Do you have a favorite blog post about math activities, games, lessons, or hands-on fun? The *Math Teachers at Play* (MTaP) math education blog carnival would love to feature your article!

We welcome math topics from preschool through the first year of calculus. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Click here to submit your blog post

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

**Don’t procrastinate:** *The deadline for entries is this Friday, February 17th.* The carnival will be posted next week at Mrs. E Teaches Math blog.

Hosting the blog carnival is fun because you get to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival often 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

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.

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Walliman says, “To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes…”

- Can you find three mistakes in the map?

Check your answers in the description on Walliman’s YouTube page.

If you enjoy this video, you can purchase the poster (or T-shirt, coffee mug, tote bag, etc.) at Red Bubble.

Map of Mathematics poster by Dominic Walliman via Flickr (CC BY-NC-ND 2.0).

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.

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People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.

Apply logic to that statement.

The conclusion simply isn’t valid.

My mathematical understanding is stuck in the early-to-mid 17th century.

After reading several intriguing quotes about the Riemann Hypothesis, I was overcome by curiosity. I looked it up. The Riemann Hypothesis is a string of nonsense syllables surrounding one magic phrase: *non-trivial zeros*. Those words create surreal images in my brain.

I cannot reliably remember *pi *past three digits. Four if you count the decimal point.

In my world, groups are friends who hang out together. People who are good at math talk about groups, and I will sometimes almost believe that I am close to understanding at least part of what they mean. Then it all slips away again.

To me, combinatorics sounds like something done by a less-than-respectable woman in studded-leather underwear and spiked heels.

The story I want to tell involves combinatorics, but only the G-rated kind.

I have forgotten most of the mathematics I ever learned. Some of it I never understood, so it passed away painlessly, without regrets. Other math I did enjoy at one time, but it perished from extended lack of use. Most of calculus is that way. I mourn its loss.

Even in the math that I normally teach — and therefore that I *should *be good at — I occasionally stumble into chasms of appalling ignorance.

My story begins with one of these.

If, in reading my blog, you discover more evidence of mathematical ineptitude, please deal gently with me. I know I am not good at math. I am just a dabbler, but I’m eager to learn.

You may be wondering, if I am not good at math, then how dare I teach it, or blog about it, or offer advice to others?

I love mathematics. I can’t stay away from it. Like Isaac Newton’s boy at the beach, I want to grab every ocean-splashed pebble I can reach. My reach does not extend very far, and my stones are not as beautiful as his, but they are my treasures nonetheless. I understand them.

And there is one thing I am relatively good at. When I understand something, I can see how to explain it to others. Usually several ways, in multiple representations. For me, this is the definition of understanding: to be able to see connections and illustrations, elaborations and parables.

This is what makes me a teacher.

Which brings me (at last!) to my story.

One of the parents from my MathCounts class brought in a combinatorics problem, and it stumped me. I was forced to invoke the *Teacher’s Emergency Response*: “I don’t know. Let me do some research, and I will get back to you.”

Here is the problem, for those who are curious (from the 2006-2007 MathCounts Handbook, Workout 9):

Four people sit around a circular table, and each person will roll a standard six-sided die. What is the probability that no two people sitting next to each other will roll the same number after they each roll the die once? Express your answer as a common fraction.

At home, I worked through the problem and got an answer that I recognized as patently ridiculous. I worked it another way and got the same answer. I left the problem on my desk and went to bed.

I am not Maria Agnesi. No one solved the problem while I was asleep.

When I tried again the next morning, my wrong answer came back like a summer fly determined to sit on my forehead and rest its wings.

Online, I checked the MathCounts website. They host a forum for coaches, which may contain a discussion of this problem. But I was not an official coach, and the forum is closed to the general public. I did belong to another [no longer active] forum, however, where I often gave math advice to struggling homeschool parents. On that forum, someone who is better at math than I am was running a diagnostic workshop. You bring the problem, and he would teach you how to solve it.

Well, I had a problem. Was I brave enough to share it? These people thought I was good at math. This was going to be embarrassing.

I humbled myself and submitted the problem. The “professor” suggested an approach I hadn’t tried. I misinterpreted his suggestion and set off on a wild goose chase, only to find my familiar answer waiting at the end of the trail. The professor asked specific, pointed questions. I saw that his questions went straight to the heart of my problem. I couldn’t answer them. I explained my reasoning step by step, showing the most logical way to derive my wrong answer.

There it was — my ignorance on display, naked and quivering, ready for dissection.

The professor had pity on me, pointed out the step where I had gone wrong, and gave me the correct step. I could see that his method worked, but it sat like a fig leaf over my still-shivering ignorance.

Why would his step work when mine would not?

How could I know what to do the next time a combinatorics problem came up?

I was too tired to think. A nasty germ had dropped into my life and made itself at home. I thanked the professor for his help and went back to bed.

Sometime during the night, as I tossed around unable to sleep, I saw it all. I understood both the *how* and the *why* of the professor’s solution. I knew the prerequisites, the things a student would have to master before even attempting the problem. I saw how to explain the key insight that broke through confusion. I sketched all the diagrams and calculations on my mental chalkboard. I *could* teach this problem.

Victory tasted sweet.

As soon as I felt well enough, I asked the professor to find me another, similar problem. I wanted to make sure I could generalize my insight and apply it in a new context. But I had no doubt of my success.

I had found a new beach pebble for my collection, and I would not let it get away.

This is what learning math feels like.

Next weekend, we will probably hear plenty of talk about “the Agony and the Ecstasy” of the Big Game. I say, football is nothing compared to mathematics.

This post is my too-late entry for Week Four of the #MTBoS #MtbosBlogsplosion blogging challenge. It’s an expanded reblog of an article that originally appeared in 2007.

CREDITS: Feature photo (top) by One Laptop Per Child. Spiral Fractal by Kent Schimke. Child on Beach photo by Dennis Wong. Dice photo by Ella’s Dad. Embarrassed Lion photo by Charles Barilleaux. Stones on Beach photo by Moyan Brenn. All via Flickr (CC BY 2.0). “Pieces of Math” poster from Loopspace (CC-BY-NC-ND).

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.

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“I used to think my job was to teach students to see what I see. I no longer believe this. My job is to teach students to see; and to recognize that no matter what the problem is, we don’t all see things the same way. But when we examine our different ways of seeing, and look for the relationships involved, everyone sees more clearly; everyone understands more deeply.”

[Feature photo (above) by jenn.davis via Flickr (CC BY 2.0).]

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This month’s post features measurement games, algebra activities, paper folding, math podcasts, the secret to avoiding commitment, a variety of number puzzles, and much more.

Click Here to Go Read the Carnival Blog!

Do you write an education or family blog? Classroom teacher, math coach, homeschooler, parent, college professor, unschooler — anyone interested in helping kids play around with math? Please consider volunteering to host the MTaP blog carnival for one month.

We still need volunteer hosts for most of 2017.

You choose the month that fits your schedule and decide how much effort you want to put in. Writing the carnival can take a couple of hours for a simple post — or you can spend several days searching out and polishing playful math gems to share.

If you want more information, read the MTaP Math Education Blog Carnival home page. Then let me know which month you want.

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Video from the Global Math Project.

And here are some additional answers.

Ask your kids the question: “What Is Math?”

I’d love to hear what they say!

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The monthly *Math Teachers at Play* (MTaP) math education blog carnival is almost here. If you’ve written a blog post about math, we’d love to have you join us! Each of us can help others learn, so in a sense we are all teachers.

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

Click here to submit your blog post

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

**Don’t procrastinate:** *The deadline for entries is this Friday, January 20th.* The carnival will be posted next week at Travels in a Mathematical World blog.

Help! I can’t keep the carnival going on my own. 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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What teacher hasn’t heard a student complain, “When am I ever going to have to use this?” Didn’t most of us ask it ourselves, once upon a time?

And unless we choose a math-intensive career like engineering, the truth is that after we leave school, most of us will never again use most of the math we learned.

But if math beyond arithmetic isn’t all that useful, then what’s the point?

If you or your student is singing the “Higher Math Blues,” here are some quotations that may cheer you up — or at least give you the strength of vision to keep on slogging.

I don’t want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that — by some mysterious agency — capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.

— Ian Stewart

The Magical Maze

That vast book which stands forever open before our eyes, the universe, cannot be read until we have learnt the language in which it is written. It is written in mathematical language, and the letters are triangles, circles, and other geometrical figures, without which means it is humanly impossible to comprehend a single word.

— Galileo Galilei

quoted by Clifford Pickover, A Passion for Mathematics

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.

— George Washington

quoted by William Dunham, The Mathematical Universe

I told myself, “Lincoln, you can never make a lawyer if you do not understand what demonstrate means.” So I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what “demonstrate” means, and went back to my law studies.

— Abraham Lincoln

quoted by William Dunham, The Mathematical Universe

In most sciences, one generation tears down what another has built, and what one has established another undoes. In mathematics alone, each generation adds a new story to the old structure.

— Herman Henkel

quoted by Noah benShea, Great Quotes to Inspire Great Teachers

Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals — the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.

— Martin Gardner

quoted by G. Simmons, Calculus Gems

I will not go so far as to say that constructing a history of thought without profound study of mathematical ideas is like omitting Hamlet from the play named after him. But it is certainly analogous to cutting out the part of Ophelia. For Ophelia is quite essential to the play, she is very charming. . . and a little mad.

— Alfred North Whitehead

quoted in The Viking Book of Aphorisms

The mathematician does not study pure mathematics because it is useful, he studies it because he delights in it, and he delights in it because it is beautiful.

— Henri Poincaré

quoted by Theoni Pappas, More Joy of Mathematics

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful. The ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.

— Godfrey H. Hardy

A Mathematician’s Apology

Mathematics is a world created by the mind of men, and mathematicians are people who devote their lives to what seems to me a wonderful kind of play!

At age eleven, I began Euclid, with my brother as tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world.

— Bertrand Russell

The Autobiography of Bertrand Russell

I love mathematics … principally because it is beautiful, because man has breathed his spirit of play into it, and because it has given him his greatest game — the encompassing of the infinite.

— Rózsa Péter

quoted by Rosemary Schmalz, Out of the Mouths of Mathematicians

Did you enjoy these? You can find plenty more on my Math & Education Quotations page.

**I would LOVE to hear YOUR favorite mathematics, education, or inspirational quote. Please share in the Comments section below!**

Never Ending Math Problem photo (above) by Danny via Flickr (CC BY 2.0). This post is part of the #MTBoS #MtbosBlogsplosion blogging challenge.

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I like to use games as a warm-up with my co-op math circle. Some homeschoolers make every Friday a game day, and some turn gaming into a family lifestyle.

If you’d like to add more play to your family’s day, check out Cait’s 2017 Gameschooling Challenge.

“Playing games with your kids offers a host of educational benefits, plus you build relationships and make memories. I am constantly amazed by the amount of learning that happens when I sit down to play games with my children.”

—Caitlin Fitzpatrick Curley

Gameschool Challenge

- How to Make Math Cards
- Game: Tens Concentration
- Math Club Nim
- Tell Me a (Math) Story
- Math Game: What Number Am I?
- Math Game: Fan Tan (Sevens)
- Horseshoes: A Place Value Game

“Games put children in exactly the right frame of mind for learning difficult things. Children relax when they play — and they concentrate. They don’t mind repeating certain facts or procedures over and over, if repetition is part of the game.”

- Number Bond Games
- Active Math Game: Rock
- Maze Game: Land or Water?
- Math Game: Chopsticks
- Addition Games with Cuisenaire Rods
- Free Multiplication Bingo Game

“Coming back from winter break can be hard. Everyone is sleepy, unfocused, and daydreaming of the holiday gifts that await them at home after school. And that’s just the teachers!”

—Andrew Gael

Beat the Back to School Blues…Play a Math Game

- Game: Times Tac Toe
- Contig Game: Master Your Math Facts
- 30+ Things to Do with a Hundred Chart
- Game: Hundred Chart Nim
- Euclid’s Game on a Hundred Chart
- The Game that Is Worth 1,000 Worksheets
- Math Game: Thirty-One
- Multiplication Models Card Game
- Review Game: Once Through the Deck
- Princess in the Dungeon Game

“If you play these games and your child learns only that hard mental effort can be fun, you will have taught something invaluable.”

- Fraction Game: My Closest Neighbor
- Game: Target Number (or 24)
- 30+ Things to Do with a Hundred Chart
- Hit Me! (A Math Game)
- Alcumus Online Problem-Solving Game
- Math Games with Factors, Multiples, and Prime Numbers
- Math Game: Logarithm War
- The Function Machine Game

“Mathematics is mental play, the essence of creative problem solving. This is the truth we need to impart to our children, more important than fractions or decimals or even the times tables. Math is a game, playing with ideas.”

—Denise Gaskins

Let’s Play Math: How Families Can Learn Math Together—and Enjoy It

They don’t have to be math! Please share in the comment section below!

This post is part of the #MTBoS #MtbosBlogsplosion blogging challenge.

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The first way to make your math blog grow is to write posts. Here’s an #MTBoS blog challenge that seems doable: Only one post a week, so maybe even I can keep up.

With the start of a new year, there is no better time to start a new blog! For those of you who have blogs, it is also the perfect time to get inspired to write again! Please join us to participate in this years blogging initiative…

Once you’ve got your post blogged, please share it with us!

The Math Teachers at Play (MTaP) blog carnival is a monthly collection of tips, tidbits, games, and activities for students and teachers of preschool through pre-college mathematics. We welcome entries from parents, students, teachers, homeschoolers, and just plain folks…

[Spiral fractal photo (above) by Kent Schimke via Flickr (CC BY 2.0).]

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If you know of any other resources, please share in the comments below. And as I find new goodies, I’ll add them to the list here:

- Hidden Figures Family Discussion Guide
- NASA Lesson Toolkits
- Lesson Plan: “When Computers Wore Skirts”
- Girls Build LA Lessons & Resource Materials
- Max’s Hidden Figures Lesson Plan
- Norma’s Resource Folder
- Norma’s Collection of Movie Quotes
- Space Math Problem Books from NASA (downloadable PDFs)
- Black STEM Like Me: Inspiring stories and interviews from the National Society of Black Engineers

- The True Story of “Hidden Figures,” the Forgotten Women Who Helped Win the Space Race (Smithsonian Magazine)
- Hidden Figures: Margot Lee Shetterly’s book about NASA’s black women mathematicians and engineers is timely and eye-opening (Scientific American)
- Official Movie Home Page
- Trailers and Cast Interviews
- Making of ‘Hidden Figures’: Re-creating the ’60s to Tell an Untold Story of Space, Sexism and Civil Rights

Before computers were machines, computers were people who computed things. This complicated task often fell to women because it was considered basically clerical. That’s right: computing triple integrals all day long qualified as clerical.

— Samantha Schumacher

Hidden Figures Movie Review

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Two of the most popular New Year’s Resolutions are to spend more time with family and friends, and to get more exercise. The 2017 Mathematics Game is a prime opportunity to do both at once.

So grab a partner, slip into your workout clothes, and pump up those mental muscles!

For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find. This year may prove to be a challenge.

**Use the digits in the year 2017 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.**

- You must use all four digits. You may not use any other numbers.
- Solutions that keep the year digits in 2-0-1-7 order are preferred, but not required.
- You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
- You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
- You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.

- You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
- You MAY use a double factorial,
*n*!! = the product of all integers from 1 to*n*that have the same parity (odd or even) as*n*. I’m including these because Math Forum allows them, but I personally try to avoid the beasts. I feel much more creative when I can wrangle a solution without invoking them.

As usual, we will need every trick in the book to create variety in our numbers. Experiment with decimals, two-digit numbers, and factorials. Remember that dividing (or using a negative exponent) creates the reciprocal of a fraction, which can flip the denominator up where it might be more helpful.

**Use the comments section below to share the numbers you find.**

But please don’t spoil the game by telling us how you made them! You may give relatively cryptic hints, especially for the more difficult numbers, but be careful. Many teachers use this puzzle as a classroom or extra-credit assignment, and there will always be students looking for people to do their homework for them.

**Do not post your solutions. I will delete them.**

There is no authoritative answer key for the year game, so we will rely on our collective wisdom to decide when we’re done. We’ve had some lively discussions in past years. I’m looking forward to this year’s fun!

As players report their game results below, I will keep a running tally of confirmed results (numbers reported found by two or more players). My expat daughter is coming home for a visit this month, however, and we’ll be traveling to see extended family. So this tally will almost certainly lag behind the results posted in the comments.

Percent confirmed: 100%

Reported but not confirmed: 0%

Numbers we are still missing: 0%

Wow!

Students in 1st-12th grade may wish to submit their answers to the Math Forum, which will begin publishing student solutions after February 1, 2017. Remember, Math Forum allows double factorials but will NOT accept answers with repeating decimals.

Finally, here are a few rules that players have found confusing in past years.

**These things ARE allowed:**

- You must use each of the digits 2, 0, 1, 7 exactly once in each expression.
- 0! = 1. [See Dr. Math’s Why does 0 factorial equal 1?]
- Unary negatives count. That is, you may use a “−” sign to create a negative number.
- You may use (
*n*!)!, a nested factorial, which is a factorial of a factorial. Nested square roots are also allowed. - The double factorial
*n*!! = the product of all integers from 1 to*n*that are equal to*n*mod*2*. If*n*is even, that would be all the even numbers, and if*n*is odd, then use all the odd numbers.

**These things are NOT allowed:**

- You may not write a computer program to do the puzzle for you — or at least, if you do, PLEASE don’t ruin our fun by telling us all the answers!
- You may not use any exponent unless you create it from the digits 2, 0, 1, 7. You may not use a square function, but you may use “^2”. You may not use a cube function, but you may use “^(2+1)”. You may not use a reciprocal function, but you may use “^(−1)”.
- “0!” is not a digit, so it cannot be used to create a base-10 numeral. You cannot use it with a decimal point, for instance, or put it in the tens digit of a number.
- The decimal point is not an operation that can be applied to other mathematical expressions: “.(2+1)” does not make sense.
- You may not use the integer, floor, or ceiling functions. You have to “hit” each number from 1 to 100 exactly, without rounding off or truncating decimals.

- Mathematics Game Worksheet

For keeping track of which numbers you’ve solved.

- Mathematics Game Manipulatives

This may help visual or hands-on thinkers.

- Mathematics Game Student Submissions

For elementary through high school students who wish to share their solutions.

For more tips, check out this comment from the 2008 game.

Heiner Marxen has compiled hints and results for past years (and for the related Four 4’s puzzle). Dave Rusin describes a related card game, Krypto, which is much like my Target Number game. And Alexander Bogomolny offers a great collection of similar puzzles on his Make An Identity page.

*2017 Adventures photo by Kitty Terwolbeck and Origami Star by uschi mitzkat via Flickr (CC BY 2.0). New Year’s Resolutions from Wikipedia.*

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John 1:1-5; 8:12 recited in English, Cantonese, Japanese, Spanish, Croatian, Turkish, and French.

In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through him, and without him was not any thing made that was made. In him was life, and the life was the light of men. The light shines in the darkness, and the darkness has not overcome it.

… Again Jesus spoke to them, saying, “I am the light of the world. Whoever follows me will not walk in darkness, but will have the light of life.”

Scripture quotations are from the ESV® Bible (The Holy Bible, English Standard Version®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.

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The carnival features prime numbers, self-referential logic, calculus puns, word problems, Pythagorean triples, arithmetic games, geometric coloring designs, and more.

Click here to go read the carnival blog!

Past carnivals are still full of mathy treasure. Check them out:

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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:

**(34****)** The Number Puzzle Game: Rachel created this fun cross between the hundred-chart jigsaw puzzle (#7) and Gomoku (#23). You can download the free 120-board version here or buy the complete set at Teachers Pay Teachers.

*[Photo by geishaboy500 (CC BY 2.0).]*

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