*[Feature photo above by Jimmie, and "79" image (right) by Steve Bowbrick via flickr (CC BY 2.0).]*

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 79th edition of the ** Math Teachers At Play** (MTaP) 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.

Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle, game, or trivia tidbits. If you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Since I’ve been spending all my free time working on my upcoming *Math You Can Play* book series, I’m in the mood for games. So I found a few games featuring prime and nonprime numbers ** [which category is #79 -- do you know?]**, and I’ll sprinkle some of my best-loved math game books throughout the carnival.

Students can explore prime and non-prime numbers with two free classroom favorites: The Factor Game (pdf lesson download) or Tax Collector. For $15-20 you can buy a downloadable file of the beautiful, colorful, mathematical board game Prime Climb. Or try the following game by retired Canadian math professor Jerry Ameis:

**Math Concepts:** multiples, factors, composites, and primes.

**Players:** only two.

**Equipment:** pair of 6-sided dice, 10 squares each of two different colors construction paper, and the game board (click the image to print it, or copy by hand).

On your turn, roll the dice and make a 2-digit number. Use one of your colored squares to mark a position on the game board. You can only mark one square per turn.

- If your 2-digit number is prime, cover a PRIME square.
- If any of the numbers showing are factors of your 2-digit number, cover one of them.
- BUT if there’s no square available that matches your number, you lose your turn.

The first player to get three squares in a row (horizontal/vertical/diagonal) wins. Or for a harder challenge, try for four in a row.

Hat tips: Jimmie Lanley.

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.

- Kids Talk About Math
- 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.)

Peggy Kaye gives parents more than fifty marvelous and effective ways to help their children learn math by doing just what kids love best: playing games.

- Daphne explains how it feels to think hard, from a child’s point of view: “You just listened, so then I could figure it out.”

- The answers to some math questions depend on how you define your terms, patterns, or ways of looking at the problem. Tabitha poses an interesting conundrum: Math in the Alphabet.

- Moaz invents a game for practicing basic addition and subtraction: Domino Number Bonds Game.

- Sadie Estrella’s niece tells how she knows fractions, because “Doubles are easy.” [TMWYK] Oranges.

- Maya struggles to grow into her growth mindset: “I don’t ever want to ask a question in math again!”

- Somwrita Sarkar’s son marvels at the idea of a million lollies plus one more: What is the biggest number?

[Back to top.]

[Back to Table of Contents.]

This fun collection of cartoony illustrations, games, and creative activities offers a common-sense approach to mathematics for those who are slightly terrified of numbers.

- My entry for this month’s carnival continues our gaming theme with Horseshoes: A Place Value Game for all ages.

- Maria Miller warns parents and teachers about the side-effects of a common practice: Should you use timed tests for math facts?

- Kelly shows how her family has fun with creative arithmetic in Math activity: The Counting Circle.

- I’ve enjoyed Julie’s posts on geometric doodling. Now her family is moving on to more “practical” geometry: Distance, Area, Volume Activities for Kids and Measuring Distance, Area and Volume.

- It’s not enough for kids to memorize and follow the steps of a math calculation. Tina Cardone shares her plan for building her students’ Number Sense, Logic, and Perseverance.

- Rodi Steinig’s math club students explore a variety of puzzles in Martin Gardner #3: Maze of Minotaur and Scrambled Boxtops.

[Back to top.]

[Back to Table of Contents.]

This collection of puzzles, games and activities is designed to stimulate and challenge people of all ages. Many of the puzzles have a long history, while others are original. Includes hints and solutions.

- Lisa Winer presents a mathemagic trick that gets her students’ attention every year in 1089 Math Magic Trick (and more). Can your kids explain why it works?

- Megan Schmidt challenges her algebra students with a deceptively non-algebraic-looking puzzle: The Un-Puzzle.

- Jennifer Wilson’s students tackle the big question of math, “How can we be sure?”, by proving conjectures about their Origami Regular Octagons.

- Cassie Cooper’s students rave over a lesson about the distance and midpoint formulas: Road Trip Across the USA.

- John Golden shares a wealth of wonderful “for cheap or free” resources for Algebra and Geometry in Such a Thing as Free.

[Back to top.]

[Back to Table of Contents.]

These mathematical recreations of paradoxes and paper folding, Moebius variations and mnemonics, both ancient and modern, will delight and perplex while demonstrating principles of logic, probability, geometry, and more.

- Kalid Azad looks at a problem from several perspectives to gain Intuition For The Law Of Sines.

- Shireen Dadmehr creates a game-like review lesson: Trig Identity Match Up Activity.

- John Chase presents his candy-corny Halloween worksheet for Calculus Students.

- “How can we count the ways?” is a more advanced question than most people realize. Egan Chernoff shares a video of one class working on Around the World (A Counting Problem Sequel).

- Keith Devlin tackles another counting problem and finds a huge difference between the (expected) abstract model and real world experience: Let’s Get Real About Math Word Problems.

- What does it mean to be “normal,” at least approximately? Bob Lochel’s students wrestle with the tricky problem of Assessing Normality in AP Stats.

- Having trouble convincing your students that
*correlation*doesn’t actually correlate with*causation*? Explore the fun at Tyler Vigen’s Spurious Correlations.

- Most of these are beyond the scope of this carnival, but advanced students may want to check out William Wu’s Undergraduate Level Math Book Recommendations for Self-Study.

- And don’t miss the 115th Carnival of Mathematics.

[Back to top.]

[Back to Table of Contents.]

Entertaining diversions for players of all ages in which only pencil and paper are needed: old favorites and less familiar games. I can’t believe Dover let this wonderful book go out of print!

- Shecky Riemann pays tribute to a giant on whose shoulders we all stand: A Martin Gardner Sunday.

- Colm Mulcahy presents a collection of Five Martin Gardner eye-openers involving squares and cubes.

- Alex Bellos asks Can you solve Martin Gardner’s best mathematical puzzles?

- Mike Lawler & son tackle the question, “Could the Koch snowflake (another treat from Gardner’s Mathematical Games column) grow tall enough to reach infinity?” Another example of why I love teaching math to my kids.

- Gary Antonick is also Remembering Martin Gardner on this week of his 100th birthday. Likewise the BBC: Martin Gardner, puzzle master extraordinaire. And Pi Guy collects more tribute articles in 100 Years of Martin Gardner.

- Finally, Michael Lugo links to A list of fifteen books that make up Gardner’s “canon.” For a taste of the treasures they contain, check out Gardner’s own retrospective:A Quarter Century of Recreational Mathematics.

[Back to top.]

[Back to Table of Contents.]

Math, history, art, and world cultures come together in this delightful book for kids. More than 70 games, puzzles, and projects encourage kids to hone their math skills.

- Frustrated with the Common Core Standards? Check out Prof. Triangleman’s Abbreviated List of Standards for Mathematical Practice — 25% or more fewer standards, all the flavor! (Original post from Christopher Danielson here.)

- Brian Stockus shares a simple but amazingly effective teaching tip in Numberless Word Problems.

- Tracy Zager seeks out strategies to answer the question, “How do we teach students to read math problems for understanding in a way that will yield empowered students who expect math to make sense?”

- John Golden asks his elementary ed students think about What’s a Problem? Fun post, and the “gotcha!” in the area investigation made me laugh.

- Dan Meyer reminds us that there’s educational gold in working on “fake world” math problems: Real Work v. Real World. But then Ben Orlin points out several Scenes from the “Real World” Where Math is Useful.

- Seth Godin talked about what it means to be Good at Math, and launched a mini-storm of responses:
- David Coffey points out how our mathematical worldview (see Skemp on Understanding) affects education, then challenges his readers to give a better answer to the question, “Whose fault is it that you aren’t good at math?“
- Patrick Honner steps up to defend the teachers, asking “Did No One Care About Seth Godin?“
- And Mike Lawler offers a potpourri of resources for anyone who really does want to have a better experience with math: Responding to David Coffey’s challenge.

[Back to top.]

[Back to Table of Contents.]

Book images are from Amazon.com, and if you click on a cover, the links take you to that book’s Amazon page, where you can read reviews and other details (and where I earn a small affiliate commission if you actually buy the book). But all of these books should be available through your public library or via inter-library loan.

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

The next installment of our carnival will open sometime during the week of **November 24-28:** MTaP 80 at Triumphant Learning. 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.

Past posts and future hosts can be found on our blog carnival information 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 would like to take a turn hosting the ** Math Teachers at Play** blog carnival, please speak up!

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

]]>

I first saw place value games on the old PBS Square One TV show (video below). Many teachers have posted versions of the game online, but Snugglenumber by Anna Weltman is by far the cutest variation. Anna kindly gave me permission to use the game in my upcoming *Math You Can Play* book series, and I added the following variation:

**Math Concepts:** place value, strategic thinking.

**Players:** two or more.

**Equipment:** one deck of playing cards, or a double deck for more than three players.

Separate out the cards numbered ace (one) through nine, plus cards to represent the digit zero. We use the queens (Q is round enough for pretend), but you could also use the tens and just count them as zero.

Shuffle well and deal eleven cards to each player. Arrange your cards in the snugglenumber pattern shown here, one card per blank line, to form numbers that come as close to each target number as you can get it.

**Score according to horseshoes rules:**

- Three points for each
*ringer*, or exact hit on the target. - One point for each number that is six or less away from the target.
- If none of the players land in the scoring range for a target number, then score one point for the number closest to that target.

For a quick game, whoever scores the most points wins. Or follow tradition and play additional rounds until one player gets 21 points (40 for championship games) — and you have to win by at least two points over your closest opponent’s score.

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

]]>

*[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 Monday, October 20*. The carnival will be posted soon afterwards at — well, we don’t have a host for this month yet. Would you like to volunteer?

**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.

]]>

Have you ever heard of *Math Storytelling Day*? On September 25, people around the world celebrate mathematics by telling stories together. The stories can be real — like my story below — or fictional like the tale of Wizard Mathys from Fantasia and his crystal ball communication system.

Check out these posts for more information:

- Happy Math Storytelling Day
- Math Storytelling Day resources
- Moebius Noodles: Math Storytelling Day archive

My story begins with an unexpected adventure in pain. Appendicitis sidewhacked my life last week, but that’s not the story. It’s just the setting. During my recovery, I spent a lot of time in the smaller room of my hospital suite. I noticed this semi-random pattern in the floor tile, which made me wonder:

- Did they choose the pattern to keep their customers from getting bored while they were … occupied?
- Is the randomness real? Or can I find a line of symmetry or a set of tiles that repeat?
- If I take pictures from enough different angles, could I transfer the whole floor to graph paper for further study?
- And if the nurse finds me doing this, will she send me to a different ward of the hospital? Do hospitals have psychiatric wards, or is that only in the movies?
- What is the biggest chunk of squares I could “break out” from this pattern that would create the illusion of a regular, repeating tessellation?

I gave up on the graph paper idea (for now) and printed the pictures to play with. By my definition, “broken” pattern chunks need to be contiguous along the sides of the tiles, like pentominoes. Also, the edge of the chunk must be a clean break along the mortar lines. The piece can zigzag all over the place, but it isn’t allowed to come back and touch itself anywhere, even at a corner. No holes allowed.

I’m counting the plain squares as the unit and each of the smaller rectangles as a half square. So far, the biggest chunk of repeating tiles I’ve managed to break out is 283 squares.

Have you and your children created any mathematical stories this year? I’d love to hear them! Please share your links in the comments section below.

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

]]>

*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 September edition is now posted at *1001 Math Problems* blog. What a fun list of math posts to browse!

Welcome to the 78th edition of the Math Teachers At Play math education blog carnival, which I am thrilled to be hosting this month in celebration of my soon-to-be-released book, Camp Logic. What is the blog carnival? It is a monthly snapshot of some interesting recent ideas and activities posted by math education bloggers all over the internet.

By tradition, I begin with a fun fact about the number 78:

Seventy-eight is the 12th triangle number, which means that it is the sum of the integers from 1 to 12. Therefore, it is also the total number of gifts given on the last day in the song “The Twelve Days of Christmas!” …

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

]]>

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.

]]>

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.*

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

]]>

*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! …

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

]]>

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.

]]>

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.

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

]]>

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

]]>

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!”

[Back to top.]

[Back to Table of Contents.]

- 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.

[Back to top.]

[Back to Table of Contents.]

- 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.

[Back to top.]

[Back to Table of Contents.]

- 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!

[Back to top.]

[Back to Table of Contents.]

- 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.

[Back to top.]

[Back to Table of Contents.]

- 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.

[Back to top.]

[Back to Table of Contents.]

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.

]]>

**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.

]]>

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.

]]>

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.

]]>