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.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday*. The carnival will be posted next week at 1001 Math Problems blog.

**Click to tweet about the carnival:**

(No spam, I promise! You will have a chance to edit or cancel the tweet.)

Help! I can’t keep the carnival going on my own. Would you volunteer to host the MTaP math education blog carnival some month this year? Hosting the 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:

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

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I’ve been looking for quotes to put at the beginning of each chapter in my math games books. I found a delightful one by Mrs. LaTouche on the Mathematical Quotations Server, but when I looked up the original source, it was even better:

I am nearly driven wild with the Dorcas accounts, and by Mrs. Wakefield’s orders they are to be done now.

I do hate sums. There is no greater mistake than to call arithmetic an

exactscience. There are Permutations and Aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of Number which it requires a mind like mine to perceive.For instance, if you add a sum from the bottom up, and then again from the top down, the result is always different.

Again if you multiply a number by another number before you have had your tea, and then again after, the product will be different. It is also remarkable that the Post-tea product is more likely to agree with other people’s calculations than the Pre-tea result.

Try the experiment, and if you do not find it as I say, you are a mere sciolist*, a poor mechanical thinker, and not gifted as I am, with subtle perceptions.

Of course I find myself not appreciated as an accountant. Mrs. Wakefield made me give up the book to [my daughter] Rose and her governess (who are here), and was quite satisfied with the work of those inferior intellects.

— Maria Price La Touche

The Letters of A Noble Woman

London: George Allen & Sons, 1908

***sciolist:** (archaic) A person who pretends to be knowledgeable and well informed. From late Latin *sciolus *(diminutive of Latin *scius *‘knowing’, from *scire *‘know’) + *-ist.*

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*Math Teachers at Play* is a traveling collection of math tidbits — games, lesson ideas, and more — from around the Internet. It moves around from month to month, and the August edition is now posted at *Math = Love* blog. What a fun list of math posts to browse!

Welcome to the 77th edition of the Math Teachers at Play Blog Carnival! I’m super excited to be hosting this carnival because I’ve been reading it for years! Yes, I am that crazy person who started reading math teacher blogs as a high school junior. I think you are going to enjoy going through the submissions. I know I found several new-to-me blogs to add to my RSS reader! …

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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.

- Click here to submit your blog post.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday*. The carnival will be posted next week at Math = Love.

**Click to tweet about the carnival:**

(No spam, I promise! You will have a chance to edit or cancel the tweet.)

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:

- Last month’s Math Teachers at Play #76
- Carnival of Mathematics

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

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How in the world can ^{1}/_{5} be the same as ^{1}/_{10}? Or ^{1}/_{80} be the same as one whole thing? Such nonsense!

No, not nonsense. This is real-world common sense from a couple of boys faced with a problem just inside the edge of their ability — a problem that stretches them, but that they successfully solve, with a bit of gentle help on vocabulary.

Here’s the problem:

*How can you divide eight sausages evenly among five people?*

Think for a moment about how you (or your child) might solve this puzzle, and then watch the video below.

I saw five things worth remembering when you talk math with your kids:

- How patiently the man waited, giving the boys time to think. After more than a quarter century of teaching, I still have trouble with that.

- How the boys looked away, moved their fingers, grimaced, and mumbled — all signs of hard thought.

- How the boys alternated between speaking and thinking. While they were speaking, their thought couldn’t advance very far. Then the other boy, the one who had been quiet, would make the next connection — but as he tried to explain his thought, he would get to a point where he was stuck. And then the first boy, who had been thinking, could speak up and take the next step.

- How important the quiet time was for each boy, as they were struggling to understand what the other person had said and to consolidate that with their own ideas.

- How the following quote from W. W. Sawyer could have been written just for this video clip:

Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying ‘No, that’s wrong.’ Rather, he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole of the art of teaching.

I also noticed that the intuitive method of counting the boys invented at first was the same way Egyptian fractions worked. In Egyptian, the exact, correct answer would have been written as a mixed number:

**1 ^{1}/_{2} ^{1}/_{10}**

Cool!

And finally, I noticed how wonderfully many “ones” the boys used to make their fractions: one sausage, one half-sausage, one plate of sausages, and one “bit” of sausage. Each of these was used as the unit at least once during the discussion.

Which brings one more video to mind:

For more about the many meanings of one, see the questions and activities at this TED-Ed video page. For tips on talking math with your kids, please see Christopher Danielson’s blog. And for more on Egyptian fractions, read The Secret of Egyptian Fractions featuring the resourceful Alexandria Jones.

Share your ideas in the comment section below. How would YOU have divided the sausages? Did you ask your kids? What did they say? I wonder how many different ways can we think of to do it….

Many thanks to Tracy Johnston Zager (@TracyZager) who shared the sausage math video on Twitter.

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I missed out on the adventures at Twitter Math Camp, but I’m having a great time working through the blog posts about it. I prefer it this way — slow reading is more my speed. Chris at *A Sea of Math* posted a wonderful game based on one of the TMC workshops. Here is my variation.

**Math concepts:** comparing fractions, equivalent fractions, benchmark numbers, strategic thinking.

**Players:** two to four.

**Equipment:** two players need one deck of math cards, three or four players need a double deck.

Deal five cards to each player. Set the remainder of the deck face down in the middle of the table as a draw pile.

You will play six rounds:

- Closest to zero
- Closest to 1/4
- Closest to 1/3
- Closest to 1/2
- Closest to one
- Closest to two

In each round, players choose two cards from their hand to make a fraction that is as close as possible (but not equal) to the target number. Draw two cards to replenish your hand.

The player whose fraction is closest to the target collects all the cards played in that round. If there is a tie for closest fraction, the winners split the cards as evenly as they can, leaving any remaining cards on the table as a bonus for the winner of the next round.

After the last round, whoever has collected the most cards wins the game.

Don’t miss any of *“Let’s Play Math!”*: Subscribe in a reader, or get updates by Email.

- Princess in the Dungeon Game
- Multiplication Models Card Game
- Quiz: Those Frustrating Fractions
- Egyptian Math: Fractions
- Subtracting Mixed Numbers: A Cry for Help

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On your mark… Get set… Go play some math!

Welcome to the 76th edition of the ** Math Teachers At Play** math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

By tradition, we start the carnival with a puzzle in honor of our 76th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

In the land of Fantasia, where people communicate by crystal ball, Wizard Mathys has been placed in charge of keeping the crystal connections clean and clear. He decides to figure out how many different ways people might talk to each other, assuming there’s no such thing as a crystal conference call.

Mathys sketches a diagram of four Fantasian friends and their crystal balls. At the top, you can see all the possible connections, but no one is talking to anyone else because it’s naptime. Fantasians take their siesta very seriously. That’s one possible state of the 4-crystal system.

On the second line of the diagram, Joe (in the middle) wakes up from siesta and calls each of his friends in turn. Then the friends take turns calling each other, bringing the total number of possible connection-states up to seven.

Finally, Wizard Mathys imagines what would happen if one friend calls Joe at the same time as the other two are talking to each other. That’s the last line of the diagram: three more possible states. Therefore, the total number of conceivable communication configurations for a 4-crystal system is 10.

For some reason Mathys can’t figure out, mathematicians call the numbers that describe the connection pattern states in his crystal ball communication system *Telephone numbers*.

**Can you help Wizard Mathys figure out the Telephone numbers for different numbers of people?**

T(0) = ?

T(1) = ?

T(2) = ?

T(3) = ?

T(4) = 10 connection patterns (as above)

T(5) = ?

T(6) = ?

and so on.

**Hint: **Don’t forget to count the state of the system when no one is on the ~~phone~~ crystal ball.

- Printable version: Crystal Ball Connection Patterns.

*[Wizard photo by Sean McGrath. (CC BY 2.0)]*

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; I’ve drawn others from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, here’s a quick Table of Contents:

- Early Learning Activities
- Elementary Exploration and Middle School Mastery
- Adventures in Basic Algebra and Geometry
- Advanced Mathematical Endeavors
- Puzzling Recreations
- Teaching Tips

**Click to tweet: Share the carnival with your friends.**

(No spam, I promise! You will have a chance to edit or cancel the tweet.)

- Amy Tanner offers Four Super Simple Counting Games that help your child build number sense, learn to estimate, begin to think about addition and subtraction, and practice counting backward.

*[My favorite perk of hosting the MTaP carnival is discovering yummy new blogs. This one definitely belongs in my rss list.]*

- Casey Rutherford’s son notices, wonders, and draws a logical conclusion — and then modifies it after further investigation: Experience Driving Misconceptions.

- There may not be any numbers, but there’s a whole lot of math going on in Teacher Tom’s post, A Current Of Curiosity.

- Joshua Greene tells how a simple pattern led to deep and interesting questions — and it only took “5 minutes in between other play”: Pattern Blocks (mini follow-up).

- Casey Rutherford reminds us of something we all know, but too easily forget: We Underestimate What Kids Can Do.

- Sarah Dees adapted an activity from the Curious George PBS show in Composing Music with Math Activity for Kids. “Seriously, this was a lot of fun. The boys wrote many compositions, and couldn’t wait to perform them for Dad when he came home from work!”

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- Amy Mascott plays 4 sums in a row: a quick & easy math game to keep her son’s addition skills and strategic thinking sharp over the summer.

- Margo Gentile suggests practicing the math facts with Picnic Time Multiplication. If I were to modify it, I’d skip saying the equations and add the ABCs back in: “I’m going on a picnic, and I’m going to bring 3 apples, 6 buffalo, 9 candy canes, and…”

- Simon Gregg’s students make a hands-on proof of “a curious and wondrous fact” in A Square of Cubes in Year 4. See also the related post: Successive cubes summed.

- Problem solving can be as much about the journey as the destination. Mike Lawler’s lesson didn’t go quite the way he’d planned in A bit of a struggle with estimation.

- Stephen Cavadino’s class stumbles on what should have been an easy review problem, and he responds with “Aaargh Ruddy BIDMAS!“

- Bryan Anderson’s class creates a variety of graphs to compare different data sets in Human Histogram.

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- Fawn Nguyen’s students have fun investigating the relationship between a circle’s diameter and circumference in Friday Bubbles.

- A couple of year ago, Elizabeth Statmore put together a fantastic game for beginning algebra students to practice a too-often-neglected skill, turning Words into Math. This summer, with the help of Twitter friends, she added a Geometry version: DIY Geometry Vocabulary Game, courtesy of the MTBoS (a collaborative effort).

- Both of the above are based on Maria Anderson’s tic-tac-toe style Block games. More advanced algebra students will enjoy Exponent Block and Factor Pair Block.

- Sue VanHattum takes a break from book editing to explore Euclidean geometry in How I’m Playing With Math Today. “Geometry is my weakness in math, and I love trying to figure out how to do these constructions.”

- Don Steward posts a grand collection of geometry puzzles in angle proofs. Each image can be printed landscape-orientation on a regular sheet of paper or added to PowerPoint for sharing with students.

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- Anna Blinstein and Kate Nowak are collecting a set of deep questions that drive parts of high school mathematics. How would your students answer these Essential Questions for Geometry & Algebra 2? Or these Essential Questions for Algebra 2? What questions would you add to the lists?

- William Wu serves up a couple of important proofs suitable for high school students: Why is e irrational? and How to prove square root of 2 is irrational (Constructive Approach)

- John Golden discusses how help students understand complex numbers in Complex Instruction, with a little help from GeoGebra. “One of the morals of the capstone class was that if mathematicians labeled a theorem as Fundamental, it’s worth your focus and understanding…”

- Neil Irwin and Kevin Quealy give a warning to all statistics students: “Human beings, unfortunately, are bad at perceiving randomness.” Read How Not to Be Misled by the Jobs Report.

- Tina Cardone tweaks some Parametric Functions lessons to work on Desmos. “It was important to begin graphing by hand so students had an understanding of how parametrics work. Some students were concerned that the
*t*value wasn’t showing up on the graph and tried to include it in some rather creative ways…”

- Rebecka Peterson steals a favorite lesson and refuses to feel guilty because “this magic should be shared.” And so she does: Slope Field Activity.

- As I’ve put my energy into working on my math books, my blogging has suffered. So I’ve started dipping into the past and bringing up oldy-but-goody articles to reblog. I especially enjoyed The Calculus Tidbits Collection.

- And don’t miss the 112th Carnival of Mathematics!

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- Fran Wisniewski shares one of my all-time favorite puzzle games: Tangrams. Print and cut out a set of pieces, or play online.

- I love Sian Zelbo’s puzzle blogs, since being targeted at kids puts them right at my level. Here are a couple of my recent favorites: Subtraction Snakes and The Painted Tetrahedron.

- Shecky Riemann challenges us to try a Li’l Game From Martin Gardner. “Whoever does this gets all the money played, in cases of draws (no winner) you each take your money back. The question is, is there any strategy by which you could be assured a win?”

- Julie’s family folds up some beautiful 3-dimensional math in Origami Icosahedron. “When the faces of solid figures protrude to form more complex solids, the shapes become star-like and are known as stellations. The icosahedron we created is the small triambic icosahedron…”

- The Math Curmudgeon’s
*MathArguments180*is still going strong, bringing us some cool recreational puzzles to debate. What would your students do with 187: Spiral or 191: Walking the Labyrinth?

- One of the great puzzles of mathematics is how to think about infinity. Along this line, Yelena McManaman and her son read the book
*Really Big Numbers*in Infinity Is Farther Than You Think. And Vi Hart posts the latest in “a potential infinity of spinoff videos” in Transcendental Darts.

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- Christina Tondevold warns us that “too often we use the concrete manipulatives incorrectly” and encourages us to give students room to think problems through for themselves in Stop Using Base 10 Blocks To ‘Teach’ The Algorithms!

- Donna Boucher takes a look at one of my favorite elementary math curricula in What is Singapore Math? “Singapore Math is really a philosophy for mathematics instruction — it’s as much about
*how*to teach as it is*what*to teach.”

- Monica Utsey reviews another curriculum I love: Beast Academy Comic Book Math. Meanwhile, Claire discovers a UK curriculum I’ve never heard of (
*Galore Park*): Finally…a maths program which works for us!

- Lucinda Leo explains How my autodidactic 9 year old is learning maths without a curriculum and Why we love Edward Zaccaro more than Khan Academy.

- So, you’ve collected your students’ responses to a rich mathematical task. Now what? David Wees experiments with Categorizing Student Strategies.

- Cindy Smith examines The Power of Specific, Non-Graded Feedback.

- Stephen Cavadino asks some important questions about assessment: “What is the big picture? What are we testing for? Should we be doing it?”

- A friend asks, “I am doubtful that he will actually be able to solve this problem he’s puzzling through. What does a good teacher do in such a situation? You have a student who is really interested in this problem, but you know that it’s far more likely that he will hit a wall (or many walls) that he really doesn’t have the tools to work through.” Ben Blum-Smith offers wise advice in Hard Problems and Hints.

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I found the pretty pictures at Flickr.com Creative Commons. John Riordan wrote about Telephone numbers in *Introduction to Combinatorial Analysis*.

And that rounds up this edition of the Math Teachers at Play math education blog carnival. I hope you enjoyed the ride.

The next installment of our carnival will open sometime during the week of August 25-29 at Math = Love. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

You can explore all our past MTaP carnival posts on our blog carnival Pinterest page.

** We need more volunteers.** Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you want to take a turn hosting the Math Teachers at Play blog carnival, please speak up!

*[Photo by Bob Jagendorf.]*

Don’t miss any of *“Let’s Play Math!”*: Subscribe in a reader, or get updates by Email.

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**Update:** The crowdfunding campaign is now closed and the book is in the final stages. It should be headed to the printer soon. Check the Playing With Math homepage for publication and ordering information.

There are only a few days left to reserve your copy of **Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers**. I don’t have time to finish the review I hoped to write, so instead I’ll share some of my favorite quotes from the book:

What do mathematicians do? We play with math. What are little kids doing when they’re thinking about numbers, shapes, and patterns? They’re playing with math. You may not believe it yet, but you can have fun playing with math, too.

— Sue VanHattum, editor

We had a discussion at the end of the club on how we are all confused now, but pleasantly so, and how important it is to rejoice in confusion and to be comfortable with it. Adults often strive very hard to get rid of any and all possible traces of confusion for kids, making things dreadfully boring.

— Maria Droujkova, after a math circle exploration of infinity

All it talkes to do mathematics is opportunity, a frustrating problem, and a bit of stubbornness.

— Ellen Kaplan, math circle leader

Our own school experiences can make it hard for us to teach without being tempted to “help them master” a concept that they may or may not be ready to master. What we never learned in school was the concept of playing around with math, allowing ideas to “percolate,” so to speak, before mastery occurs, and that process may take time.

— Julie Brennan, homeschooler

The most profound learning often takes place silently and invisibly, in between activities and away from prying eyes. It is here that all those pieces of information, having been shaved from actual experience, are pulled inward to jostle against one another in various combinations and arrangements until gradually, or sometimes suddenly, a new understanding emerges.

— Holly Graff, unschooler

I do a mean T. Rex impression and the class was convulsed in giggles — the perfect way to enter a “hard” math lesson. I chucked the planned lesson for the day, and we went with the dinosaurs, and eventually various other creatures with different numbers of digits. I asked the class how the T. Rex would count. After all, it has only three fingers. I’ll admit to a lot of roaring and stomping as I, the T. Rex, became more and more frustrated trying to write a note to my mother in which I wanted to tell her that I had eaten those four velociraptors.

— Michelle Martin, elementary teacher

It is the process of sharing — of not only creative and insightful problem-solving approaches, but also memorable moments filled with camaraderie, generosity, and incomparable joy. That is why I love math.

— Luyi Zhang, math major

Remember that joy and passion lead to more learning than duty ever did.

— Sue VanHattum, editor

This book truly captures the joy and passion of learning (and teaching) mathematics. Whether you love math and want to share it with your kids, or whether you fear and loathe math and need help getting over that hurdle so you won’t pass your fear on, Playing With Math will encourage you to see math more deeply and play with it more freely.

- Why play with math? Because play is the best way to learn, from the Introduction to
*Playing with Math* - Becoming Invisible, by Bob Kaplan and friends

If I’m reading the website aright, the crowdfunding campaign for Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers ends in the early wee hours of Sunday morning. Be sure to place your order by Saturday, July 19th!

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

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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.

- Click here to submit your blog post.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday extended through the weekend*. The carnival will be posted next week at Let’s Play Math.

**Click to tweet about the carnival:**

(No spam, I promise! You will have a chance to edit or cancel the tweet.)

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!

We need more hosts! 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:

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

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It turns out that the people who do well in math are those who make connections and see math as a connected subject. The people who don’t do well are people who see math as a lot of isolated methods.

— Jo Boaler

Math Connections

If you or your children struggle with math, Boaler’s non-profit YouCubed.org may help you recover your joy in learning.

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

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The monthly math education blog carnival *Math Teachers at Play* features games, lessons, puzzles, activities, and teaching tips from classroom teachers, homeschoolers, and self-educated learners around the Internet world. Check out the 20 posts of mathematical fun in the June edition:

Math(s) Teachers At Play #75 via CavMaths

Hello, and welcome to the 75th issue of the Math(s) Teachers at Play Blog Carvinal! For those of you who are unaware, a “blog carnival” is a periodic post that travels from blog to blog and has a collection of posts on a certain topic.

…

This is the first time I’ve hosted a carnival and there were some excellent submissions. I enjoyed reading them all and have discovered some new blogs. I have also input some posts I’ve seen this month which I thought were excellent too…Click here to go read Math(s) Teachers At Play #75 via CavMaths.

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**Update:** The crowdfunding campaign is now closed and the book is in the final stages. It should be headed to the printer soon. Check the Playing With Math homepage for publication and ordering information.

There’s a problem: Most people don’t like math. Why is that? Perhaps it has something to do with the way math is taught in school. As a teacher to my own kids and mentor to homeschooling parents, I’ve been fighting math anxiety for decades.

This book is one part of the solution.

**Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers** features more than thirty authors who tell delightful stories of learning to appreciate math and of sharing their enthusiasm with their communities, families, or students. After every chapter is a puzzle, game, or activity to get you and your kids playing with math, too.

You can read a couple of excerpts at *PlayingWithMath.org*:

- Why play with math? Because play is the best way to learn, from the Introduction to
*Playing with Math* - Becoming Invisible, by Bob Kaplan and friends

Whether you love math and want to share it with your kids, or whether you fear and loathe math and need help getting over that hurdle so you won’t pass your fear on, Playing With Math will encourage you to see math more deeply and play with it more freely.

I’ve been waiting for this book for years, and I’m thrilled to see it finally come together. As I read the advance copy (review coming soon!), I am amazed at how many different ways there are to think about math. Each writer has a new perspective and unique insight, and my quotes journal is filling up with inspiration.

Today is the first day of our crowd-funding campaign. For a contribution of $25, we’ll send you a book as soon as it’s printed.

You can contribute anything from $1 to $5000 (with rewards at each contribution level) to help us pay for our illustrators, editors, page layout person, and printing. This is our way of asking for community support for this book as part of the production process. We hope to build lots of energy around the ideas in the book through this campaign.

Besides contributing, here’s another way you can help: Think of five friends who would enjoy this book.

- Do you have friends who get frustrated helping their kids with math homework?
- Or who teach young kids but don’t feel comfortable with math themselves?
- Do you have friends who enjoy math?
- Or who want ideas to share with the kids in their lives?
- Do you know someone who might want to start a math circle?
Would you send them a quick message, to let them know we’re here?

I’m hoping for the power of exponential growth with this. Our outrageous goal is to change the way people all over this country, and maybe even the world, think about math. If you each send this to five friends who might enjoy the book, and each of them sends it to five friends, and each of them … Well, pretty soon we cover the world, right?

In fact, if we kept it going through eleven steps, that would make 5 to the 11th power, or over 40 million people. Does Sue dream big? Yep.

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

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*[Photo by Olga Berrios via flickr.]*

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.

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*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday, June 20*. The carnival will be posted next week at CavMaths blog.

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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:

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This week I have a series of quotes about calculus from my first two years of blogging. The posts were so short that I won’t bother to link you back to them, but math humor keeps well over the years, and W. W. Sawyer is (as always) insightful.

**I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:**

Eldest daughter had her first calculus lesson last night: finding the limit as delta-*t* approached zero. The teacher found the speed of a car at a given point by using the distance function, calculating the average speed over shorter and shorter time intervals. Dd summarized the lesson for me:

“If you want to divide by zero, you have to sneak up on it from behind.”

This kicked off my week with a laugh:

Today I said to the calculus students, “I know, you’re looking at this series and you don’t see what I’m warning you about. You look and it and you think, ‘I trust this series. I would take candy from this series. I would get in a car with this series.’ But I’m going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it.”

—Rudbeckia Hirta

Learning Curves Blog: The Harmonic Series

quoting Alexandre Borovik

Rudbeckia Hirta has a great idea for a new TV blockbuster:

And here’s a quick quote from W. W. Sawyer’s Mathematician’s Delight:

If you cannot see what the exact speed is, begin to ask questions. Silly ones are the best to begin with. Is the speed a million miles an hour? Or one inch a century? Somewhere between these limits. Good. We now know something about the speed. Begin to bring the limits in, and see how close together they can be brought.

Study your own methods of thought. How do you know that the speed is less than a million miles an hour? What method, in fact, are you unconsciously using to estimate speed? Can this method be applied to get closer estimates?

You know what speed is. You would not believe a man who claimed to walk at 5 miles an hour, but took 3 hours to walk 6 miles. You have only to apply the same common sense to stones rolling down hillsides, and the calculus is at your command.

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I hear so many people say they hated geometry because of the proofs, but I’ve always loved a challenging puzzle. I found the following puzzle at a blog carnival during my first year of blogging. Don’t worry about the arbitrary two-column format you learned in high school — just think about what is true and how you know it must be so.

**I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:**

One of the great unsolved problems of antiquity was to trisect any angle using only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass. Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator or something.

One “cheat” that works is to fold your paper. I will show you how it works, and your job is to show why …

*[Click here to go read Puzzle: Patty Paper Trisection.]*

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