever.

  • Singapore 3, Beast 4
  • Kitchen Table Math 1-2
  • Playing with Math
  • Random worksheets
  • Lots of games!

The Baby (6) — Loves math. Loves workbooks.

  • Singapore 1
  • Games
  • Kindle Apps like Dragon Box and Dragon Box Elements (which she just finished!)

Other materials we sometimes use include:

  • Math-U-See
  • Living Math

What do you use for math?

Passive Agressive Magic Roses Explain Binary (Repost)

A few years ago, the two older kids (who were 10 and 6 at the time) and I read a really amazing book, Computational Fairy Tales by Jeremy Kubica. It’s $3.03 on the Kindle, so it doesn’t exactly break the bank.
The entire book presents programming concepts using little stories about a medieval kingdom and a girl who needs to finish a quest.

I love this book because it does a great job of presenting the logic of programming, and programming concepts — so far we’ve read about boolean logic (AND, OR, and NOT), loops, if-else statements, algorithms, binary, variables, variable names, and so forth. Each section introduces an idea and uses a humorous story to illustrate it.

My 6 year old really liked the story for binary, which involved some magical roses with the passive-aggressive tendency to turn blue when they hadn’t had any rain. Only they didn’t all turn blue. They had an algorithm for turning blue as the days passed, which just happened to show the number of days. In binary!

In order to really help her understand, I made up a little craft today to play passive-aggressive roses with her.

Make Your Own Passive Aggressive Binary Flowers

You’ll need paper, markers/pens, and tape. A ruler might help cut or measure things. Gandalf is optional.

Cut out five strips of paper and fit them to a paper towel tube. Make them long enough to go all the way around, with a small overlap. Then, mark each one with a column: 1s, 2s, 4s, 8s, 16s. Have a handy child draw a blue flower and a red flower for each strip.

Tape each strip around the paper towel tube so that the column names stick up like tabs and the paper strips easily slide around the tube.

Make sure the 16s are on the left, counting down to the ones column all the way on the right.

The kids put a pink wizards hat on Gandalf (they lost the grey one) so we could have someone play the part of Marcus the magician who owns the roses.

After a night of rain, all the roses are red. Red stands for 0 (or off or false). Each column with a red flower gets a zero. All zeros add up to 0. So it’s been 0 days of no rain.

The next day, the first flower turns blue, because it didn’t rain. So the ones column gets a 1, and 1 of the ones equals 1. 1 day since it rained.

It doesn’t rain again. So the ones flower flips again. The flower on his left always flips colors when the flower to his right flips to red (AND ONLY RED). So the second flower flips, and the other flowers to his left don’t. 1 in the twos column plus 0 in the ones column equals 2.

And again it doesn’t rain, so the ones flower flips, but since it flipped to blue, the twos flower stays blue. 1 two plus 1 one equals 3.

And still no rain! Poor flowers. The ones flower flips to red, which makes the twos flower flip, too. The twos flower flipped to red, so the fours flower flips! 1 four plus 0 twos plus 0 ones equals 4.

Keep on going, to see five.


And two days later, eight! Which is a really fun one, of course.

Something tells me she’ll remember binary numbers.

Destroying Electronics to Make a Case for Algebra

I’m finding a lot of half-written blog posts in my drafts folder. This is another one of those things that actually happened a year or two ago and I never finished writing about it.

We are finally embarking on our electronics course, using Make: Electronics (Learning by Discovery) as our guide. It took a while to find all of the required parts, but we eventually did. If you need to find parts, I recommend: Digi-Key and Mouser Electronics. You can (or used to be able to) buy an already-assembled kit of parts from the author, but it included a lot of things we already had around the house, so it wouldn’t really help us save anything.

One reason I really like the book is that it encourages you to destroy things in order to see how they work. Often people are held back by worrying they might break something. It takes a lot of anxiety out of the situation if you are encouraged to break it!

For example, one experiment involves destroying an LED by hooking it up to the battery without a resistor. My son really likes LEDs though, so he really didn’t like the idea that we were killing them in order to enjoy ourselves. That motivated him to learn how to put resistors in the circuit to keep the LEDs from being destroyed.

Then we discovered that if the resister is too strong, the LED gets dim. He didn’t like that. So I showed him how the voltage, resistance, and current are related — Ohm’s law. He could use Ohm’s law to protect his precious LED by figuring out the exact resistance to make the LEDs as bright as possible without breaking it.

The catch is that you need to use algebra….

Here’s a great Ohm’s Law simulator on PheT: Ohm’s Law

Pi Day — This Friday

Just a quick warning that this very Friday is Pi Day! The day we celebrate 3.14.

I gathered together some fun Pi Day activities:

Other Pi Day activity lists:

And don’t forget to plan a really big party for next year — 3/14/15 at 9:26:53 will be amazing! (3.141592653…)

Spring 2012 Homeschool Portfolio Review: Math and Science

So, you may notice I never posted a plan of what we were doing for the Spring 2012. Well, that’s because we were in one of those frustrating times where it seems like nothing is working and the year was going to be horrible. So I didn’t really expect to stick to anything. I left it wide open to see what would happen. I think the kids liked that, because despite the fact I’ve been just so sick and miserable, we did an amazing amount of stuff! So much, in fact, that I had to split this up into multiple posts.


The Boy and I had all sorts of issues with math. He wants to do all his work in his head, but he just doesn’t have the working memory to actually do it! He is capable of so much more math, but if it involves writing, he simply won’t. In a few years, I’m sure he’ll be able to keep more in his head, if he’s anything like his parents, but for now I’m just going to have to back off and let him stay where he is comfortable.

So we reviewed addition, subtraction, multiplication and division in one to five digit numbers. He learned how to do the same actions on decimals and fractions, though I’m sure he only retained a little of it. He still doesn’t have a really good grasp on the decimal system to understand how easy it is to multiply and divide by 10. We did a few lessons on probability and he learned how to express probabilities as fractions and percentages. Then we moved on to Beast Academy, a new elementary series from the company that makes Art of Problem Solving. The Boy did the entire practice test in one shot because the answers were *fun*. They would work out to interesting numbers, or there was a tricky short cut that made him feel like he was cheating, but of course just proved he knew the math well. The books themselves are cartoons filled with little jokes and interesting games and problems. It’s a hit!

The Girl continued in Singapore, moving to Singapore 1B. She likes it, just a few pages at a time. Like her brother, she always thinks she wants more, but then it’s overwhelming and she shuts down, so I have to make sure to stop her before she gets upset. She worked on reading two-digit numbers (yay Bingo!), adding and subtracting numbers under twenty, probability of coin flips, skip counting, simple multiplication, symmetry, bar charts (which she invented for herself!), and finding the unknown (simple algebra).

Both kids also enjoyed a lot of books and activities from the Living Math curriculum, which goes through math concepts from cultures we’re studying in history. We made Chinese counting sticks, quipus, used an abacus, learned cuneiform numbers, and all sorts of other things.

The baby enjoys patterns, shapes, and counting things.


I don’t even know where to begin with science. They are surrounded by science. Science is in their genes (well, yes, literally, but I’m using it as a metaphor here, people!).

They both use Bernard Nebel’s Building Foundations of Scientific Understanding for some ideas of lessons, activities, and related books, but that’s usually only necessary when I’m especially exhausted or it’s the dead of winter and we just aren’t running into science often enough. Otherwise, we visit science places, read science books, do astronomy, raise many animals and plants, and play with science all day long.

The Boy investigated lasers, nuclear fission, chain reactions, naming conventions in organic chemistry, making molecules, static electricity, lightning, circuits and electronics, flight (in balloons, helicopters, and planes), vacuums, and how soaps work.

The Girl enjoyed mixing jello and proteases, gasses and pressure, and classifying fruits and vegetables.

Together they worked on raising a mantis, crickets, mealworms, and moths and learned a lot about food webs and metamorphosis. They helped build, tend, and harvest in the garden. They studied the anatomy of flowers, insects, and arachnids, and unfortunately, a prolonged study of the human digestive system. They also learned an awful lot about fermentation. We took nature walks in Maryland and Alabama and compared and contrasted the plants and animals that lived there and discussed adaptations for living in different environments. We studied the water cycle, pH, and made our own indicators. We talked about the types of energy and how energy changes forms (and how roller coasters and swings are excellent for demonstrating kinetic vs. potential energy). We investigated the three main forms of matter and their properties and identified the materials different objects are made out of and why someone would choose that particular material. We went to a real archaeology dig! We investigated flight more and took a trip to the Air and Space museum. We also studied levers and pulleys and simple machines made from them.

And that’s just the things I was aware of and remember.

Today’s Spontaneous Lesson: The Prisoner’s Dilemma

This morning, the kids noticed there was but half a donut and one mini muffin (blueberry) remaining. They attempted to work it out amongst themselves — The Girl suggested they simply split both in half and share. The Boy decided to go double or nothing and suggested that they play Rock, Paper, Scissors for the entire half donut.

Now, we all know how 5 year olds play rock, paper, scissors. Their first choice is almost always rock. Therefore The Boy knows if he just plays paper, he’s going to beat her 99% of the time. She even knows this! So I suddenly hear the tiny sounds of a whimpering girl and call them over to hear what happened.

I let her know that she doesn’t have to go along with what he decides. He doesn’t get to declare that donut-based discussions end in a game that we all know he’s going to win. “Next time, just refuse to play it, ok?” I let her know. Then I tell her the *whole* donut half is hers. The boy grumbles and looks surly. He goes up to his room for a little while.

While he’s gone, I talked to my daughter and let her know I thought it was sweet she wanted to split it with him, and I told her not to change. I also let her know that since she was the first one to ask about the donut, I probably would have given her it anyway.

She walks off and The Boy comes back and we have a talk. I let him know that it isn’t nice at all to take advantage of his little sister that way. It was his actions that caused it to go double-or-nothing and made him lose his part of his donut.

Then, we talk about The Prisoner’s Dilemma. It’s a thought experiment that was invented about 60 years ago to explore why people cooperate or not. The very basic version goes something like this: A crime is committed, like a bank robbery. The police pick up two witnesses, but don’t have enough evidence to charge them and/or convict them of a crime, so they want to get at least one prisoner to talk, or both. So they separate the two suspects and let them know the possibilities. If both prisoners stay quiet, they will probably still be locked up for a month on other charges. If both prisoners rat each other out, they will get three months in jail (the justice system likes easy cases). However, if one betrays the other, but the other stays quiet, the betrayer goes *free* and the silent one spends a year in jail.

At first it can seem difficult to figure out what to do — do you trust your partner? Is he really, in fact, guilty? The thing is, it may not even matter to you if he’s guilty or trust worthy. You may notice that no matter what he does, you’ll spend less time in jail if you betray him. Sneaky of the police, isn’t it? If you don’t see that yet, look at this chart:

B silent B talks
A silent 1 month each A gets 1 year, B goes free
A talks A goes free, B gets 1 year Both get 3 months

No matter what B does, A receives less jail time for talking. If B is silent, talking saves A one month. If B talks, talking will save A *nine* months!

Of course, the actual decision might be based on what B will do to you when he gets out of jail. 😉

There is a lot of research on game theory, and the psychology of envy, where researchers run little games and change the variables to see exactly what it takes to get you to betray your friend, or take the spoils, or whatever. A really interesting study about monkeys show that animals will change their opinions on their rewards based on what other animals get: Monkeys are happy with cucumbers unless other monkeys are getting grapes.

TV game shows even like to play around with game theory. Currently running around the internet is this amusing 6-minute clip from “Golden Balls”. At the end of the game, two players remain, with a pot of money. The very last round requires them to choose to split the money, or steal the money. If they both choose split, they do. If one chooses split and the other chooses steal, the stealer gets the whole pot. If they both steal, no one gets any money. Frequently people choose to steal just because they figure if they don’t get any money, no one else should. They don’t want to end up looking the fool. This guy chose a completely different approach:

I Guess This is What Unschooling Is Like

For those of you who aren’t homeschoolers, or don’t know a lot about it, there are actually a lot of different categories of homeschoolers. These are really general categories and there is a lot of overlap and squishiness about the categories, but sometimes it’s helpful to explain to other people the sort of philosophy you have about these things. It’s not entirely unlike explaining what sorts of foods you eat — low carb, vegetarian, kosher, and so forth. Broad categories that everyone stretches this way and that to make it work for them.

I probably can’t do justice to all the flavors of homeschooler right here, but if you’re interested the Homeschool Diner has a list they compiled.

We don’t really fit into any particular group. We have fewer rules than many families, but we’re not radical unschoolers without bedtimes or required chores or anything. I like a lot of the ideas of classical schooling, such as using original sources and mastery of concepts, but we’re not obsessed with following anyone’s particular idea of it and no one is learning latin right now! I buy curricula, but we don’t necessarily follow it, we use it as another source. We sometimes do unit studies, sometimes not. In fact, anytime I try to follow any schedule or routine or list, the kids object.

We are dedicated to randomness.

Lately, I’ve managed to injure myself in annoying ways, or get sick, or find some other reason to be busy, or cranky, or unprepared, and we’ve had a week or two (ahem) here or there (cough) where maybe we weren’t all at the kitchen table doing math worksheets every morning, if you know what I mean.

But the kids still learn. It really hard to keep them from learning, as it turns out. Boredom actually causes them to do all sorts of things. And kids can make anything fun.

One day a few weeks ago, all of us were sick with a fever, a cold, or bronchitis, so my son was playing on the computer. He was using Minecraft, along with a friend of his half way across the country, and he managed to do an entire day of school-worthy activities in just about every subject we need to cover.

This is what a home school sick day looks like: he had to multiply out the gold he won in the minecraft RPG he and his friend invented and divide by 64 to see how many stacks that would be (math). He’s making logic gates to power his doors and traps (science). He has to type to me to communicate (English). He taught his sister about the immune response system (health). He made a sculpture of a creeper (Art) and composed a song about how it holds his treasure chests (Music). As soon as I fix the printer, he can print and mail a certificate for another Junior Ranger badge (history — it’s about Clara Barton). 

It’s semesters like this one that makes me wonder if I’m going to eventually just relax, let go of the reins of control, and just be an unschooler. I wonder how far away that even is…

Tangram French Toast

For math, one resource we use is the Living Math web site. Instead of using standard math textbooks, it introduces math concepts through living books — story books and history books and books that play with math. Even better, it is organized chronologically and has the ability to be synchronized with our history spine (well, spines — I’m coordinating Story of the World and History Odyssey together). Each living math lesson goes along with four chapters or so of history.

It has a lot of fun activities and great lists of picture books and activity books. We’ve practiced body counting, used an abacus, and made quipus and counting sticks.

Recently, part of the lesson involved reading the story Three Pigs, One Wolf, and Seven Magic Shapes which introduces tangrams. I used our paper cutter to make each kid their own set of magic shapes in their favorite color out of card stock so they could replicate the pictures in the book.

A house!

A day or two later, the kids wanted french toast for lunch, so I made tons of it. I always ask them how they want it cut. When I was little, I learned my letters by having my mom cut them into my toast. I’ve done the same with my kids (I cannot explain how very hard the letter S is) and they even ask for snails, dinosaurs, and other crazy shapes. That day, they asked for the magic shapes. After cutting three sets of shapes in card stock, I had enough practice to actually do a pretty good job in french toast, if I do say so myself!

Play Doh Serendipity

It’s fun when the kids discover things on their own. The other day, my two girls were playing with Play Doh, and they decided the stack it up by color, thus reinventing the bar graph. (And making me deliriously happy, because I love categorizing things…)

Planting the Three Sisters and Other Companions

Against my better judgement, we’re going to try planting corn this year! It was an utter failure when I was a kid, but I am in Maryland, and corn is supposed to grow really well here. Of course, I’m going to have the bare minimum amount of corn to really expect it to fertilize well, which might be an issue. Another problem is that we’re in a windy area, and the wind might blow all the pollen away before it can fertilize. We did have some fertilization issues last year in the cucumbers and squash, but that might be because of their varieties.

Not only are we planting corn, but we’re using the three sisters method. It was the way many Native American tribes planted their crops. It involves three different plant types: corn (maize, really), squash, and beans. They are naturally complimentary crops — the corn makes a great trellis for the beans to climb and the beans in turn help stabilize the corn against the wind. Beans also fix nitrogen back into the soil, helping to fertilize the other plants. The squash act as a ground cover, blocking weeds from growing and shading the soil to help the soil keep from drying out as quickly. If you plant a spiny squash, it can also discourage predators.

 I read a nearly 100-year-old account of a Native American woman’s recollections of how she and her tribe farmed, using this method in Buffalo Bird Woman’s Garden.

For information about planting your own garden with the Three Sisters method, check out Renee’s Garden.

A Cherokee tribe in Alabama posted some three sisters myths online.

The farmer’s almanac has more information about companion planting. Some of these most gardeners are familiar with, such as planting basil and marigolds with tomatoes. There are also plants that need to planted away from each other, such an onions and beans.

My plan is to plant two 4′ x 4′ raised beds. One has early varieties of corn, squash, and beans, the other will have varieties the mature in a more regular length of time. If you divide the beds into 1′ x 1′ squares, each has 16 squares. I plan on putting five squash plants in five squares (the corners and center). The other 11 squares will each get 2-3 corn plants and 2-3 bean plants. If you’ve never heard of square foot gardening, this can seem awfully close, but the “experts” indicate that it does actually work, if you can water everything enough and fertilize often. That’s where the compost pile and the beans’ ability to fix nitrogen really comes in handy. 

And yes, this is just another way to make homeschooling fun — we get to learn all sorts of things:

  • Science — Life cycle of seeds, soil science, nutrition.
  • Social studies — Native American culture, traditions, stories.
  • Math — building the raised beds requires a lot of measuring and engineering, volume calculations to determine how many bags of dirt to buy, figuring out how many seeds to grow, timing everything just right, writing and reading charts of planting, and more!

Wish us luck — we barely had winter this year, which is a double edged sword. I think we’ll get to start the garden 1-2 months earlier than last year, and get some nice cool weather for the broccoli and such, but the bugs will probably be overwhelming. But the kids are pretty excited!