God’s Perfection in Mathematics

One evening about a month ago, my six-year-old brother asked a question that was designed to stump the oldest of us. “What’s fifty times fifty?” He loves starting with the hardest number to multiply that he can fathom, and then multiply that by itself, the new number by itself again, and keep going—until even the calculator groans and returns an E+, ‘Overflow’, or simply starts showing uninterpretable decimals.

Squares 01

But since fifty times fifty isn’t too big, I set it up on the whiteboard for him and gave him the answer. “Two thousand five hundred.”

“So…what’s forty times forty?”

I can’t remember exactly how the conversation went from there, but we ended up calculating several squares in the 47-52 range. After looking at the ones on the board, I suddenly wondered if there was a pattern. If we could possibly predict the next one.

472 = 2,209
482 = 2,304 (difference from 472: 95)
492 = 2,401 (difference from 482: 97)
502 = 2,500 (difference from 492: 99)
512 = 2,601 (difference from 502: 101)
522 = 2,704 (difference from 512: 103)

If there is a pattern, 532 should be 522 plus 105. It is—2,809.

After this, Mom went back to 1 and wrote down the squares of the first 12 numbers, to see if they followed the same pattern.

Squares 02

Should give you an idea of what she did. The differences are the bottom row of numbers.

They do. Each difference is precisely two numbers greater than the last one. Incredible, isn’t it? And while it’s amazing, we also realize that God has known all along and He made it that way for a reason.

So there’s your math lesson for the day. A terribly impractical, but undeniably fascinating pattern.

Reading, Art, and Guilt — a Guest Post

Twice in the past two months I have had an “ah-ha!” moment. Both times, I suddenly had an answer to something that I had been feeling guilty about for years.

I was reading by the time I was three years old. When I was a baby, someone gave my mom a book, something about “Teach Your Baby to Read.” I was the first baby, so she had time, and she made flashcards to put on objects all over the house. I can’t remember not being able to read, and I’m guessing maybe she eventually regretted teaching me that young, as I quickly developed an addiction to reading! I remember being excited to start first grade, but then being very disappointed because the first day of first grade the reading lesson was simply, “God.” I was reading whole books by then! I spent hours and hours reading thousands of books as I grew up, and put that love of books to good use when I started a bookstore in my late teens. However, after I got married, little by little I started feeling guilty for loving to read, and guilty for taking time to read when there were other things to do, as there always are. Comments some people made such as, “I only ever read the Bible and ___________(church paper),” or, “Reading is a waste of time for me,” added to that feeling of guilt. I still read, because I can’t make myself stop reading, but always with a slight feeling of guilt.

Reading, Art, and Guilt

One of my son’s art projects.

Last year, my daughter came in from her bedroom one morning saying that she felt like the Lord had given her an idea. She wondered what I thought of a website devoted to book reviews. She would include warnings with the reviews of anything that parents might want to know about the book before giving it to their child, and build a search function to help parents find books about a particular area they were studying. After we all prayed about it, she built the website, and soon I started writing some reviews for her of books I read to myself or aloud to the other children. Still, I felt somewhat guilty about loving to read!

A couple of months ago, a couple of my children and I went to a book fair. As usual, we came away with a large stack of books, including a few that we already owned. We had to stop at a friend’s house to drop something off on our way home, and offered her the duplicate books. She was happy to take them, thanking me for the recommendations for her children, since she has a hard time knowing if a book will be worth reading or not. I was thinking about that little exchange after we left her house, and suddenly the thought came to me that part of my ministry to other people is to be able to recommend books for them and their children! God gave me the gift of being able to read exceptionally fast, and therefore I am able to read a lot more books than most people, which means I can help people by pointing them to the books they need! What a revelation. I still have to be careful not to let myself read when there are other jobs that really need doing (after all, I have a husband and eight children who like to eat three meals a day), but I no longer feel guilty about reading while I rock the baby.

My other revelation came just a few weeks ago. I have been homeschooling our children for 11 or 12 years now. Somewhere around 10 years ago, I picked up an art course at a book fair, and decided that we would do art classes—doesn’t everyone do art classes? Don’t children need to learn art? I decided that once a week, while the youngest two (I think) napped, I would do an art lessons with the three oldest children. We did—a grand total of three lessons! After that, until I ended up selling the art course when we moved overseas six years ago, I kept intending to get back to it, but life was constantly in the way. Anyway, I have very little interest in art or crafts of any kind. There was always a guilty feeling in the back of my mind, though, that my children were missing out because I was not making time to teach them any drawing or modeling or any kind of crafts.

A few weeks ago, my middle sons spent two days holed up in their workshop every spare minute, building something. When I finally got to see it, I was astounded. Those boys had cut a large circle out of a piece of plywood, and painted a railroad track around the edge. They painted roads and fields on the board, and built tiny houses. They unwrapped copper wire from the motor of a defunct washing machine, and built fences by drilling holes through twigs that they glued into holes they drilled in the board. They strung telegraph wires around the track the same way. They glued tiny trees into place, and made stick figures out of copper wire to put in various places. They even made little wooden cars and a train engine. What is all that, but art? And I had nothing to do with it! I don’t have to teach art to my children! If they are interested, they will learn by themselves. All I have to do is give them free time and allow them to use the materials and tools they find and want to use.

Believe it or not, a great weight has lifted from my mind since I realized these two simple things. Guilt has a way of dragging us down, and other people’s expectations can make moms feel very guilty. At least, that is the effect on me. When I don’t do or believe the same as the people I am around, I tend to feel guilty about that, as if I am wrong—but guess what! God didn’t make us all the same! I have a unique ministry—and so do you. It would have been nice not to have to wait so long to find mine, but I am thankful to not feel guilty anymore about reading and art!

Emma-BioEmma Filbrun is a stay-at-home homeschooling mother of eight children, and in between chasing toddlers and keeping the tribe fed you can usually find her reading a story to several of the children or directing operations from her rocking chair (where her baby puts mommy time high on the agenda). She shares the mishaps and adventures of a large family on her blog, Lots of Helpers.

Midweek Mix-Up — the Cold War and a Free Outlining Course

Hello again! In today’s midweek mix-up, I’ve got some great resources for you, as well as some fascinating books I’ve been listening to lately.

Reading this week…

I haven’t actually “read” much this week—mostly because I’ve been doing quite a bit of computer work, and when I’m doing that I can’t read. But I have been listening to a lot of books, and I suppose that counts as well!

Amy Carmichael: Rescuer of Precious Gems, by Janet & Geoff Benge

Amy Carmichael: Rescuer of Precious Gems, by Janet & Geoff Benge
Progress: Finished (last week: 89%)

This is a beautiful retelling of Amy’s life. There was a lot about her early life, which I enjoyed immensely—often, we tend to hear the most about her time in India, and little about the rest of her life. I hadn’t realized before that she spent a while working in Japan before eventually being called to India, so that—along with the legacy she led and left behind her—was very encouraging for me. Highly recommend this biography—I’ll be putting a review of the book on the main site after a while.

The Lilies of the Field, by William E Barrett

The Lilies of the Field, by William E Barrett
Progress: Finished

I loved the story of Homer Smith—how he just happened to come across a group of four German nuns who badly need help, his coming an answer to prayer. Mother Maria Marthe put him right to work building a chapel for her, but he thinks she’s a bit crazy to ever expect him to be able to do it on his own.

Even though this story is a bit different from the books I usually read, it was fascinating and I’m planning to review it soon.

The Mouse That Roared A Novel, by Leonard Wibberley

The Mouse That Roared: A Novel, by Leonard Wibberley
Progress: 68%

What happens when a little country is slighted by a bigger country—namely, the United States? Add in the current world events—the cold war—and the little country running out of money to feed their citizens. The government of the Duchy of Grand Fenwick decides the only way to get enough money to feed their citizens—and settle their quarrel with the US—is to declare war on the US. There’s no way such a small country could win the war—but when they accidently seize the most dangerous atomic weapon in the world, they have suddenly won the war. This is a very humorous tale, one that I’m enjoying even though I’m sure I’ll get more out of it in a few more years.

Inspiring posts this week…

  • 12 Letters That Didn’t Make the Alphabet — Mom sent this to me earlier this week. Who knew that there were twelve other letters we could be using now—but generally aren’t? The only one that we actually use anymore is ampersand (“&”). Remember that old Apple Pie ABC rhyme? “…X, Y, Z and ampersand all wished for a piece in hand….”
  • Tips for Writers Who Don’t Work Well With Outlines — Great post. I think I tend to be on the outlining side, but many of these tips would apply to me, as well.
  • Two Harvard Professors Reveal One Reason Our Brains Love to Procrastinate — I found this post fascinating. Useful tips on how to change the way you look at procrastination, and how to practice being productive.
  • Grammar Websites For Writers — This is a great list of resources, not only for writers, but for homeschoolers as well. Some of the spotlighted websites are for editing, others are for researching and learning about grammar. I’ll be bookmarking this one for future use!
  • 5 Reasons To Pray Before You Write — I’m guilty of not doing this enough. It’s wonderful to have a reminder of where my responsibilities should lie, even if I always seem to forget this until all else has failed.

Resource of the week…

I’ve got two resources for you this week!

For Writers:

Write Your Non-Fiction Book Quickly and Easily: The Magic of Outlining

This is a free outlining course by Nancy Hendrickson, a renowned author and writing coach. I don’t know how long it will be free, but it looks very useful, and I’m planning to take time to go through it soon. My outlining skills need a lot of help.

For Homeschool Moms:

Get a free lifetime membership!

From the website:

Easy-to-use online homeschool and private school planning.

In just a few minutes you can set up your school year & subjects, create lessons & assignments, record grades, and more.


  • Grade recording
  • Easy drag-and-drop interface
  • Copy/paste lessons easily
  • Print weekly lesson plans
  • Ongoing improvements based on your feedback

My aunt recently shared this on Facebook. If you want to get a free lifetime membership on the site, simply go to the site, sign up for a two week trial, and put in the referral code FFL15. No payment info to enter, and within seconds of signing up you can be planning away! I don’t know how long this deal is going to be available.

If you want simpler version of planning, you could try making your own chart for each child—I cover that in depth on this post.

Midweek Mix-Up — Pride and Prejudice and a Free High School Biology Curriculum

Welcome to another round of midweek mix-up! I’ve been doing a lot of reading this past week, beyond a few breaks to do other necessary work and spending some quality sibling time.

Books I’ve been reading this week:


The Sound of Diamonds, by Rachelle Rea

The Sound of Diamonds, by Rachelle Rea
Progress: 45% (last week: 24%)

This story has grown more interesting, and the romance thread has grown stronger, too. I’m taking the opportunity to study how romance books work, and will find it interesting to see how the story ends.

The Annotated Pride and Prejudice, by David M. Shapard

The Annotated Pride and Prejudice, by David M. Shapard
Progress: Finished.

I’m not a big fan of romance, but I loved reading Pride and Prejudice. Probably part of the reason I enjoyed it so much was because it’s an older book—I’m finding that classical literature has a glory all its own, even though it is hard to get into. I’ve also watched a movie based on the book before, and listened to a version of the story on LibriVox, as well, so it was interesting to compare the original story with my memories of the audiobook and the differences with the movie. The annotations for the story were very in-depth, providing a lots of interesting tidbits from Jane Austen’s life and letters, explanations of the social structure of the times, and many other fascinating facts and quotes about the story and the time period it was set in.

This isn’t a book for the faint of heart, though. At close to 800 pages long (the spine is just over 1 ½ in. thick), I highly doubt I ever would have gotten through it but for the fact that I had to read it as part of my school curriculum. In the end it was highly interesting, and all the notes make a study of the time period very informative.

Amy Carmichael: Rescuer of Precious Gems, by Janet & Geoff Benge

Amy Carmichael: Rescuer of Precious Gems, by Janet & Geoff Benge
Progress: 89% (last week: 55%)

I am loving Amy Carmichael. We have a Trailblazer book about her, but that only tells about her time in India. I’m really enjoying this glimpse into her life as a whole, and seeing how God worked through her to touch so many lives. Her life story is certainly a challenge to me!

Useful posts this week:

  • 24 Ways to Develop Your Muse — I’ve used a lot of these methods before—most of them unconsciously. But they are some of the best methods out there for ideas. I especially like #3—something that has proved very true for me!
  • Writing Out of an Era — So many tips in here for learning more about the historical period you are writing about! I am definitely going to try some of these next time I’m writing a historical novel—they sound so fun!
  • Discovering rare and interesting instruments — I’ve only heard of one of these six rare instruments before, so I found this post fascinating. This post would be very useful in teaching your children about different musical instruments, especially if they enjoy music. I think my favorite one here would be the Nyckelharpa—it has a beautiful sound!
  • Goal Setting for Beginners [Podcast] — This podcast (This is Your Life with Michael Hyatt) is always inspiring to me whenever I take time to listen to it. I enjoyed this quick refresh on Michael Hyatt’s goal-setting principles, and immediately after listening, I typed up this year’s goals into Evernote. I’m now planning to add a few “due-by” dates to some of them.

Resource of the week:

Otter’s Christian High School Biology Curriculum

Otter’s Christian High School Biology Curriculum

From the website:

Otter’s Biology is a FREE Christian biology curriculum that incorporates a free high-quality textbook, videos, tons of labs to choose from with a multitude of budget and interest options, living books, a free workbook & answer key, incorporated Greek & Latin roots vocabulary, an independent study schedule, and more! If you are a secular family or a family that believes in evolution, the schedule and labs will still work for you, too (more instructions concerning that are included below)!

This looks like a wonderful (free!) resource for high schoolers who want to study biology! The woman who put this together has a daughter who is a RN student, and she has consulted with her quite a bit as to what was helpful for her prep work, and what wasn’t so helpful. I will be looking into this further, because I believe it could be helpful to me in pursuing nursing as well, but you might find it useful too.

Midweek Mix-Up: A Full Week, and Scripture Memorization

Hello everyone! Welcome to this week’s version of midweek mix-up! I’ve had several full days of work this past week, so I haven’t had as much time to read as I had last week. That’s okay, though, because it’s good to learn that sometimes life just happens. This way, I have the chance to really appreciate the time I do have to work and read—even if it is less than I would ideally like.

Books I’m reading this week:

The Sound of Diamonds, by Rachelle Rea

The Sound of Diamonds, by Rachelle Rea
Progress: 24% (last week: 15%)

The tension is rising. There is definitely going to be a romantic element in the story, but what proportion it takes is yet to be determined. So far, Gwyn has narrowly escaped death, had her worst fear realized, and is now hoping that a lie will get her across the channel to a semi-safe country.

Winterdance, by Gary Paulsen

Winterdance: The Fine Madness of Running the Iditarod, by Gary Paulsen
Progress: Just finished.

Grandma read this onto mp3 for my brothers, and I just finished listening to it today. Technically, no, I didn’t read it—but it was close enough I think I can count it as actually having read it.

Winterdance is very well written. The story is about a man who ran the Iditarod—the huge dog race in Alaska. It tells of him starting with hardly any knowledge at all about dogs, or the race, or anything—and how he somehow blundered his way to Alaska and ran the race. Fascinating adventures, and apparently it actually is a true account.

There were a few words I wouldn’t use through the story, and Grandma said she did leave one paragraph out because of its content—the story was fine without it.

If I can get this book in print, I’ll definitely be reviewing it—it is a beautiful story of dogs, the relationships you can have with them, and a very humorous account of a rookie running the Iditarod for the first time.

Useful posts this week:

  • Conflict Vs. Tension – A Guest Post by Melissa Tagg! — Very encouraging! I love how she explained conflict vs. tension, and applied that to life as well as to writing. That note at the end was also very encouraging—somehow, involving God in everything we do really does add a lot of depth to our lives.
  • Submission – a Heart Matter — I especially loved this note near the end of the post: “…Personally, I know that my father doesn’t like us to wear the color black. He has never said ‘thou shalt not wear black’ but because that is his desire, we try to honor him in that.” I love seeing some of the small ways I, as a young woman, can learn to submit!
  • The Go Teen Writers Summer Writing Challenge and a Giveaway — This is partly a guest post, partly a challenge. The guest post part is pretty interesting—Lydia Howe (aka Aidyl Ewoh) is telling how she wrote 100 words every day for 1,000 days, and how we can do the same. In that time, she traveled to three different continents, published three books, and fought Lyme’s disease, along with other adventures. The challenge is designed to help you get some work done in the next three months. I’m seriously considering joining—I always find the Go Teen Writers challenges extremely helpful.

Resource of the week:

Ever wanted an easier way to teach your child memory verses? Say hello to FreeBibleMusic.com! The songs on here are free to download and use. There are three different artists that helped create this “Scripture song bank”—Abigail Miller (I love her music!), Buddy Davis, and Kirk Gable/the Kirk Gable Band.


Out of the sixty-six books of the Bible, there are only twelve books that there are no scripture songs for: Ruth, 2 Kings, Ezra, Esther, Joel, Obadiah, Jonah, Nahum, Zephaniah, Haggai, Philemon, and 2 John.

Also of interest—there is a small section of stories for children on this site. These stories were apparently written and then acted out by Lydia Howe—the same girl who just passed the 1,000 day mark above—and her family. The twelve stories are roughly five minutes long each, and are fun adventures your children will enjoy.

Writers: What was the last writing challenge you participated in?

(For me, this would be Camp NaNoWriMo in April—I failed horribly.)

Your Three-Year-Old Can Write, part 2: Examples

We’ve established the fact that teaching writing to your children from an early age is important. Today, I’d like to give you a few examples of what my young brothers write about, and how your youngsters can write too.

Your Three-Year-Old Can Write, part 2: Examples

Photo courtesy of Pixabay/Efraimstochter | License: CC0 1.0

Tip #1: Ask Them to Tell You About a Recent Experience

Sometimes, a story can spring from a simple life experience. In the following story, my brother was telling what he saw when we went to visit a local zoo called Willowbank.

We going to Willowbank and we go into the office. We see eels at Willowbank. I see ducks. I feed ducks bread. They ate it all gone. The monkey was going up to the branch and up to another one branch, one, two branches. That long branch! There were chickens in the chicken pen. —J, two and a half years old

Tip #2: Write Down Their Imagined Stories

Sometimes, my brother will come through with a story to tell to whoever will listen to him. This was a product of one of those occasions—when Mom was able to write it down. Obviously, she did not edit—she just wrote it as he told her. Right now, it may not make a whole lot of sense—but it will definitely be fun to read in years to come!

A man was taking a walk with his dog and he was walking on the road with his dog and he was going to motels and he was going into motels watching motel clean the living room up with the vacuum and vacuum his garden up and taking a walk with his dog and the daddy dog died and humongous bushes and there was a lion in the bushes. —N, three years old

Just for fun, here’s another example:

I was walking through the woods one day. A bear jumped out of the forest, and I speared it. I had flint and steel in my pocket, and I started a fire. I had forked sticks up on top so I could dry the meat and the skin. I made metal forked sticks out of flat sticks of steel. And I had that bear for my tea. It tasted like cow meat.

I went out diving one day, and speared a shark. I had a string so I could tie it onto the tail. I pulled it to shore. Then I speared a seal. I chucked it into the sea, and the other sharks ate it. I washed my hands, and I went back to the forest.

Another bear jumped out at me. I was dragging the whale still. I speared the bear, and I put it in my small freezer. It wasn’t very small. I chopped off feet. I was close to a sea. I chucked them in the sea, and the sharks ate them. —J, four and a half years old

Tip #3: Let Them Tell About Their Daily Life!

In this next example, my brother reiterated his daily life. Obviously, this was how he said it then–fun to compare with how he talks now.

… Sheep is going in paddocks when I chase them. I chase your cow, Mom. I chase Mom’s cows when they go in cow’s water. I go home. I am sweating over the place. I go in the house. Daddy is coming home after lunch. When I come I eat glue. … I can taste really good. I not taste it. I go to the pen and wait for the boys to get done getting the cows. When they come they go running. They go running lot of times. They scream. —J, two and a half years old

Tip #4: Ask Them What They’d Like to Write About

In the following example, my brother asked to watch a video about lions. Mom found one on Youtube for him, and he based this piece on that.

I want to write about lions. They jump. And they jump onto the rocks. They eat animals. They save baby lions. They play with little lions. They sleep a lot and baby lions sleep a lot. They eat giraffes and zebras. And kill animals. —N, three years old

Tip #5: Encourage the Different Forms of Writing They May Choose

This poem was not an assignment at all—my brother just decided to make his story into a poem of sorts. Definitely something you want to encourage if you see your child wants to do something like this!

Pick up trash.
Pick up trash.
Pick up trash.
On the beach.
Rolling, rolling sea.
With the picked-up trash go on the rolling, rolling sea.
With the hat on the rolling, rolling sea.
Pick up trash.
Pick up trash.
Pick up trash on the rocks.
—J, three and a half years old

Tip #6: When They’re Ready, Give Them Assignments

The following was an assignment that came from our science course. After several years of writing, he was ready to do something a bit more intensive than just retelling his life or telling a story. For this particular assignment, he had to pick a bird, do a bit of research about it (with some help, of course), and then write a few sentences about the bird.

Bald eagles go high up in trees to have a nest. They migrate from north to south in North America. Their favorite food is fish. They are big. They are a meter long. They are two meters wide, from one tip of the wing to the other one. They live in North America, close to the sea. They aren’t actually bald. They are black and white. Their beaks are yellow. —J, five and a half years old

One of the beauties of starting early is that you get to watch them slowly get better at turning their thoughts into coherent words, sentences, and eventually, paragraphs. While it may be hard to start your youngsters writing at an early age—especially if you have a baby or toddler to watch at the same time!—don’t despair. If you can do it, wonderful! If not, they’ll learn later. Either way, you’re doing great—have fun!

How to Create Effective Incentives for School Work

Sometimes, it is hard to get school done. Almost as hard as pulling hen’s teeth. This is where incentives for school work are needed—with simple rewards, your students can learn to work faster and harder.

Near the beginning of the school year, for a week or so anyway, it’s fairly easy to get the work done fast. Past the first month or so, the momentum starts to slow down—until it’s only a fraction of the original speed, and we’re all tired of how long it’s taking to get anything done.

How to Create Effective Incentives for School Work

Photo courtesy of Pixabay/Hebi65 | License: CC0 1.0

A few years ago, after seeing how slow we were going, Mom decided to implement a rewards system where if we got a prescribed amount of work done by lunch time then we could get a treat. It worked—and we used the system for several months, before we all got tired of eating the same reward every day.

Three Ways to Create Incentives:

  1. Find simple rewards. They don’t have to be very fancy—they just have to be effective. For a while, we were using simple peanut butter balls (see recipe below). Everyone who got done in time received a peanut butter ball, and those who didn’t just missed out.
  2. Find simple consequences. Sometimes, a child does not get his work done no matter how many rewarding incentives you give them. For example, say a child is way behind on his math. Since he is so far behind, and not catching up—even though he could have easily finished within an hour or two—a simple consequence could be digging a bucket of potatoes the next day for Mom if he doesn’t get done by a certain time. This is an easy enough chore, usually done in fifteen minutes or so.
    (Note: I am not encouraging enforced labor simply because a chore is not done in time. This kind of incentive is only used when there is an ongoing problem, and when the student can easily catch up by applying himself.)
  3. Create heavier-duty rewards for habits. Recently, Mom has been trying to teach my brothers some life-long habits. Instead of just telling them to work on them, she decided to help them keep track of how they’re doing. Each day they successfully complete a job associated with the habit, they earn 5¢. Every day they miss, they lose 5¢.

Consistency is a key to making incentives work. For busy Mothers, though, it is hard to remember who gets what reward.

One way Mom has combated this problem is by giving a universal reward to everyone. She also has a set consequence for those who particularly struggle. For example, one of my brothers loves to sleep outside. He is normally allowed to sleep outside, but on the days he doesn’t finish his school work in time he has to sleep inside. This is a very simple consequence, but most of the time it does the job—his work gets done early.

Peanut Butter Balls RecipePeanut Butter Balls Recipe

  • ½ cup peanut butter
  • ¼ cup dessicated coconut (+ some to coat balls in)
  • ¼ cup raisins
  • 1 tsp. honey (or other sweetener)

Mix well, roll into roughly 1″ balls, roll in coconut.

For variations: I’ve sometimes added cocoa powder, or cinnamon and cloves, to give different flavors. It is also possible to add vanilla, almond, caramel, or other essences to give different tastes. Chocolate chips and dried mixed fruit are good replacements for the raisins. Feel free to experiment—this is just the base recipe!

Even though the rewards for school work well done can be very small, they are effective. Mid-school blues are hard to push away, but by being creative, the work can become more fun again.

How have you used incentives before? Did they work?