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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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!

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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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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.

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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.

[Note: Sometimes the automated Google form refuses to load in my browser. If you have trouble, leave a link to your entry in the comments below.] - Browse all the past editions of the
*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.

**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 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:

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

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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.

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

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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.]*

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

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Do you subscribe to the Scribd subscription reading service? My *Let’s Play Math* ebook is now available to Scribd subscribers:

- Let’s Play Math ebook on Scribd
- Download a PDF Excerpt (Intro & 1st chapter)
- Or find the book at these retailers: Amazon.com (and Amazon UK, and in the other Amazons worldwide); iTunes bookstore; Barnes & Noble; Kobo;or Smashwords

**Reviews of Let’s Play Math**

Combined with all the linked resources, this book is going to transform how I teach my kids maths. No more dabbling in “real maths” but then running back to the workbooks when anxiety strikes — with this approach I can teach my kids to think like mathematicians without worrying about leaving gaps.

My favourite section of the book is “One Week of Real Mathematics”, which contains examples of what one week’s worth of math playtime might look like. I love having this starting point to show me what a balanced “maths diet” might look like.

I knew the well-travelled road (maths curricula) wasn’t for us, but I lacked confidence in my ability to guide my children through uncharted territory. Let’s Play Math is the map and the guidebook I’ve been looking for. With it in my hand I can’t wait to take my children by the hand and head off to explore the wonderful world of maths.

— Lucinda Leo

Navigating By Joy

A beautiful book that explains the “why” and “how” of teaching math from a Constructivist perspective. It is well researched, well annotated, and includes loads of activities that you can try with kids K-12 at home. While reading the book, I found myself remembering a lot of things I had forgotten from my teacher-training … I have to say that there were so many parts of this book that I highlighted that I really gave my Kindle a workout!

There is a whole section that I’m going to come back to this summer, to keep my kids busy. But was especially useful to me at this moment, were the talking points for helping kids solve problems on their own. Yes, I at one point learned all of talking points, but I really needed the refresher.

My son’s school does Continental Mathematics League, and those problems are really hard. I’m going to print up all of the talking points and post them in our kitchen so that my husband and I will have a list of questions to prompt our son’s thinking.

— Jennifer Bardsley

Teaching My Baby To Read

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Over the years, some of my favorite blog posts have been the *Word Problems from Literature*, where I make up a story problem set in the world of one of our family’s favorite books and then show how to solve it with bar model diagrams. The following was my first bar diagram post, and I spent an inordinate amount of time trying to decide whether “one fourth was” or “one fourth were.” I’m still not sure I chose right.

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

Cimorene spent an afternoon cleaning and organizing the dragon’s treasure. One fourth of the items she sorted was jewelry. 60% of the remainder were potions, and the rest were magic swords. If there were 48 magic swords, how many pieces of treasure did she sort in all?

[Problem set in the world of Patricia Wrede's Enchanted Forest Chronicles. Modified from a story problem in Singapore Primary Math 6B. Think about how you would solve it before reading further.]

How can we teach our students to solve complex, multi-step story problems? Depending on how one counts, the above problem would take four or five steps to solve, and it is relatively easy for a Singapore math word problem. One might approach it with algebra, writing an equation like:

… or something of that sort. But this problem is for students who have not learned algebra yet. Instead, Singapore math teaches students to draw pictures (calledbar modelsormath modelsorbar diagrams) that make the solution appear almost like magic. It is a trick well worth learning, no matter what math program you use …

*[Click here to go read Solving Complex Story Problems.]*

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The new *Math Teachers at Play* math education blog carnival is up for your browsing pleasure. Each month, we feature activities, lessons, and games about math topics from preschool through high school. Check it out!

Here’s a peek at a few of the entries:

Origami

Learn how to make Origami Stars, Tessellation Stars, and Chaotic Stars at Math Munch. I think once your students or children see this, you will find Transforming Ninja Stars littering your house and classroom!

Pi

Here’s a fun activity to explore other ways to get the number Pi on the calculator from William Wu at Singapore Maths Tuition.

Math Games

Math Hombre shares a coordinate grid game that also calculates area of rectangles. And all you need is some grid paper and dice.…And much more!

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.

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

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My free time lately has gone to local events and to book editing. I hope to put up a series of blog posts sometime soon, based on the Homeschool Math FAQs chapter I’m adding to the paperback version of *Let’s Play Math*. [And of course, I'll update the ebook whenever I finally publish the paperback, so those of you who already bought a copy should be able to get the new version without paying extra.]

But in the meantime, as I was browsing my blog archives for an interesting “Throw-Back Thursday” post, I stumbled across this old geometry puzzle from Dave Marain over at MathNotations blog:

Jake shows Jack a piece of wood he cut out in the machine shop: a circular arc bounded by a chord. Jake claimed that the arc was not a semicircle. In fact, he claimed it was shorter than a semicircle, i.e., segment AB was not a diameter and arc ACB was less than 180 degrees.

Jack knew this was impossible and argued: “Don’t you see, Jake, that O must be the center of the circle and that OA, OB and OC are radii.”

Jake wasn’t buying this, since he had measured everything precisely. He argued that just because they could be radii didn’t prove they had to be.

Which boy do you agree with?

**Pick one side of the debate, and try to find at least three different ways to prove your point.**

If you have a student in geometry or higher math, print out the original post (but not the comments — it’s no fun when someone gives you the answer!) and see what he or she can do with it.

Dave offers many other puzzles to challenge your math students. While you are at his blog, do take some time to browse past articles.

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

- Puzzle: Patty Paper Trisection
- More Than One Way to Solve It
- More Than One Way to Solve It, Again
- Puzzle: Patty Paper Trisection
- Homeschooling High School Math

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The *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 Triumphant Learning 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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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 15 posts of mathematical fun in April’s edition:

Here’s a peek at a few of the entries:

Check out the following awesome blogs!

Math Strategies

There is such an emphasis on learning math facts that our children do not spend enough time learning strategies that will help them solve math problems. Read about two types of strategies for solving math problems—working left to right and regrouping into what you know.

- Crystal Wagner

Nim Games

This is a game that is generally used to show how math can be involved in game play. I explain the rules of the game as well as the mathematical strategy involved. There is also a script where users can compete against the computer

- Aftermath

Day 85 – Related Rates

Two separate trucks carrying a very long wind turbine blade need to turn the corner. Describe how their speeds vary throughout the turn. The blog is dedicated to these types of discussion starters, at all levels.

- Curmudgeon

…

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.

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

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