Fun with the Impossible Penrose Triangle

I found this delightful animation today:


The ball is traveling around a shape that can’t exist in our real world: the Penrose triangle. This illusion is the basis for some cool art, like Escher’s Waterfall. And I’m using it in my Math You Can Play books as a design on the back of my playing cards:


Want to Play Around with the Penrose Triangle?

Here’s a few links so you can try it for yourself:

Penrose Lego by Erik Johansson (CC BY 2.0)

Penrose Lego by Erik Johansson (CC BY 2.0)

Book Update


I’ve sent the first two Math You Can Play books to a copy editor (she edits the text part), so my focus this month is on finishing the illustrations and downloadable game boards. And designing the book covers — I think I’ll call this latest iteration done.

If everything stays on schedule, both Counting & Number Bonds and Addition & Subtraction should be available by mid- to late-spring. Fingers crossed…

Tabletop Academy PressGet monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

Join My Mailing List for Math Tips and Book Updates

Tabletop Academy Press

Tabletop Academy Press:
Learning is a lifelong adventure.

Are you looking for playful ways to help your children learn math? Now you can get math tips and activity ideas by email, as well as find out when I put out a new book or revise an old one.

Check out my shiny new emailing list:

I hope to send out a “Math Snack” (no-preparation math activity idea) at least once a month. In the meantime, your sign-up bonuses include a 4-page article on solving word problems and a pre-publication peek at my new Math You Can Play book series of games for preschool to prealgebra.

Tabletop Academy Press has been my publishing name since way back when my books were printed at the local copy shop and stapled together by hand for sharing with local homeschoolers. Seems like ancient days!

Free This Weekend


Our Christmas gift to you: my daughter’s fantasy adventure Banished will be FREE for Kindle on this weekend only, December 11-15.

I don’t know whether the other Amazons (UK, CA, AU, IN, etc.) will also run the sale, but I hope so.

As I type, the paperback edition is also on sale at a 10% discount, though we have no control over how long Amazon will be offering that price. Banished is part of the Kindle Matchbook program, so if you buy a copy of the paperback, you can get the ebook for free — even after our weekend sale runs out.

Read an excerpt: the first four chapters of Banished

Don’t have a Kindle? You can get a Kindle app that will let you read Teresa’s book on almost any device.

Watch for Upcoming Books

The second book in The Riddled Stone series is scheduled for publication in Spring 2015, and so are the first two volumes of my Math You Can Play series. If you want a head’s-up when these books arrive, be sure to join my Tabletop Academy Press Updates email list:

100% secure. We never share your information!

Let’s Play Math on Scribd


Do you subscribe to the Scribd subscription reading service? My Let’s Play Math ebook is now available to Scribd subscribers:

Reviews of Let’s Play Math

Combined with all the linked resources, this book is going to transform how I teach my kids maths. No more dabbling in “real maths” but then running back to the workbooks when anxiety strikes — with this approach I can teach my kids to think like mathematicians without worrying about leaving gaps.

My favourite section of the book is “One Week of Real Mathematics”, which contains examples of what one week’s worth of math playtime might look like. I love having this starting point to show me what a balanced “maths diet” might look like.

I knew the well-travelled road (maths curricula) wasn’t for us, but I lacked confidence in my ability to guide my children through uncharted territory. Let’s Play Math is the map and the guidebook I’ve been looking for. With it in my hand I can’t wait to take my children by the hand and head off to explore the wonderful world of maths.

— Lucinda Leo
Navigating By Joy

A beautiful book that explains the “why” and “how” of teaching math from a Constructivist perspective. It is well researched, well annotated, and includes loads of activities that you can try with kids K-12 at home. While reading the book, I found myself remembering a lot of things I had forgotten from my teacher-training … I have to say that there were so many parts of this book that I highlighted that I really gave my Kindle a workout!

There is a whole section that I’m going to come back to this summer, to keep my kids busy. But was especially useful to me at this moment, were the talking points for helping kids solve problems on their own. Yes, I at one point learned all of talking points, but I really needed the refresher.

My son’s school does Continental Mathematics League, and those problems are really hard. I’m going to print up all of the talking points and post them in our kitchen so that my husband and I will have a list of questions to prompt our son’s thinking.

— Jennifer Bardsley
Teaching My Baby To Read

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

Monday Morning Surprise

2013-09-16 number1 in teaching math, closeup

This is a good way to start the week. Amazon rankings are like a roller-coaster ride, so this won’t last for long — but I’ll enjoy it while I can. :)

If you’re curious about my book, here is the introduction and first chapter, free to download:

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

lets play math sample pages

Sample Chapter from Let’s Play Math Book

As I’ve been working on the layout for the paperback edition of Let’s Play Math: How Homeschooling Families Can Learn Math Together, and Enjoy It!, I thought, “Why not post an excerpt?” So here is the introduction and first chapter, free to download:

This excerpt isn’t exactly how the paperback will look, because it’s based on the current ebook edition. For the paperback, I’ll be adding plenty of new illustrations — not quite a picture on every page, but close. (Yes, that’s one reason it’s taking soooo long to finish!)

For Example …

Here is one of the new illustrations, along with its caption:

Fractals are self-similar, which means that subsections of the object look like smaller versions of the whole thing. Your children may enjoy making a Sierpinski triangle with tortilla chips.


Want To Buy the Book?

Let’s Play Math should be available wherever you usually buy ebooks. Here are links to the major U.S. sites:

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


Back to School Sale

Princess Kitten, way back in the beginning.

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:

Please feel free to share the coupon code with your friends.

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:

Continue reading

photo by Sphinx The Geek via flickr

Homeschooling High School Math

photo by ddluong via flickr

photo by ddluong via flickr

Feature photo (above) by Sphinx The Geek via flickr.

Most homeschoolers feel at least a small tinge of panic as their students approach high school. “What have we gotten ourselves into?” we wonder. “Can we really do this?” Here are a few tips to make the transition easier.

Before you move forward, it may help to take a look back. How has homeschooling worked for you and your children so far?

If your students hate math, they probably never got a good taste of the “Aha!” factor, that Eureka! thrill of solving a challenging puzzle. The early teen years may be your last chance to convince them that math can be fun, so consider putting aside your textbooks for a few months to:

On the other hand, if you have delayed formal arithmetic, using your children’s elementary years to explore a wide variety of mathematical adventures, now is a good time to take stock of what these experiences have taught your students.

  • How much of what society considers “the basics” have your children picked up along the way?
  • Are there any gaps in their understanding of arithmetic, any concepts you want to add to their mental tool box?

Continue reading

My Ebook: Kindle & Smashwords Updates Available


If you bought an early edition of my ebook Let’s Play Math, you can now update your copy to the latest version.

This update includes:

How To Update

If you bought at Smashwords, the latest update is always available for download at their site.

If you are an customer, you can get the updated version of this book by going to Manage Your Kindle. Find the book in your Kindle Library, click on the “Update Available” link next to the book’s title, and then follow the update prompts. After you do this, all of your Kindle devices that have the ebook currently downloaded will be updated automatically the next time they connect to wireless. If you tucked the book away in a folder, the update will replace it there, rather than cluttering up your home screen.

Also Available

Through the Smashwords distribution program, my ebook is finally spreading to other online booksellers:

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

homeschool success feature image

How to Recognize a Successful Homeschool Math Program

photo by danielrmccarthy

photo by Dan McCarthy (cc-by)

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.”

photo by Jason Bolonski (cc-by)

photo by Jason Bolonski (cc-by)

Continue reading

Let’s Play Math Now in All Digital Formats


For all of you who read ebooks in formats other than Amazon’s Kindle, my book is now available on Smashwords in almost every format imaginable:

Since Smashwords distributes to various online booksellers, this means it may show up at Barnes & Noble and the iBookstore sometime soon. I have no control over who decides to carry the book, but if you happen to see a copy for sale anywhere, I’d love to hear about it!

Advantages of using Smashwords: In addition to all the different format choices, Smashwords also gives you access to free updates whenever I change the file. (I have found a few typos I need to correct one of these days…) Also, the free sample is slightly longer than the one at Amazon.

Disadvantages: You have to load the file onto your ebook reader manually (try the free program Calibre). Also, some of the file formats are wonky, because Smashwords insists on using its automatic “meatgrinder” program — for instance, the html format didn’t handle exponents correctly, the mobi file had a couple of bad links in the table of contents, and the epub included every single answer-to-sample-problem in its ncx toc. If you’re reading on a Kindle, the hand-formatted Amazon file is much nicer.

Continue reading

Book Updates


My ebook Let’s Play Math has a new cover. Do you like it?

After wrestling with the files for a couple of months, I finally figured out how to add the toc.ncx navigation (the ebook magic that lets you skip ahead to the next chapter). While I was messing around, I added a few more references, expanded a couple of sections, and fixed all the typos that we’ve found so far.

I sent Amazon an email asking them to give everyone who already bought a copy the option to get the latest version. Unfortunately that’s not automatic, but if the powers that be decide that these changes were “major,” you should get an email telling you how to update.

Continue reading

Let’s Play Math Book Update

I love math, but had forgotten why I developed a love for math in the first place. This book made me realize how experiences in my childhood lit a spark in me … Denise Gaskins shows us how we can ignite this fire in our own children.

I believe her suggestions are invaluable for homeschoolers, but essential for the many parents whose children are learning to dislike math in school.

— Carrie
Review at, December 1, 2012

If you’ve wavered on whether to pick up my math book, be warned: This is the last month for the introductory sale price. In January, the price will go up to $5.99 — which is still much less than what the original edition sells for, used.

Of course, if you’re a member of Amazon Prime, you can borrow the book (or my daughter’s novel) for free!

You don’t need a Kindle to read an ebook. You can access it on your computer, tablet, or smart phone using Amazon’s Kindle Cloud Reader or a Kindle Reading App.

Continue reading

Poll: Math Ebooks?

Two of my daughters are attempting NaNoWriMo this year. So I’m thinking I might keep them company and give the EBookWriMo Challenge a try. What topic should I write about?

Don’t like any of my ideas? Enter your suggestion in the poll, or leave a comment below!

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

Introducing the “Let’s Play Math!” Book, Beta Version

This blog originally grew out of my Homeschool Math Manuals series published in the 1990s, and when I typed a post, I often added new tips, activities, or examples. Now the stories are coming full circle: I’ve entered the enriched blog-post versions back into the book manuscript, fixed all the typos I could find, deleted obsolete references, and added a list of my favorite “living” math books and internet links.

But no writer can accurately judge her own work. A professional editor is helpful, but he or she can’t see the book with a real homeschooler’s eye. Most writers look for beta-readers among their friends or acquaintances. As we live in a rural area, my supply of potential victims helpers is limited. So I decided to try an ebook experiment: Use to find readers willing to pay the price of a Caramel Macchiato for a pre-publication beta version of my book.

All of the books in the Math Ebooks Beta Series are designed to supplement your current math program — to help you teach math with ANY curriculum. If you would like to help me improve the books, please grab a notepad and jot down your thoughts as you read:

  • Let’s Play Math:
    How Homeschooling Families Can Learn Math Together, and Enjoy It!

    Discover new ways to explore math as a family adventure, playing with ideas. True mathematical thinking involves the same creative reasoning that children use to solve puzzles. Introduce your children to the “Aha!” factor, the thrill of solving a challenging puzzle, and build thinking skills with toys, games, and library books. Find out how to choose math manipulatives, or make your own, and learn how to tackle story problems with confidence. Let’s Play Math will give you a wealth of motivating, hands-on ideas for teaching home school math.

Edited to Add a Clarification

If you are interested in my book but don’t have time to take notes and send me comments, that’s OK. Feel free to take advantage of the beta price anyway — there’s absolutely no obligation.

I hope you and your children enjoy the adventure of learning math together!

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

Mathematicians Love to Play

[Photo by Windell Oskay via flickr. Part 3 of my Homeschooling with Math Anxiety Series.]

Mathematicians love to play with ideas. They experiment with puzzles. They tinker with the connections between shapes and numbers, patterns and logic, growth and change. To a mathematician, the fun of the game is in experimenting, in trying new things and discovering what will happen. Many modern strategy games were invented primarily for the fun puzzle of analyzing who would win.

Continue reading

Mathematicians Ask Questions

[Photo by walknboston via flickr. Part 2 of my Homeschooling with Math Anxiety Series.]

Wise mathematicians are never satisfied with merely finding the answer to a problem. If they decide to put effort into solving a math puzzle, then they are determined to milk every drop of knowledge they can get from that problem. When mathematicians find an answer, they always go back and think about the problem again.

  • Is there another way to look at it?
  • Can we make our solution simpler or more elegant?
  • Does this problem relate to any other mathematical idea?
  • Can we expand our solution and find a general principle?

Continue reading

Maths homework

How Can I Teach Math If I Don’t Understand It?

[Feature photo (above) by wonderferret, photo (right) by University of the Fraser Valley, both via flickr (CC BY 2.0). This post is the first of three in my Homeschooling with Math Anxiety Series.]

Our childhood struggles with schoolwork gave most of us a warped view of mathematics. We learned to manipulate numbers and symbols according to what seemed like arbitrary rules. We may have understood a bit here and a bit there, but we never saw how the framework fit together. We stumbled from one class to the next, packing more and more information into our strained memory, until the whole structure threatened to collapse. Finally we crashed in a blaze of confusion, some of us in high school algebra, others in college calculus.

Continue reading

Book Update, and Self-Publishing Info

photo by Darwin Bell via flickr

As you may know, I’ve been working hard on my Let’s Play Math! books, and I’m still hoping to get at least couple of them out this summer. (Though if I keep thinking of more sections to add, I may never get them done!) I’m also finishing up the editing on my daughter’s novel and plan to release it soon.

One of the most useful resources I’ve found for self-publishing information is Joel Friedlander’s blog, The Book Designer. The last time I published my books, a dozen years ago, I made nearly every one of the mistakes he mentions in Amateur Hour Books and 5 Book Design Mistakes to Avoid.

Continue reading


Tell Me a (Math) Story

feature photo above by Keoni Cabral via flickr (CC BY 2.0)

My favorite playful math lessons rely on adult/child conversation — a proven method for increasing a child’s reasoning skills. What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town?

As soon as your little ones can count past five, start giving them simple, oral story problems to solve: “If you have a cookie and I give you two more cookies, how many cookies will you have then?”

The fastest way to a child’s mind is through the taste buds. Children can easily visualize their favorite foods, so we use mainly edible stories at first. Then we expand our range, adding stories about other familiar things: toys, pets, trains.

Continue reading

Update: My Math Books

photo by goXunuReviews via Flickr

Are you a homeschooler? Are you happy with your current curriculum, or would you like to break out of the textbook mold and explore math through “living” books and activities? Whether you hope to replace your math program or just to supplement it, I can show you ways to turn math into a learning adventure for the whole family. Your children will build a stronger foundation of understanding when you teach math as a game, playing with ideas.

Nearly a year ago, I wrote:

This blog originally grew out of my books, and now it’s coming full circle: New, expanded editions of my long-out-of-print books are ripening on the vine, growing out of the blog. To bring them to harvest, I’m going to need your help.

It has taken much longer than I had hoped to whip the manuscripts into form. My new goal is to publish ebook editions, since I will be able to sell them for about half what the original books cost twelve years ago. I’m hoping that I can finish at least a couple of the ebooks by mid-summer.

Continue reading

Used Book Price Shock

Someone mentioned one of my old books on the Living Math forum, which made me curious how the used copies were doing at These are simple little books, 100 loose pages comb-bound together. I have seen ridiculous prices before, but this one takes the cake.

Thankfully, there are a few used book dealers with more sense, or at least with more reasonable computer-automated pricing routines.

I am still at work revising (and greatly expanding) the old books so I can publish new editions. If you haven’t voted yet in my “What Do You Want from a Math Book?” survey, I’d love to hear your opinion!

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

Quotations XXVI: On Teaching Math

photo by chrisrobinson1945 via flickr

As I continue to polish the manuscript for my math games book, I’ve been looking for short quotations to put at the beginning of each chapter. I’ve gathered a lot of math quotations over the years, from my own reading and from quote-collection websites. But there’s a problem with using most of these in a book, since to do it right I would have to dig up the original source of each quote and then write a letter to the publisher for permission to use it. And pay a fee that, depending on the publisher’s sense of self-importance, can run into the hundreds of dollars. Bother!

So I went digging around my rss reader to see what sort of inspiration I could find. Bloggers love to be quoted, right? And most of them are happy to give permission via email, which makes my job ever so much easier.

Here are some of the gems I’m considering. I’d love to hear your favorite quotes from math bloggers, too — or favorite passages from your own blog. Please comment!

It’s amazing that this vision of math as “getting to the right answer on your first try” even exists. I have to make, unmake, remake so many mistakes to get where I’m going. I think all mathematicians work that way.

Somehow, a big part of the experience of math is trouble. Frustration is the status quo. But when you get something—the thrill!

Dan Finkel
Good Mistakes, Constant Mistakes

Continue reading

Working on My Let’s Play Math! Books

Workplace stress caused by an unsuitable work ...

Image via Wikipedia

This blog originally grew out of my books, and now it’s coming full circle: New, expanded editions of my long-out-of-print books are ripening on the vine, growing out of the blog. To bring them to harvest, I’m going to need your help.

The Books

I’m working on the games books first because I think they will be the most helpful supplements to any math program.

  • Let’s Play Math! Number Games for All Ages
    This book will include games like Tens Concentration and Hit Me, as well as tips for teaching negative numbers, the times table, and more. Never before published, because it was planned as the fifth book in my earlier how-to-teach-homeschool-math series, but my self-publishing experiment ended after book four.
  • Others to be announced, if I ever get the first two done…

Continue reading