A Penny for Your Math

You know you’re a math teacher when you see a penny in the parking lot, and your first thought is, “Cool! A free math manipulative.”


My homeschool co-op math students love doing math with pennies. They’re rather heavy to carry to class, but worth it for the student buy-in.

This month, I’m finishing up the nearly 150 new illustrations for the upcoming paperback edition of my Let’s Play Math book. I’m no artist, and it’s been a long slog. But a couple of the graphics involved pennies‌—‌so when I saw that penny on the ground, it made me think of my book.

And thinking of my book made me think it would be fun to share a sneak peek at coming attractions…

The Penny Square: An Example of Real Mathematics

Real mathematics is intriguing and full of wonder, an exploration of patterns and mysterious connections. It rewards us with the joy of the “Aha!” feeling. Workbook math, on the other hand, is several pages of long division by hand followed by a rousing chorus of the fraction song: “Ours is not to reason why, just invert and multiply.”

Real math is the surprising fact that the odd numbers add up to perfect squares (1, 1 + 3, 1 + 3 + 5, etc.) and the satisfaction of seeing why it must be so.

Did your algebra teacher ever explain to you that a square number is literally a number that can be arranged to make a square? Try it for yourself:

  • Gather a bunch of pennies‌—‌or any small items that will not roll away when you set them out in rows‌—‌and place one of them in front of you on the table. Imagine drawing a frame around it: one penny makes a (very small) square. One row, with one item in each row.
  • Now, put out three more pennies. How will you add them to the first one in order to form a new, bigger square? Arrange them in a small L-shape around the original penny to make two rows with two pennies in each row.
  • Set out five additional pennies. Without moving the current four pennies, how can you place these five to form the next square? Three rows of three.
  • Then how many will you have to add to make four rows of four?
Twenty-five is a square number, because we can arrange twenty-five items to make a square: five rows with five items in each row.

Each new set of pennies must add an extra row and column to the current square, plus a corner penny where the new row and column meet. The row and column match exactly, making an even number, and then the extra penny at the corner makes it odd.

Can you see that the “next odd number” pattern will continue as long as there are pennies to add, and that it could keep going forever in your imagination?

The point of the penny square is not to memorize the square numbers or to get any particular “right answer,” but to see numbers in a new way‌—‌to understand that numbers are related to each other and that we can show such relationships with diagrams or physical models. The more relationships like this our children explore, the more they see numbers as familiar friends.

The Penny Birthday Challenge: Exponential Growth


A large jar of assorted coins makes a wonderful math toy. Children love to play with, count, and sort coins.

Add a dollar bill to the jar, so you can play the Dollar Game: Take turns throwing a pair of dice, gathering that many pennies and trading up to bigger coins. Five pennies trade for a nickel, two nickels for a dime, etc. Whoever is the first to claim the dollar wins the game.

Or take the Penny Birthday Challenge to learn about exponential growth: Print out a calendar for your child’s birthday month. Put one penny on the first day of the month, two pennies on the second day, four pennies on the third day, etc. If you continued doubling the pennies each day until you reach your child’s birthday, how much money would you need?

Warning: Beware the Penny Birthday Challenge! Those pennies will add up to dollars much faster than most people expect. Do not promise to give the money to your child unless the birthday comes near the beginning of the month.

A Penny Holiday Challenge

The first time I did pennies on a calendar with my homeschool co-op class was during December, so we called it the Penny Christmas Challenge:

  • How many pennies would you need to cover all the days up to the 25th?

I told the kids that if their grandparents asked what gift they wanted for Christmas, they could say, “Not much. Just a few pennies…”

LPM-ebook-300The Penny Square, Dollar Game, and Penny Birthday Challenge are just three of the myriad math tips and activity ideas in the paperback edition of Let’s Play Math: How Families Can Learn Math Together and Enjoy It. Coming in early 2016 to your favorite online bookstore…

Free-Learning-Guide-Booklets2Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.

Miscellaneous Tidbits

A Nice Surprise

When I got online this morning, I discovered that Let’s Play Math had hit #1 in the UK bestseller list for Parent Participation in Education—‌and I missed it!

But I did get a screen shot of my book sitting pretty at #2:


Playful Math Snacks for October: Mental Math Games

Draft version of the new paperback edition cover. Coming in early 2016...
Draft version of the new paperback edition cover. Watch for it in 2016…

My October “Let’s Play Math” newsletter went out on Wednesday afternoon to everyone who signed up for Tabletop Academy Press math updates. This month’s issue focused on playing math games with your children, and it also included the latest updates on the Let’s Play Math paperback edition (coming not quite as soon as we’d hoped).

If you didn’t see it, check your Updates or Promotions tab (in Gmail) or your Spam folder. And to make sure you get all the future newsletter, add “Denise at Tabletop Academy Press” [Tabletop Academy Press @ gmail.com] to your contacts or address book.

And if you missed this month’s edition, no worries—‌there will be more playful math snacks coming in November. Click the link below to sign up today, and we’ll send you our free math and writing booklets, too!

Remember: Newsletter subscribers are always the first to hear about new books, revisions, and sales or other promotions.

How to Update Your Math Game Ebooks


The Math You Can Play books grew from more than twenty years of playing math with children—‌at my house, at the library, in the park, and in group workshops. The 42 kid-tested games in these books are simple to learn, quick to play, and require minimal preparation.

I love these books because they help even the busiest parents enjoy playing math with their children.

Now that the publication dust has settled and the typos and formatting glitches have been sorted out, I’ve updated all the Math You Can Play ebook files to match the paperback editions.

Changes include:

Do I Need an Update?

None of these changes have a major effect on the readability or value of the books. If you like your book as is, you aren’t missing anything vital.

Still, if you want the most up-to-date information, then check the title page of your ebook. Right under copyright date, the new edition says, “Ebook Version 1.3.”

If your book has a lower version number (or no version number at all), you may want to upgrade to the new edition.

Continue reading How to Update Your Math Game Ebooks

Learning to Think is Hard Work


“Learning to think a problem through can be hard work‌—‌and that is exactly what makes it fun.”

—Denise Gaskins

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from my book Let’s Play Math: How Families Can Learn Math Together‌‌—‌And Enjoy It. Background photo courtesy of Chris_Parfitt (CC BY 2.0) via Flickr.

Free-Learning-Guide-Booklets2Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.

Murphy Strikes My Paperbacks :(

The colors are supposed to go all the way off the edge.
The colors are supposed to go all the way off the edge. They worked just fine in the pre-publication proof…
Murphy’s Law struck today, and the paperback books that looked so good in the proof copies turned out to have a cover glitch, at least in the ones I ordered from Amazon. I’m working with CreateSpace to make sure it gets straightened out—but that means the books may show up as “unavailable” for awhile.

As with any print-on-demand glitch, if you got a badly printed book you can ask Customer Support to replace it.

It could be worse. The interior of the book is fine, at least in my copy. And of course, the ebook versions are totally unaffected.

If you are trying to use the discount code for newsletter subscribers, remember that it’s good through the end of the month. I may even extend the expiration date, if this cover problem persists, but I sure hope to have it fixed in a couple of days.

Free-Learning-Guide-Booklets2Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.

30% Discount for Email Newsletter Subscribers


Counting-GamesAddition-Games600x800[Feature photo (above) by Glen Wright via Flickr (CC BY 2.0).]

Wouldn’t it be wonderful if math was something your children WANTED to do?

With the Math You Can Play series, your kids can practice their math skills by playing games with basic items you already have around the house, such as playing cards and dice.

Paperback editions of the first two Math You Can Play books will be out any day now. If you’re subscribed to my Tabletop Academy Press Updates email newsletter, I’ll be sending you a 30% discount code by Thursday, or as soon as both books pass through the last few publishing hoops…

Free-Learning-Guide-Booklets2Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.