## Rabbit Trails and Fibonacci Poetry

### Homeschooling Memories…

Well, I hadn’t planned on spending my day that way. But one of the great things about homeschooling is the freedom to follow rabbit trails.

While browsing the Carnival of Homeschooling, I found a link to Farm School blog’s article Fib Foolery, which sent me to Gotta Book for his articles The Fib and More Fibbery (read the comments on both threads, but be warned that some are crude) and several other posts, all of which set me off on a morning of poetic fun.

A “Fib” is a Fibonacci poem. It’s based on syllable count, like a haiku, but the lines follow the Fibonacci counting series: 1, 1, 2, 3, 5, 8… Each number is the sum of the previous two numbers.

I knew what I was going to share at our Tuesday Teatime and Poetry Reading that afternoon.

Here’s the best one I’ve come up with so far:

Math:
Word
Problem,
Mental play.
Archimedes shouts,
“Eureka! I figured it out.”

### The Kids Join the Fun

While we always enjoyed our tea and poetry times, that day was the only one that inspired the kids to actually write poetry themselves.

My 7yo dd was so proud to be able to count syllables and write:

Cat.
Soft.
Pretty,
But sleeping.

While my 12yo ds really took off, creating more than a dozen Fibs. His first two are still his favorites:

Ducks
Have
No luck,
But they do
Have many feathers.
Hunters like to shoot ducks a lot.

and

Paul
Is
Revered
A lot by
Paul Revere’s Fan Club.
What is Paul’s last name, anyway?

Feature photo: “Rabbit” by Save the Bay via Flickr (CC BY 2.0).

## Noticing Fractions in a Sidewalk

My daughters didn’t want to admit to knowing me, when I stopped to take a picture of the sidewalk along a back street during our trip to Jeju. But aren’t those some wonderful fractions?

What do you see? What do you wonder?

Here is one of the relationships I noticed in the outer ring:

$\frac{4 \frac {2}{2}}{20} = \frac {1}{4}$

And this one’s a little trickier:

$\frac{1 \frac {1}{2}}{12} = \frac {1}{8}$

Can you find it in the picture?

Each square of the sidewalk is made from four smaller tiles, about 25 cm square, cut from lava rock. Some of the sidewalk tiles are cut from mostly-smooth rock, some bubbly, and some half-n-half.

I wonder how far we could go before we had to repeat a circle pattern?

## A Review for my Daughter’s Novel

“… a captivating fantasy story with a well-thought-out plot … people who like medieval-style fantasies with wraiths, spirits, and even an attacking swamp tree will enjoy the story. I certainly did, and the excitement, adventure, and suspense will easily keep the reader’s attention …”

— Wayne S. Walker
Home School Book Review

Thank you, Mr. Walker!

As a fantasy fan myself, I agree that Teresa did a great job on this book. She improved in every way from Book #1 — more world building, more complex plotting, and a deeper emotional identification with the characters. I can’t wait to see what she writes next.

#### Find out how the adventure began:

Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.

## New Internet Math Reference Pages

The Internet boasts a wide-ranging assortment of math websites, and for years I maintained (or mostly neglected) a huge page of reference links. This spring I’ve been working on the paperback edition of my book‌—‌with its appendix of favorite books and internet sites‌—‌and I decided to revise my blog links to match.

So this week, I’m in Jeju, South Korea, visiting my daughter who teaches English there. In between seeing touristy sites and gorging ourselves on amazingly delicious food, she took me to a beautiful coffee shop that overlooks the beach in Aewol.

Great place to work on my blog!

The long monster list morphed into eight topical pages. I hope you find something useful.

I will try to keep these pages up to date, but the Internet is volatile. If you find a broken link, you can search for the website by name or enter the defunct URL into the Internet Wayback Machine at Archive.org.

And if you know of a fantastic website I’ve missed, please send me an email (LetsPlayMath@gmail.com, or use the comment form on my “About” page). I appreciate your help.

Feature photo above by Fractal Ken via Flickr (CC BY 2.0). Korea photos ©2015 Denise Gaskins, all rights reserved. For more math resource suggestions, check out my Math with Living Books pages. They’re not finished yet, but I’ll be working on them next.

## New Fantasy Novel by Homeschooled Teen Author

After months of editing, formatting, proofreading, sweat, and tears:

Teresa Gaskins’s new ebook Hunted: The Riddled Stone ~ Book Two is available now at Amazon worldwide.

To celebrate the release of Hunted, the ebook version of Banished‌—‌the first book in the Riddled Stone series‌—‌will be on sale for 99 cents for the next few weeks.

Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.

## Math Storytelling Day: The Hospital Floor

[Feature photo above by Christiaan Triebert via flickr (CC BY 2.0).]

Have you ever heard of Math Storytelling Day? On September 25, people around the world celebrate mathematics by telling stories together. The stories can be real — like my story below — or fictional like the tale of Wizard Mathys from Fantasia and his crystal ball communication system.

### My Math Story

My story begins with an unexpected adventure in pain. Appendicitis sidewhacked my life last week, but that’s not the story. It’s just the setting. During my recovery, I spent a lot of time in the smaller room of my hospital suite. I noticed this semi-random pattern in the floor tile, which made me wonder:

• Did they choose the pattern to keep their customers from getting bored while they were … occupied?
• Is the randomness real? Or can I find a line of symmetry or a set of tiles that repeat?
• If I take pictures from enough different angles, could I transfer the whole floor to graph paper for further study?
• And if the nurse finds me doing this, will she send me to a different ward of the hospital? Do hospitals have psychiatric wards, or is that only in the movies?
• What is the biggest chunk of squares I could “break out” from this pattern that would create the illusion of a regular, repeating tessellation?

I gave up on the graph paper idea (for now) and printed the pictures to play with. By my definition, “broken” pattern chunks need to be contiguous along the sides of the tiles, like pentominoes. Also, the edge of the chunk must be a clean break along the mortar lines. The piece can zigzag all over the place, but it isn’t allowed to come back and touch itself anywhere, even at a corner. No holes allowed.

I’m counting the plain squares as the unit and each of the smaller rectangles as a half square. So far, the biggest chunk of repeating tiles I’ve managed to break out is 283 squares.

## Reblog: A Mathematical Trauma

Feature photo (above) by Jimmie via flickr.

My 8-year-old daughter’s first encounter with improper fractions was a bit more intense than she knew how to handle.

I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:

Photo (right) by Old Shoe Woman via Flickr.

Nearing the end of Miquon Blue today, my youngest daughter encountered fractions greater than one. She collapsed on the floor of my bedroom in tears.

The worksheet started innocently enough:

$\frac{1}{2} \times 8=\left[ \quad \right]$

## A Pretty Math Problem?

As we were doing Buddy Math (taking turns through the homework exercises) today, my daughter said, “Oooo! I want to do this one. It’s pretty!”

She has always loved seeing patterns in math. I remember once, years ago, when she insisted that we change the problems on a worksheet to make the answers come out symmetrical. 🙂

## How To Master Quadratic Equations

feature photo above by Junya Ogura via flickr (CC BY 2.0)

A couple of weeks ago, James Tanton launched a wonderful resource: a free online course devoted to quadratic equations. (And he promises more topics to come.)

Kitten and I have been working through the lessons, and she loves it!

We’re skimming through pre-algebra in our regular lessons, but she has enjoyed playing around with simple algebra since she was in kindergarten. She has a strong track record of thinking her way through math problems, and earlier this year she invented her own method for solving systems of equations with two unknowns. I would guess her background is approximately equal to an above-average algebra 1 student near the end of the first semester.

After few lessons of Tanton’s course, she proved — within the limits of experimental error — that a catenary (the curve formed by a hanging chain) cannot be described by a quadratic equation. Last Friday, she easily solved the following equations:

$\left ( x+4 \right )^2 -1=80$

and:

$w^2 + 90 = 22 w - 31$

and (though it took a bit more thought):

$4x^2 + 4x + 4 = 172$

We’ve spent less than half an hour a day on the course, as a supplement to our AoPS Pre-Algebra textbook. We watch each video together, pausing occasionally so she can try her hand at an equation before listening to Tanton’s explanation. Then (usually the next day) she reads the lesson and does the exercises on her own. So far, she hasn’t needed the answers in the Companion Guide to Quadratics, but she did use the “Dots on a Circle” activity — and knowing that she has the answers available helps her feel more independent.

## How to Recognize a Successful Homeschool Math Program

After teaching co-op math classes for several years, I’ve become known as the local math maven. Upon meeting one of my children, fellow homeschoolers often say, “Oh, you’re Denise’s son/daughter? You must be really good at math.”

The kids do their best to smile politely — and not to roll their eyes until the other person has turned away.

I hear similar comments after teaching a math workshop: “Wow, your kids must love math!” But my children are individuals, each with his or her own interests. A couple of them enjoy an occasional geometry or logic puzzle, but they never voluntarily sit down to slog through a math workbook page.

In fact, one daughter expressed the depth of her youthful perfectionist angst by scribbling all over the cover of her Miquon math workbook:

• “I hate math! Hate, hate, hate-hate-HATE MATH!!!”

Translation: “If I can’t do it flawlessly the first time, then I don’t want to do it at all.”