# Back to School Sale

Princess Kitten, way back in the beginning.

Our homeschool runs a bit off-schedule from the rest of the U.S. school system, as we are still finishing up last year’s work. Even so, we’re calling this month the “beginning” of Kitten’s high school years, which seems to me like something to celebrate.

Therefore, I’m launching a one-week sale on my math book:

Update: I’ve just opened up a Ganxy showcase with the sale price, for anyone who would prefer to buy the ebook (in pdf, mobi, and epub) directly from me:

# 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. :)

Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.

# 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.

# Logic Puzzle: Imbalance Problems

Kitten and I have been slogging through the decimals chapter in AoPS Pre-Algebra. She hates arithmetic, so I tried skipping ahead to the algebra puzzle in the exercises, but she refused to be taken in: a decimal problem with an x in it is still a decimal problem.

So I let her off early and pointed her toward these logical “algebra” puzzles instead:

Puzzle by Paul Salomon

By Denise Gaskins Posted in Puzzles

# Reviews for my Daughter’s Book

I cleaned up the clutter on my other blog, and so I decided to make a page about my daughter’s book, which meant taking the time to pull out excerpts from her reviews. And since I hadn’t posted anything about her on this blog for a couple of months, I thought I’d brag a bit to you all, too.

## Reviews of Banished

Banished is a captivating fantasy story with a well-thought-out plot that would be a credit to any writer. But it is especially remarkable coming from a thirteen-year-old student who has been homeschooled all her life.

Teresa Gaskins actually wrote this book as a project for the National Novel Writing Month program. One noteworthy thing about the book is that there is no sexuality or bad language (the euphemistic interjection “Blasted” is used once), so, other than those who object to the presence of any kind of magic in books, parents can let their kids read the novel with no reservations.

However, be forewarned. When you reach the final page and find the words, “Not the End…,” you will cry, “Oh! No!” The story does not resolve itself at the end and then pick up in a sequel. Rather, the plot is left hanging at the end and will continue in another book. I for one feel as if I simply can’t wait to read the next installment to find out what happens to Chris and his friends. It’s that good!

— Wayne at Home School Book Review

# 5 Stars at Home School Book Review

Wayne at Home School Book Review just posted a very kind review of my daughter’s book:

Banished is a captivating fantasy story with a well-thought-out plot that would be a credit to any writer. But it is especially remarkable coming from a thirteen-year-old student who has been homeschooled all her life.

However, be forewarned. When you reach the final page and find the words, “Not the End…,” you will cry, “Oh! No!”

I for one feel as if I simply can’t wait to read the next installment to find out what happens to Chris and his friends. It’s that good!

Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.

# New Fantasy Fiction Book by 13yo Homeschooler

My 13-year-old daughter just released her first book on Kindle:

• Banished (The Riddled Stone, Book One)
Falsely accused of stealing a magic artifact, Chris is forced to leave home, never to return. As he and three friends travel toward the border, however, they are warned of great danger approaching the land. They set out to solve an ancient riddle — but will they be able to save the kingdom, or will the quest cost them their lives?

[Update 7/6/12: The paperback book is now "In Stock" at Amazon (yay!). They are even including the book in their buy-3-get-1-free promotion for books and home/garden items.]

Teresa (also known as Princess Kitten) has done the NaNoWriMo Youth Program as part of her language studies for the past three years and has written many stories on her blog, but this is the first time we’ve followed through and published one of her books.

Of course I’m biased, but I think she did a pretty good job, as first books go. It’s clearly the beginning of a series, so she sets up more plot threads than she resolves — but I did convince her not to wait for this year’s NaNoWriMo to start Book Two. (I want to find out what happens next!)

Anyway, if you or your kids enjoy fantasy fiction and are interested in reading something written by a teenage homeschooler — and if you have a Kindle or Kindle Reading App — please download the sample chapters of her book and check it out. She would love to get some reviews!

Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.

By Denise Gaskins Posted in Family

# PUFM 1.1 Counting

Photo by Iain Watson via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.

Many things in mathematics need to be understood relationally — that is, in relationship to other concepts. But some things just need to be memorized. How do you know which is which? A homeschooling friend pointed out that one thing children definitely need to memorize is the counting sequence from 1-100 and beyond. While there are some patterns that make counting easier, one does just have to memorize which “nonsense sounds” we have attached to each number.

Another sort-of counting that young students should master is subitizing — recognizing at a glance how many items are in a small group. Children do this instinctively, but we can help them develop the skill by playing subitizing games.

[Aside: In writing this blog post, I ran into some nostalgia. Back when we first did these PUFM lessons, my daughter Kitten was only a toddler. I wrote, "I've tried to do lots of counting with my youngest, who hasn't quite gotten beyond, '...eleven, twelve, firteen, firteen, nineteen, seven,...' The numbers tend to start appearing randomly after she gets past 10." Ah, memories.]

# More Than One Way to Solve It, Again

photo by Annie Pilon via flickr

We continue with our counting lessons — and once again, Kitten proves that she doesn’t think the same way I do. In fact, her solution is so elegant that I think she could have a future as a mathematician. After all, every aspiring novelist needs a day job, right?

If only I could get her to give up the idea that she hates math…

## Permutations with Complications

How many of the possible distinct arrangements of 1-6 have 1 to the left of 2?

# More Than One Way to Solve It

Photo by Eirik Newth via flickr.

In a lazy, I-don’t-want-to-do-school mood, Princess Kitten was ready to stop after three math problems. We had gotten two of them correct, but the last one was counting the ways to paint a cube in black and white, and we forgot to count the solid-color options.

For my perfectionist daughter, one mistake was excuse enough to quit. She leaned her head against me as we sat together on the couch and said, “We’re done. Done, done, done.” If she could, she would have started purring — one of the most manipulative noises known to humankind. I’m a soft touch. Who can work on math when there’s a kitten to cuddle?

by tanjila ahmed via flickr

Still, I managed to squeeze in one more puzzle. I picked up my whiteboard marker and started writing:

DONE
DOEN
DNOE
DENO
DNEO
ONED
ODNE

# The (Mathematical) Trouble with Pizza

Photo by George Parrilla via flickr.

Kitten complained that some math programs keep repeating the same kind of problems over and over, with bigger numbers: “They don’t get any harder, they just get longer. It’s boring!”

So we pulled out the Counting lessons in Competition Math for Middle School. [Highly recommended book!] Kitten doesn’t like to compete, but she enjoys learning new ideas, and Batterson’s book gives her plenty of those, well organized and clearly explained.

Today’s topic was the Fundamental Counting Principle. It was review, easy-peasy. The problems were too simple, until…

Pizzas at Mario’s come in three sizes, and you have your choice of 10 toppings to add to the pizza. You may order a pizza with any number of toppings (up to 10), including zero. How many choices of pizza are there at Mario’s?

[The book said 9 toppings, but I was skimming/paraphrasing aloud and misread.]

• Can you figure out the answer?

# Summer Slowdown

It happens this way every summer: I think that when school’s out, I’ll have time to catch up on things. But school is never out, because we’re homeschoolers — and something else always comes up to make us even more busy than normal. This year, an emergency forced dh to move his engineering office from town to home. It’s great to have him close at hand, but spring cleaning has turned into a total house reorganization to make room.

Niner's baby snapping turtle sitting on her wrist

And then Niner and Kitten adopted a couple of new pets. Here’s a picture of Niner’s new snapping turtle. The old one is getting so big he eats feeder fish by the dozen, but she plans to release him back into the creek as soon as the spring floods go down. Kitten rescued two baby birds (normally the dogs take care of wind-blown fledglings), so we have to find room for yet another cage in our menagerie.

In the meantime, this month’s Math Teachers at Play carnival is coming home to my blog, so I’d better get to work on that. If you would like to share a blog post about learning, teaching, or just playing around with math, I’d love to have you send it in. Just click here and fill out the handy automatic submission form.

Update, July 2011: Niner wrote a blog post on the turtles, with photos. Kitten had one of her babies die (sad!) but the other grew up enough to be released into the woods across the creek.

[Photo by Nestor Galina.]

Our power finally came back on this afternoon after a couple of cold, dark nights.

## Staying Warm

We heated the house with candles and stove-top burners (propane). We found that if you get enough candles lit in a room, it really can make a difference, and the stove was able to keep the kitchen in the upper-50’s, even above 60 degrees at times, which was pretty comfortable. We dressed in lots of layers and wore gloves, drank a plenty of coffee and hot chocolate, listened to oldies on the battery-powered radio, and went to bed early each night. (Hooray for sleeping bags!)

# Planning a New Math Club

[Photo by Waponi.]

A few years ago, I had several (potentially) future engineers in our homeschool math club, and we enjoyed the challenge of MathCounts and AMC puzzles — but the current crop of local homeschool students is another story.

Last year’s contest-based club meetings dwindled to one student. Even before the recent MathCounts rule changes, I knew I needed a new plan. The final straw was Kitten, whose moaning complaint that she “hates math” has begun to drive me crazy.

So, what’s a homeschool math teacher to do?

# A Little Bit of This, a Little Bit of That…

It’s high time I got back on track with my Alexandria Jones posts, so I’ve been working hard on a short introduction to probability, to go along with The Birthday Surprise. Or, more honestly, I’ve been procrastinating on a short intro … well, anyway, here’s a little of what I’ve been reading around the interwebs lately.

# Congratulations, Kitten!

[Photo by dougwoods.]

Today is my daughter Princess Kitten’s blogiversary. Check out her post:

And then take some time to browse her blog. I think you’ll enjoy her stories. She’s even written a few things about math:

[Update: I just noticed that this is the 500th post to be published on Let's Play Math! blog. Wow! I guess Kitten and I will both be celebrating today...]

Don’t miss any of “Let’s Play Math!”:  Subscribe in a reader, or get updates by Email.

# Rate Puzzle: How Fast Does She Read?

[Photo by Arwen Abendstern.]

If a girl and a half
can read a book and a half
in a day and a half,
then how many books can one girl read in the month of June?

Kitten reads voraciously, but she decided to skip our library’s summer reading program this year. The Border’s Double-Dog Dare Program was a lot less hassle and had a better prize: a free book! Of course, it didn’t take her all summer to finish 10 books.

# Hobbit Math: Elementary Problem Solving 5th Grade

[Photo by OliBac. Visit OliBac's photostream for more.]

The elementary grades 1-4 laid the foundations, the basics of arithmetic: addition, subtraction, multiplication, division, and fractions. In grade 5, students are expected to master most aspects of fraction math and begin working with the rest of the Math Monsters: decimals, ratios, and percents (all of which are specialized fractions).

Word problems grow ever more complex as well, and learning to explain (justify) multi-step solutions becomes a first step toward writing proofs.

This installment of my elementary problem solving series is based on the Singapore Primary Mathematics, Level 5A. For your reading pleasure, I have translated the problems into the world of J.R.R. Tolkien’s classic, The Hobbit.

[Note: No decimals or percents here. Those are in 5B, which will need an article of its own. But first I need to pick a book. I'm thinking maybe Naya Nuki...]

## Printable Worksheet

In case you’d like to try your hand at the problems before reading my solutions, I’ve put together a printable worksheet:

# Prime Numbers Are like Monkeys

[Photo by mape_s.]

I’m afraid that Math Club may have fallen victim to the economy, which is worse in our town than in the nation in general. Homeschooling families have tight budgets even in the best of times, and now they seem to be cutting back all non-essentials. I assumed that last semester’s students would return, but I should have asked for an RSVP.

Still, Kitten and I had a fun time together. We played four rounds of Tens Concentration, since I had spread out cards on the tables in the library meeting room before we realized that no one was coming. Had to pick up the cards one way or another, so we figured we might as well enjoy them! She won the first two rounds, which put her in a good mood for our lesson.

I had written “Prime numbers are like monkeys!” on the whiteboard, and Kitten asked me what that meant. That was all the encouragement I needed to launch into my planned lesson, despite the frustrating dearth of students. The idea is taken from Danica McKellar’s book Math Doesn’t Suck.

# Buddy Math

[Photo by OakleyOriginals.]

Kitten strongly dislikes math when forced to do it on her own, so I am trying to get back into the habit of doing “Buddy Math” with her. We take turns working the problems in her workbook: mine, hers, mine, hers, and so on down the page. We work each problem out loud, explaining how we got the answer and checking each other as we go.

In a way, it is like Charlotte Mason-style narration applied to math, since my daughter has to process her thoughts in order to explain how she worked the problem, which fixes the math concepts more deeply in her mind.

# Homeschool Kids Write

No, it’s not math, but it looks like a great way to kick-start Princess Kitten’s long-neglected blog. She sat down at the computer and browsed the links to other kids’ posts for over an hour last night, occasionally laughing out loud. Then she opened her Dashboard and started to type a response to the green assignment.

I’ll have to let her know there’s a new post up today. Check it out:

• Homeschool Kids Write

Maybe I can even get her to send something in to the next Homeschool Kids Blog Carnival. It’s worth a try…

## Update

Unfortunately, Homeschool Kids Write has disappeared from the web. The Wayback Machine link gives a taste of what the site was like, but It’s just not the same without the Mr. Linky connections to all the children’s writings.

Kitten did three of the writing assignments. And not only did she enter the Homeschool Kids Blog Carnival, she even hosted one edition!

My baby is growing up…

Don’t miss any of “Let’s Play Math!”:  Subscribe in a reader, or get updates by Email.

# More Backwards Math

[Photo by *clairity*.]

Have you ever noticed how very different little girls are from little boys, in the way they play and in the way they think about things? Princess Kitten has been playing around with Backwards Math again, and my first thought was, “No boy would ever have done this with numbers.”

# Welcome to Blogland, Niner!

Photo by Niner.

The daughter who supplies my header photos has started a blog to show off her pictures:

Niner’s SnapFair
[It's pronounced "NEE-ner."]

Update: She no longer posts to that blog, but has been writing and posting photos, recipes, and craft projects to her new blog — College & The Years After.

Her photography skills continue to improve, and her sense of humor comes through in the stories that accompany each photo. I’m sure she’d love to have you stop by and visit!

# Backwards Math

Photo by Complicated.

Princess Kitten is recovering from her cold and getting some energy back. She came to me and said wistfully, “I wish I could do backwards math.”

I looked up from my keyboard. “Backwards math? What do you mean?”

“Umm. It’s kinda hard to explain, but I can show you.”

# Happy Birthday, Princess Kitten!

Our youngest child turns 9 today. Time shoots by at rocket speed, doesn’t it? Every year, the older kids complain that their baby sister isn’t allowed to grow up — they still feel like being nine years old themselves!

I have mentioned before our family tradition of the “hidden present.” [See this post and that.] Every year, one birthday present is hidden somewhere in the house, with the clue placed in an envelope to be opened after all the other gifts are unwrapped.

# Pre-Algebra Picture Puzzles

Maria at Homeschool Math Blog has posted a fun set of worksheets:
Pan balance problems to teach algebraic reasoning.

Princess Kitten, at nearly 9yo, keeps telling me, “I hate math, but I like algebra.” So I printed all four pages for her to try. These get pretty complicated, and the 2-variable problems had her flummoxed for awhile. But after an explanation and bit of pouting (I think she hates math because she’s such a perfectionist that she can’t bear to get something wrong, even the first time), she came back and conquered the toughest ones.

Don’t miss any of “Let’s Play Math!”:  Subscribe in a reader, or get updates by Email.

# Welcome, Princess Kitten!

Not to be outdone by her older brother, Princess Kitten insisted on starting a blog of her own:

Kitten’s Purring

I have given them a section of my blogroll. If you are interested, they would both love to have you drop by and read their stories. Chickenfoot is writing in the “fractured fairytale” vein, at least for now, while Kitten’s tales tend toward animal adventures.

This teacher’s opinion: It certainly beats those dreaded “Pretend you’re a pencil” essays!

Don’t miss any of “Let’s Play Math!”:  Subscribe in a reader, or get updates by Email.

# Improper Fractions: A Mathematical Trauma

Feature photo (above) by Jimmie via flickr. 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:

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

# Number Bonds = Better Understanding

[Rescued from my old blog.]

A number bond is a mental picture of the relationship between a number and the parts that combine to make it. The concept of number bonds is very basic, an important foundation for understanding how numbers work. A whole thing is made up of parts. If you know the parts, you can put them together (add) to find the whole. If you know the whole and one of the parts, you take away the part you know (subtract) to find the other part.

Number bonds let children see the inverse relationship between addition and subtraction. Subtraction is not a totally different thing from addition; they are mirror images. To subtract means to figure out how much more you would have to add to get the whole thing.