If you missed this month’s edition, no worries—here are some great puzzles from the Let’s Play Math blog archive:

- Logic: The Centauri Challenge
- Raymond Smullyan Excerpts at Dover Publications
- Sample The Moscow Puzzles
- Logic Puzzle: Imbalance Problems
- Puzzle: Logic Test
- Lewis Carroll’s Logic Challenges

There will be more playful math snacks coming in September. Click the link below to sign up now, and we’ll send you our free math and writing booklets, too!

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

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Counting all the fractional variations, my massive blog post 30+ Things to Do with a Hundred Chart now offers nearly forty ideas for playing around with numbers from preschool to prealgebra.

Here is the newest entry, a variation on #10, the “Race to 100” game:

**(11.5)** Play “Odd-Even-Prime Race.″ Roll two dice. If your token is starting on an odd number, move that many spaces forward. From an even number (except 2), move backward — but never lower than the first square. If you are starting on a prime number (including 2), you may choose to either add or multiply the dice and move that many spaces forward. The first person to reach or pass 100 wins the game.

[Hat tip: Ali Adams in a comment on another post.]

And here’s a question for your students:

- If you’re sitting on a prime number, wouldn’t you always want to multiply the dice to move farther up the board? Doesn’t multiplying always make the number bigger?

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

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Welcome to the 89th edition of Math Teachers at Play (MTaP) Blog Carnival! MTaP is a monthly blog carnival with a collection of tips, games, and activities for teachers of students of all ages … Click here to read the whole post at Mrs. E Teaches Math.

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

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The world’s largest and most popular online education competition is returning in October 2015. For more details visit http://worldeducationgames.com.

We did this one year, but my daughter has never liked any math with time pressure, and these games were all about racing to get as many answers as you could in a short amount of time. Fun for kids who thrive on that sort of thing.

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

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It’s carnival time again. Activities, games, lessons, hands-on fun — if you’ve written a blog post about math, we’d love to have you join our *Math Teachers at Play* (MTaP) math education blog carnival.

Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

**Don’t procrastinate:** *The deadline for entries is this Friday, August 21*. The carnival will be posted next week at Mrs. E Teaches Math.

Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog. If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

- Browse past editions of the
*Math Teachers at Play*blog carnival - Carnival of Mathematics
- Carnaval de Matemáticas

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“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.

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One of the most persistent math myths in popular culture is the idea that *mathematics is primarily about getting right answers*.

The truth is, the answer doesn’t matter that much in math. What really matters is *how you explain that answer*. An answer is “right” if the explanation makes sense.

And if you don’t give an explanation, then you really aren’t doing mathematics at all.

Here is a short sequence of numbers. Can you figure out the rule and fill in the next three blanks?

2, 3, 5, 7, ___, ___, ___, …

Remember, what’s important is not which numbers you pick, but rather *how you explain your answer*.

Perhaps the sequence is the prime numbers?

2, 3, 5, 7, 11, 13, 17, …

The prime numbers make a wonderful sequence, though it isn’t the one I was thinking of.

Perhaps the sequence is the odd numbers?

2, 3, 5, 7, 9, 11, 13, …

But how do you explain that even number 2 at the beginning of the row?

This is the answer I thought of. As far as I know, no one else has described this exact sequence, so I get to name it. Letting kids name their math is a great motivator for creativity—everyone likes to name something after themselves.

Let me introduce you to the Gaskins Counting-By Sequence. The first number tells you what interval you are counting by, and the second number tells you where to start counting. From there on, it’s automatic.

The natural numbers 1, 2, 3, 4… form a basic Gaskins Counting-By Sequence. Other examples would include any list of multiples that starts with the *n*×1 term.

I liked my counting-by answer. Still, I wondered if I could come up with at least one more possibility, so I kept thinking. And then I found:

2, 3, 5, 7, 10, 13, 16, …

Again, I couldn’t find any reference online to this exact sequence. The OEIS had eleven almost-matches, but each list veered off after a few more numbers.

Hey, that means I got two bits of original mathematics from a single puzzle. Cool!

I named this Denise’s Differences Sequence. You count the differences between the numbers, and each difference is repeated according to its value: +1 once, +2 twice, +3 three times, etc. You can start with any two numbers, and then the difference between them determines the rest of your list.

Incidentally, the sequence of differences in my list (1, 2, 2, 3, 3, 3…) is called the Self-Counting Sequence.

What do you think? Can you come up with yet another rule to explain the numbers in this puzzle?

Or invent a new sequence. Give it a name. I’d love to hear how you explain it!

Please share your answers in the comment section below.

Feature photo (top) by Blondinrikard Fröberg and math partners photo (above) by woodleywonderworks via Flickr (CC BY 2.0).

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So, here is issue 88 of the Math(s) Teachers at Play blog carnival. This acts as a round up of some cool blog posts that have been published since issue 87 over at cavmaths. As usual people have submitted entries, which I will supplement with some posts that I have really enjoyed reading in the last few weeks.

Click here to read the blog carnival post at mathematicsandcoding.

*[Feature photo (top) by Pratham Books, 88 cards photo by Bailey Weaver, both via Flickr (CC BY 2.0).]*

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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:

And this one’s a little trickier:

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?

- This week’s topic
- The summer photo challenge schedule
- Enjoy archived math photos from around the world

**How to Play:** Take a walk around your neighborhood to see what sort of math you can find. Post a photo to Twitter or Instagram, with hashtags to mark it as a Summer Math Challenge photo. Describe what you’re seeing. Re-tweet and share others’ photos if you like. Encourage your friends to play!

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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.

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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…

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If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math, now is the time to send in your favorite blog post for next week’s *Math Teachers at Play* (MTaP) math education blog carnival.

**Don’t procrastinate:** *The deadline for entries is this Friday, July 24*. The carnival will be posted next week at mathematicsandcoding.

If you haven’t written anything about math lately, here are some ideas to get your creative juices flowing…

**Elementary Concepts:**As Liping Ma showed, there is more to understanding and teaching elementary mathematics than we often realize. Do you have a game, activity, or anecdote about teaching math to young students? Please share!**Arithmetic/Pre-Algebra:**This section is for arithmetic lessons and number theory puzzles at the middle-school-and-beyond level. We would love to hear your favorite math club games, numerical investigations, or contest-preparation tips.**Beginning Algebra and Geometry:**Can you explain why we never divide by zero, how to bisect an angle, or what is wrong with distributing the square in the expression ? Struggling students need your help! Share your wisdom about basic algebra and geometry topics here.**Advanced Math:**Like most adults, I have forgotten enough math to fill several textbooks. I’m eager to learn again, but math books can be so-o-o tedious. Can you make upper-level math topics come alive, so they will stick in my (or a student’s) mind?**Mathematical Recreations:**What kind of math do you do, just for the fun of it?**About Teaching Math:**Other teachers’ blogs are an important factor in my continuing education. The more I read about the theory and practice of teaching math, the more I realize how much I have yet to learn. So please, fellow teachers, don’t be shy — share your insights!

Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog. If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

- Browse past editions of the
*Math Teachers at Play*blog carnival - Carnival of Mathematics
- Carnaval de Matemáticas

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Inspired by my recent Infinite Cake post, this month’s issue focuses on math proofs without words. What fun!

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

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

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For help learning the Times Table facts, check out my multiplication blog post series:

Encourage your family to play with math every day:

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To create your own Happy Mathematics Day sign, see yesterday’s post.

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