Math Concepts: division as equal sharing, naming fractions, adding fractions, infinitesimals, iteration, limits Prerequisite: able to identify fractions as part of a whole

This is how I tell the story:

We have a cake to share, just the two of us. It’s not TOO big a cake, ‘cuz we don’t want to get sick. A 8 × 8 or 16 × 16 square on the graph paper should be just right. Can you cut the cake so we each get a fair share? Color in your part.

How big is your piece compared to the whole, original cake?

But you know, I’m on a diet, and I just don’t think I can eat my whole piece. Half the cake is too much for me. Is it okay if I share my piece with you? How can we divide it evenly, so we each get a fair share? How big is your piece?

How much of the whole, original cake do you have now? How can you tell?

I keep thinking of my diet, and I really don’t want all my piece of cake. It looks good, but it’s still just a bit too big for me. Will you take half of it? How big is that piece?

Now how much of the whole, original cake do you have? How could we figure it out?
[Teaching tip: Don’t make kids do the calculation on paper. In the early stages, they can visualize and count up the fourths or maybe the eighths. As the pieces get smaller, the easiest way to find the sum is what Cohen does in the video below—identify how much of the cake is left out.]

Even for being on a diet, I still don’t feel very hungry…

“… 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 …”

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.

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.

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.

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!

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.

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:

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:

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. :)

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:

and:

and (though it took a bit more thought):

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.