Each monthly carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun. It’s like a free online magazine of mathematical adventures. What fun!

Simon Gregg put this carnival together a few weeks ago, and I should have posted a link before now, but it’s been a hard few months here, and too many things got shoved aside. Still the posts are evergreen — helpful and inspiring no matter when you read them.

This carnival offers summer camp activities, dancing geometric patterns, new books to enjoy, pattern blocks, the math of peg solitaire, Q-bitz fraction talks, and a taste of some great math conversations on Twitter. And plenty more!

Click Here to Read the Carnival Blog

Do you have a favorite blog post about math activities, games, lessons, or hands-on fun? The Playful Math 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.

To submit a blog article for consideration, fill out this form:

**Don’t procrastinate: The deadline for entries is this Friday, May 25.** The carnival will be posted next week at Math Hombre blog.

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

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

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I’ve been working on my next *Playful Math Singles* book, based on the popular Things to Do with a Hundred Chart post.

My hundred chart list began many years ago as seven ideas for playing with numbers. Over the years, it grew to its current 30+ activities.

Now, in preparing the new book, my list has become a monster. I’ve collected almost 70 ways to play with numbers, shapes, and logic from preschool to middle school. Just yesterday I added activities for fraction and decimal multiplication, and also tips for naming complex fractions. Wow!

Gonna have to edit that cover file…

In the “Advanced Patterns” chapter, I have a section on math debates. The point of a math debate isn’t that one answer is “right” while the other is “wrong.” You can choose either side of the question — the important thing is how well you support your argument.

Here’s activity #69 in the current book draft.

When you add fractions, you face a problem that most people never think of. Namely, you have to decide exactly what you are talking about.

For instance, what is one-tenth plus one-tenth?

Well, you might say that:

of one hundred chart

+ of the same chart

= of that hundred chart

But, you might also say that:

of one chart

+ of another chart

= of the *pair* of charts

So what happens if you see this question on a math test:

+ = ?

If you write the answer “”, you know the teacher will mark it wrong.

Is that fair? Why, or why not?

CREDITS: Feature photo (above) by Thor/geishaboy500 via Flickr (CC BY 2.0). “One is one … or is it?” video by Christopher Danielson via TED-Ed. This math debate was suggested by Marilyn Burns’s blog post Can 1/3 + 1/3 = 2/6? It seemed so!

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

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“In 2018, I want to change the world.

…

I want to make it possible for more children to claim math as their favorite subject.

…

Math is how we describe our world when words are not enough. Everyone deserves to speak math and to play math, to enjoy its beauty and its power.”

— Geoff White

The Grade 10 Math Crunch, or Hitting the Wall at Grade 10

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo by Bobby Johnson on Unsplash.

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

]]>“At heart, mathematical thinking is little more than formalized common sense. It always has been. Which means it is something we can all do.”

— Keith Devlin

How Today’s Pros Solve Math Problems

If you have some time to spend pondering big ideas, dig into Devlin’s entire series of posts about what real-world mathematics looks like and the implications for math education:

- Déjà Vu, All Over Again
- How Today’s Pros Solve Math Problems: Part 1
- How Today’s Pros Solve Math Problems: Part 2
- How Today’s Pros Solve Math Problems: Part 3 (The Nueva School course)
- Calculation was the price we used to have to pay to do mathematics

And a related series on K–12 school math:

- All The Mathematical Methods I Learned in My University Math Degree Became Obsolete in My Lifetime
- Number Sense: The Most Important Mathematical Concept in 21st Century K-12 Education

“Make no mistake about it, acquiring that modern-day mathematical skillset definitely requires spending time carrying out the various procedures. Your child or children will still spend time ‘doing math’ in the way you remember.

“But whereas the focus used to be on mastering the skills with the goal of carrying out the procedures accurately — something that, thanks to the learning capacity of the human brain, could be achieved without deep, conceptual understanding — the focus today is on that conceptual understanding.

“That is a very different goal, and quite frankly a much more difficult one to reach.”

— Keith Devlin

All The Mathematical Methods I Learned in My University Math Degree Became Obsolete in My Lifetime

In honor of Women’s History Month, this carnival features quotes from fifteen women mathematicians.

If you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Let the mathematical fun begin!

They came from many countries and followed a variety of interests.

They conquered new topics in mathematics and expanded the world’s understanding of old ones.

They wrestled with theorems, raised children, published articles, won awards, faced discrimination, led professional organizations, and kept going through both success and failure.

Some gained international renown, but most enjoyed quiet lives.

They studied, learned, and lived (and some still live) as most of us do — loving their families and friends, joking with colleagues, hoping to influence students.

I think you’ll find their words inspiring.

“What I really am is a mathematician. Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved.”

—Julia Robinson (1919–1985)

“All in all, I have found great delight and pleasure in the pursuit of mathematics. Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more.”

—Karen Uhlenbeck (b. 1942)

And now, on to the main attraction: the blog posts. A few 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.

- Talking Math with Kids
- Elementary Exploration and Middle School Mastery
- Adventures in Basic Algebra and Geometry
- Advanced Mathematical Endeavors
- Puzzling Recreations
- Teaching Tips

“I would like to encourage mathematicians, indeed anyone who has responsibility for the learning of mathematics, to model their own intuitive processes, to create the conditions in which learners are encouraged to value and explore their own and their colleagues’ intuitions. This seems to me to be a necessary step which provides a justification for, but is prior to, the search for convincing argument and, ultimately, proof.”

—Leone Burton (1936–2007)

- Rodi Steinig highlights activities from a five-week course in Embodied Mathematics for 5–7-year-olds.

- The idea of Zero is a powerful math concept. Christopher Danielson and daughter discuss Cocoa Puff or Cocoa Puffs: The Language of Nothing.

- Megan Schmidt plays school with her daughter — who is always happy to do math if it means putting off bedtime — in Fraction Frenzy.

- For my carnival entry, I’ll share a recent guest post. Funville Adventures: Blake’s Story offers a great way to launch a math chat with your kids. And be sure to follow the rest of the Funville Web Tour!

- Conversation is an excellent tool for developing deep foundations in math. Lacy Coker explains 5 Keys to Math Narration for Improved Fluency and Conceptual Understanding.

“I especially want to thank the teachers, including my mother, who inspired me — those who awakened my sense of curiosity, showed me that there was ‘wow!’ in mathematics.”

—Doris Schattschneider (b. 1939)

“For me, mathematics is a part of Nature’s beauty, and I am grateful for being able to see it. Whatever mathematics I happen to teach, I love to communicate its beauty to my students.”

—Marina Ratner (1938–2017)

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- Ioana suggests ways to get your students playing with (and creating their own) Mathemagic: Exploring Sudoku and Other Magic Squares.

- Paula Beardell Krieg and her students create images based on Fraction & more Fractions. I want to try these projects with my co-op math kids one of these days.

- How well can your children estimate fractions? Test their (and your own!) skill with Daniel Scher’s puzzle Deducing The “Mystery” Fraction.

- I love Don Steward’s resource blog! These from one fraction to another puzzles were a fun challenge.

- Ron King encourages middle-school-and-up students to think about their futures in his version of The Million Dollar Project.

“We had few toys. There was no movie house in town. We listened to the radio. But our games were very elaborate and purely in the imagination. I think actually that that is something that contributes to making a mathematician — having time to think and being in the habit of imagining all sorts of complicated things.”

—Mary Ellen Rudin (1924–2013)

“Aren’t truth and beauty enough? In fact, I have often reminded my students that the best mathematical achievements took place when the question, ‘What is it for?’ was not asked.”

—Bhama Srinivasan (b. 1935)

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- Nicola Waddilove shares a free printable card-sorting activity for Solving Simple Equations.

- John Golden prompts math debates about relationships between integers and variables in Walk the [Number] Line.

- Don Steward will push your students’ understanding of linear equations to a new level with these radiating equations.

- Benjamin Leis’s students tackle a particularly tough probability question and a beautiful project from George Hart’s geometric sculptures: 3/20 Visible Math.

- James Tanton challenges us to try our own math/science experiment in Time Does Not Run Clockwise. Here’s Proof!

“Mathematics is a way of thinking. It requires no tools or instruments or laboratories. It may be convenient to have a pen and paper, a ruler and a compass, but it is not essential: Archimedes managed very well with a stretch of smooth sand and a stick.”

—Kathleen Ollerenshaw (1912–2014)

“When I was eight or nine, the thing I liked best when playing with my dolls was to sew clothes for them. It was fascinating to me that by putting together flat pieces of fabric one could make something that was not flat at all, but followed curved surfaces.”

—Ingrid Daubechies (b. 1954)

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- Patrick Honner proposes “a fun little exploration involving a simple sum of trigonometric functions”: sin(x) + cos(x).

- Introduce your students to hyperbolic geometry as One on Epsilon authors Clara Valtorta and Phillip Isaac discuss

Thinking outside the coordinate plane.

- Paradoxes are a great way to get students thinking. Murray Bourne challenges us to imagine The object with finite volume but infinite surface area.

- Do your young mathematicians have a favorite theorem? I bet they’d enjoy Mike Lawler and sons’ Simplified version of the Banach-Tarski paradox.

- And don’t miss the 155th Carnival of Mathematics.

“I remember when I took calculus in college, the only book I took home over the Christmas holidays was my calculus book. I wanted to do those word problems. I worked on one problem for the whole two weeks before I solved it. When the light dawned, I was so happy! I don’t believe I ever felt so rewarded. I was hooked. After that, to the amazement of my fellow students, I recall sitting on campus doing calculus problems for recreation.”

—Gloria Hewitt (b. 1935)

“I would like to win over those who consider mathematics useful, but colourless and dry — a necessary evil. No other field can offer, to such an extent as mathematics, the joy of discovery, which is perhaps the greatest human joy.”

—Rózsa Péter (1905–1977)

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- Rob Eastaway plays around with dots in Thinking
*outside*outside the box.

- Jae Ess’s students love this new type of puzzle: Strimko Puzzle Review. This looks like a great opportunity for the “Now make up your own” extension.

- Kelly Darke reviews one of my favorite playgrounds of recreational math: This is Not a Math Book, It is a Magical Math Book.

- With only a few materials — scissors, paper, and maybe snap cubes — you can dive deep into the rabbit hole of math with Mike Lawler’s collection of 15 (+1 bonus) ideas for a 6th grade math camp.

- Malke Rosenfeld explores loops of hyperbolic crochet and quotes Margaret Wertheim on the Value of Embodied Knowledge.

- Sue VanHattum poses a twist on a fiendishly-difficult (at least to me!) Logic Puzzle – What Does Your Friend See?

“[Mathematical research] is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks — and with some luck you might find a way out.”

—Maryam Mirzakhani (1977–2017)

“Many problems from combinatorics were easily explained, you could get into them quickly, but getting out was often very hard. Finding the right problem is often the main part of the work. Frequently a good problem from someone else will give you a push in the right direction, and the next thing you know you have another good problem. You make mathematical friends and share the fun!”

—Fan Chung (b. 1949)

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- Joe Schwartz points out that the learning process is messy when you let your students make Decisions — but oh, so valuable!

- Sonya Post wraps up a series of posts on number studies by showing how she and her son write Math Compositions. “What I am looking for is … his ability to apply the general principles of addition, subtraction, multiplication, division and fractions to a specific number, begin anywhere and transform what he knows into multiple expressions.”

- Do your students give up too easily? Jenise Sexton may have the answer: They Called Me A Murderer.

- Fawn Nguyen shares How I Use “Between Two Numbers” to get her students estimating and make them comfortable with large numbers.

- If you want something new to try, but you’re not really sure what, explore Sarah Carter’s series of Monday Must Reads — a weekly compilation of her favorite Twitter posts, featuring activities and puzzles for all ages. (Yes, I drew a few of this carnival’s posts from her collections.)

“I believe that math is in grave danger of joining Latin and Greek on the heap of subjects which were once deemed essential but are now, at least in America, regarded as relics of an obsolete, intellectual tradition. How do you teach the beauty of mathematics, how do you teach them to solve problems, to acquaint them with various strategies of problem-solving so they can take these skills into any level of mathematics? That’s the dilemma we face.”

—Evelyn Boyd Granville (b. 1924)

“We are surrounded with ever-widening horizons of thought, which demand that we find better ways of analytic thinking. We must recognise that the observer is part of what he observes and that the thinker is part of what he thinks. We cannot passively observe the statistical universe as outsiders, for we are all in it.”

—Gertrude Cox (1900–1978)

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Photos and quotations are from the MacTutor History of Mathematics archive. To learn more about the women who have influenced math history, check out Agnes Scott College’s Index of Women Mathematicians and Wikipedia’s Timeline of women in mathematics.

“Carnival 115” background image is by Fractal Ken via Flickr (CC BY 2.0).

And that rounds up this edition of the Playful Math Education Blog Carnival. I hope you enjoyed the ride.

The next installment of our carnival will open sometime during the week of April 24, at a blog location yet unknown…

** We need more volunteers!** Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math — if you would like to take a turn hosting the Playful Math Education Blog Carnival, please let me know.

You can leave a comment here below or email me directly.

Want us to consider your post for next month’s carnival? 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.

**Funville Adventures** is a math-inspired fantasy that introduces children to the concept of functions, which are personified as magical beings with powers.

Each power corresponds to a transformation such as doubling in size, rotating, copying, or changing color. Some Funvillians have siblings with opposite powers that can reverse the effects and return an object to its original state, but other powers cannot be reversed.

In this way, kids are introduced to the mathematical concepts of invertible and non-invertible functions, domains, ranges, and even functionals, all without mathematical terminology.

We know about Funville because two siblings, Emmy and Leo, were magically transported there after they went down an abandoned slide.

When they came back, Emmy and Leo shared their adventures with their friends and also brought back the following manuscript written by their new friend Blake.

Hi everyone! My name is Blake and I live in Funville. Before I met my new friends Emmy and Leo, I didn’t know there were places outside of Funville, but now I do! Emmy explained to me that people from her world don’t know about Funvillians and our powers, so she suggested that I write to you and tell you a bit about myself.

Each Funvillian has a special power. My friend Doug’s power is to make things twice as big. He can look at a cookie and make it double in size! Which really isn’t fair but it’s still nice, since he’s good at sharing the now mega-cookies with the rest of us. His brother Harvey can make things twice as small. Sometimes when Doug and Harvey are arguing, they make the same thing big and then small and then big and small over and and over again, which is really quite funny to watch.

My power is to erase things. In comes in very handy when I want to redo a drawing or clean up a spill. But it gets tricky sometimes when I play games.

Games in Funville are the best! I imagine they must go somewhat differently where you are, since in Funville everyone uses their powers while playing. Emmy calls this “cheating,” but we think it’s all in good fun! It makes games very exciting, but it also makes it hard to decide who wins. If my friend Heather uses her power to make the soccer ball too heavy to move when the score is 1-to-1, we usually have to declare a tie and play something else (I suspect she does this whenever she’s bored of playing soccer).

For a while, every time I tried to use my power to play a game, it didn’t work very well. The first time I played checkers I accidentally erased the checkerboard. We drew it back on, but it took awhile, because we had to guess how many squares there should be, and we had to try it a few times before it looked right again. The second time I erased the scoreboard in the fifth inning of a baseball game because I wanted to start over, but then it got dark before we could finish the game.

I don’t even get invited to play Scrabble anymore because I always erase letters I don’t like. I know I probably shouldn’t do this, but I just can’t help myself! And then sometimes I even forget what the letters were by the end of the game, so now we have too many blank scrabble tiles and we don’t know what they should be.

But then Emmy and Leo taught me about games you can play on paper, which we hadn’t been playing in Funville before. Leo taught me how to play tic-tac-toe, and soon everyone in Funville was playing it! Well, I guess not the original version — we had to change it to tic-tac-elephant, so that my friend Constance could play (her power is to turn anything into an elephant).

And Emmy taught me how to play hangman, where you come up with a word and the other players have to try to guess it one letter at a time. Harvey always beats me at that one when he’s guessing, because he keeps making the parts of the hangman so small that I can’t see them and I forget they are there, and so I keep drawing the same arm over and over again while he gets more guesses. And I always beat him when I’m guessing, because I can erase the parts and he forgets, too!

Whenever we play these games, it’s mine to shine — whenever a game is finished, I can erase the paper, and we get to play all over again!

Sometimes it’s tough having a power that can’t be reversed, and I wish I was like Harvey and Doug, who can always undo each other’s mistakes. But other times I’m proud I can erase things. It’s not always what we want, but sometimes a clean slate is exactly what we need.

Dear reader, now it’s your turn to have fun with powers!

Talk with your children about ideas inspired by the *Funville Adventures* story.

For example, think of one of your favorite games to play on paper. (If you don’t have any, you can think of board games instead.) Would having Blake’s power help in the game?

Blake also mentions his friends Doug, Harvey, and Constance in his story. Would one of their powers be more useful? Or funnier?

Come up with your own powers that you’d like to have while playing each of your favorite games.

For inspiration, enjoy this father’s conversation with his son after reading *Funville Adventures.*

And if you’d like, you can play The Function Machine Game to experiment with functions of numbers. Be sure to let your kids have a turn making up function rules for you to solve!

- Read the other blogs in the Funville Web Tour
- Visit the Funville Page on Natural Math
- Check out
*Funville Adventures*on Amazon

**Sasha (A.O.) Fradkin** has loved math from an early age and seeks to share that love of math with others. After receiving her PhD in mathematics from Princeton University, she worked for several years as a professional mathematician and taught enrichment math to children ages 4-10 at the Golden Key Russian School. Currently, Sasha is the Head of Math at the Main Line Classical Academy, an elementary school in Bryn Mawr, PA. She develops their math curriculum and teaches children in grades K-5. She writes a blog, Musings of a Mathematical Mom, about her teaching as well as various math adventures with her two daughters, and enjoys pondering exciting and engaging ways to present the beauty of mathematics to young children.

**Allison (A.B.) Bishop** grew up with a passion for writing and initially disliked math because it was presented as formulaic. She belatedly discovered the creative side of mathematics and science, and now sees it as a vital component of the curiosity that drives her life. She is currently a professor of computer science at Columbia University as well as a quantitative researcher at the Investors Exchange. She remains an avid fiction enthusiast and writer, and is always seeking new ways to expose young minds to creative mathematical thinking and fuel their scientific curiosity.

To celebrate Valentine’s Day, Sonya at Arithmophobia No More and Lacy from Play, Discover, Learn (two of my favorite homeschooling bloggers) teamed up to offer a HUGE set of hands-on mathy goodness.

As a bonus, I’m throwing in a signed copy of one of my books — winner’s choice.

But you have to act fast. The giveaway ends Saturday, February 17, 2018, at midnight (CT).

Click the links.

Drool over the prizes.

Submit your entry today.

[Shipping to U.S. addresses only.]

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“Cultivating thinking skills is the main reason for teaching math. It is the mind’s perfect playground for shaping up.

…

To begin developing thinking, you must first have a child who is curious. For without curiosity, there is only forced thinking.

…

The problem with traditional math is it jumps to the punchline.

…

Absolutely no mystery or suspense is developed in traditional math books. Why? Apparently, someone thought math was without mystery. That math is a definitive subject of rules and algorithms that all have been discovered.

…

We must persuade children that math is a worthy pursuit through interesting stories, examining quirky math properties, and asking good questions.”

— Lacy Coker

5 Tips to Cultivate Math Curiosity

My K-2nd-grade homeschool co-op math class will be following many of the tips in Lacy’s article.

Our topic is “Math Storytime,” so we’ll be starting with picture books, exploring the ideas they bring up, and finding things to notice and wonder about.

I’m looking forward to it.

But picture books aren’t just for little kids. They can be great discussion-starters at any age. Have you enjoyed math books with your students?

I’d love to hear your suggestions!

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo courtesy of Bekah Russom on Unsplash.

Of all the myths about mathematics, the one I find most blatantly wrong is the idea that some people are just born knowing the answers. In my experience, when you confront a genuine puzzle, you start out not knowing, no matter who you are.

…

Moreover, “knowing” the answers can be a trap; learning mathematics is about looking at what you thought you understood and seeing that there’s deeper mystery there than you realised.

— Dan Finkel

A Mathematician at Play Puzzle #1

If you’d like to practice learning mathematics by confronting genuine puzzles, Dan’s “A Mathematician at Play” series looks like a wonderful place to start.

Some of these puzzles are classics, others are original. All of them involve some kind of thinking or insight that strikes me as pretty, or surprising, or delightful.

— Dan Finkel

A Mathematician at Play Puzzle #1

Dan plans to post new puzzles on the Math 4 Love blog every Monday for the next few months. And sharing spoilers on each following Friday, if you want to verify your answers.

Check it out!

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo courtesy of Amy on Unsplash.

“Teach mathematics the way we learn any other subject: Make it visual, make it concrete, not dependent on meaningless, abstract symbols, employ all the senses!

…

If math is such an important subject (and it is) why teach it in a way that is dependent on a child’s weakest mental ability: memory, rather than her strongest mental ability: imagination?”

— Geoff White

The Grade 10 Math Crunch, or Hitting the Wall at Grade 10

How can we stir up our students’ imagination?

Teachers have struggled with this question for years — perhaps since the beginning of the profession.

Consider these comments by W. W. Sawyer in Mathematician’s Delight:

“Earlier we considered the argument, ‘Twice two must be four, because we cannot imagine it otherwise.’ This argument brings out clearly the connexion between reason and imagination: reason is in fact neither more nor less than an experiment carried out in the imagination.

“People often make mistakes when they reason about things they have never seen. Imagination does not always give us the correct answer. We can only argue correctly about things of which we have experience or which are reasonably like the things we know well. If our reasoning leads us to an untrue conclusion, we must revise the picture in our minds, and learn to imagine things as they are.

“When we find ourselves unable to reason (as one often does when presented with, say, a problem in algebra) it is because our imagination is not touched. One can begin to reason only when a clear picture has been formed in the imagination.

“Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination.”

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo by Mehmet Kürşat Değer on Unsplash.

Let’s resolve to have fun with math this year. Ben has posted a preview of 2018’s mathematical holidays. Iva offers plenty of cool ways to think about the number 2018. And Patrick proposes a new mathematical conjecture.

But my favorite way to celebrate any new year is by playing the Year Game. It’s a prime opportunity for players of all ages to fulfill the two most popular New Year’s Resolutions: spending more time with family and friends, and getting more exercise.

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

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

**Use the digits in the year 2018 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.**

- You must use all four digits. You may not use any other numbers.
- Solutions that keep the year digits in 2-0-1-8 order are preferred, but not required.
- You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
- You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
- You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.

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

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

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

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

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

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

As players report their game results below, I will keep a running tally of confirmed results (numbers reported found by two or more players). My family has been going through the annual ritual of pass-the-flu-bug, however — and whenever we finish that game, we’ll be traveling to see extended family. So this tally will almost certainly lag behind the results posted in the comments.

Percent confirmed: 100%

Reported but not confirmed: none.

Numbers we are still missing: none.

Wow!If you are still working your way through the puzzle (as I am), take heart — it can be done.

Students in 1st-12th grade may wish to submit their answers to the Math Forum, which will begin publishing student solutions after February 1, 2018. Remember, Math Forum allows double factorials but will NOT accept answers with repeating decimals.

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

**These things ARE allowed:**

- You must use each of the digits 2, 0, 1, 8 exactly once in each expression.
- For this game, 0! = 1.
- Unary negatives count. That is, you may use a “−” sign to create a negative number.
- You may use (
*n*!)!, a nested factorial, which is a factorial of a factorial. Nested square roots are also allowed. - The double factorial
*n*!! = the product of all integers from 1 to*n*that are equal to*n*mod*2*. If*n*is even, that would be all the even numbers, and if*n*is odd, then use all the odd numbers.

**These things are NOT allowed:**

- You may not write a computer program to do the puzzle for you — or at least, if you do, PLEASE don’t ruin our fun by telling us all the answers!
- You may not use any exponent unless you create it from the digits 2, 0, 1, 8. You may not use a square function, but you may use “^2”. You may not use a cube function, but you may use “^(2+1)”. You may not use a reciprocal function, but you may use “^(−1)”.
- “0!” is not a digit, so it cannot be used to create a base-10 numeral. You cannot use it with a decimal point, for instance, or put it in the tens digit of a number.
- The decimal point is not an operation that can be applied to other mathematical expressions: “.(2+1)” does not make sense.
- You may not use the integer, floor, or ceiling functions. You have to “hit” each number from 1 to 100 exactly, without rounding off or truncating decimals.

- Mathematics Game Worksheet

For keeping track of which numbers you’ve solved.

- Mathematics Game Manipulatives

This may help visual or hands-on thinkers.

- Mathematics Game Student Submissions

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

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

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

*2018 Equation photo by Iva Sallay and 2018 Sparkles by NordWood Themes on Unsplash. Semiprime Blues cartoon by Ben Orlin.*

I love the expressions on the boys’ faces. So many different ways to manifest hard thinking!

Here’s the question:

No calculator allowed. But you can talk it over with a friend, as the boys on the right are doing.

You can even use scratch paper, if you like.

And if you’d like a hint, you can figure out square numbers using this trick. Think of a square number made from rows of pennies.

Can you see how to make the next-bigger square?

Any square number, plus one more row and one more column, plus a penny for the corner, makes the next-bigger square.

So if you know that ten squared is one hundred, then:

… and so onward to your answer. If the Russian schoolboys could figure it out, then you can, too!

Simon Gregg (@Simon_Gregg) added this wonderful related puzzle for the new year:

Welcome to the 114th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of articles by bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

If you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

By the way, I found a cool, semi-self-referential trivia tidbit about our carnival number: 2^{7} − 14 = 114. And if you put 114 dots into a 1←7 Exploding Dots machine, you’ll get the code 222. Pretty neat!

As you scroll through the links below, you find several puzzle graphics from the wonderful Visual Patterns website. Use them as conversation-starters with your kids: What do you notice? How does each pattern grow? For older students: Can you write a formula to describe how each pattern? What will it look at stage 43?

Setting the mood: Enjoy this bit of seasonal fidgeting from Vi Hart (@vihartvihart).

If you don’t understand some of the references, that’s normal! Pick a phrase, Google it, and enjoy the fun of learning something new.

And now, on to the main attraction: the blog posts. Some 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.

- Seasonal Math Activities
- Talking Math with Kids
- Elementary Exploration and Middle School Mastery
- Adventures in Basic Algebra and Geometry
- Advanced Mathematical Endeavors
- Puzzling Recreations
- Teaching Tips

Let the mathematical fun begin!

You don’t have to celebrate Christmas to enjoy many of these activities — but really, I couldn’t find much for the other winter holidays. A few calculation worksheets with clip art, which is not my idea of playful math.

Do you know of any great math-related seasonal games, crafts, or activities I missed? Please add them to the comments section below!

- Play with a new math project every day with one of these mathematical Advent calendars for all ages. Or try your hand at the first post in the Chalkdust Christmas Conundrum series.

- Have a big bag of colorful bows? Dyan (@andnextcomesl) suggests letting your kids try Graphing with Gift Bows. And be sure to save your wrapping paper tubes to make her Christmas Boredom Buster: Jingle Bell Run.

- Karyn (@TeachBesideMe) demonstrates a Hanukkah STEM activity: Paper Circuit Menorah. Or try making her Gingerbread House Paper Circuits.

- Chelsey (@buggyandbuddy) shares two fun craft activities for kids: Symmetrical Snowflakes, and Symmetry Christmas Tree. Not to mention a simple and surprisingly graceful Paper Strip Angel Ornament.

- Bethany (@mathgeekmama) offers a free printable game for addition and subtraction: Grow a Christmas Tree Farm. For older kids, check out her series of Christmas Algebra Riddles.

- Check out Sarah’s (@FrugalFun4Boys) Pattern Block Snowflakes. I think I’ll use them to wrap up my elementary Math Art class on Friday. You may also enjoy 25 Awesome Stem Challenges for Kids (With Inexpensive or Recycled Materials!)

- Paula (@PaulaKrieg) celebrates paper-snowflake time and shares a new discovery: Spiraling Paper Ornament. I think those triskele globes will be the perfect final project for my middle school Math Art class this week.

- Iva (@findthefactors) brings us A Gift-Wrapped Puzzle for the holidays. Or play with her Oh Christmas Tree multiplication puzzle collection.

- On this blog, my fictional math adventurer Alexandria Jones shares a few holiday stories, including How to Make a Flexagon Christmas Card.

- I adore Svenja’s (meine.svenja) beautiful stained-glass Tracing-Paper Poinsettias. And I love the fun of Matthew’s (@mscroggs) Christmas Flexagons (and more).

- Challenge your students with the real-world problems in Brian’s (@Yummymath) Pre-Winter Holiday Activities. Or check out the newest Annual Holiday Puzzles.

- Alex (@alexbellos) shows how to make geometric holiday cards: Solving for Xmas. Can you solve his holiday puzzles about Christmas wish lists, Victorian mince pies, and present-sorting machines?

- Clarissa (@c0mplexnumber) demonstrates how to make beautiful, challenging origami snowflakes. She recommends beginners try the first few folds — which create a pretty cool design on their own. Let it Snow… You may also enjoy her other Christmas projects.

- And finally, try your hand at a few assorted Christmas math problems and puzzles from Transum. Or these challenge worksheets from Oxford University Press: Foundation Questions, and Shapes and Space.

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- Chris (@ChrisHunter36) refuses to teach his daughter a math trick, pushing instead for conceptual understanding. She remains unrepentant: I’m Not The Finger Man. You may also enjoy Keira.

- Counting is harder than you think! Sasha (@aofradkin) and daughter explore the mysteries in Counting crocodile legs. And check out her new math chapter book Funville Adventures.

- Next semester, my homeschool co-op class will be “Math Storytime,” and I’m finding lots of great books to read at Kelly’s (@KellyDarkeMath) blog. I love how her kids jump into doing the math in Life is No Fun When You’re a Remainder of One. And look at what happens when Magic Emerges from a Cookie Fiasco.

- Graham’s (@gfletchy) daughter doesn’t like to work with fractions. Follow her creative thinking in Reasoning with Fractions Through the Lens of a 10 Yr Old. For older students talking about fractions, see 3-Act Task: A 5th-grade lesson captured.

- Talking math isn’t just for elementary kids. Sarah (@csarahj) draws out students’ understanding — and misunderstandings — in Making A Hodgepodge of High School Number Talks Matter. And be sure to read her moving post I am Those Kids. So much food for thought!

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- Christina (@BuildMathMinds) discusses The Best Way To Teach Subtraction so that it reinforces a child’s current understanding. And explains how looking at relationships can build Number Sense for Upper Elementary.

- Greg (learn-with-math-games) modifies the traditional 24 Game to explicitly practice multiplication: Combine 4 Numbers. You may also enjoy his Fraction Number Line Concentration game.

- Michelle (@ResearchParent) launches a mixed-grade-level co-op math class using Low Floor High Ceiling Math Problems. And if your child is struggling with the times tables, check out her Interactive Multiplication Cards.

- Iva (@findthefactors) plays around with perfect squares in 961 is a Perfect Square in More Ways Than One. And be sure to explore her daily multiplication logic puzzles.

- If you’ve followed my blog for long, you know I like to play with dot grid paper. So of course, I was delighted to find Spatial Learning’s Isometric Dot Paper Activities, and the follow-up Cube Stack Activity. What a great way to build geometric intuition!

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- Kate (@k8nowak) takes a look at sense-making in early algebra: Respecting the Intellectual Work of the Grade. And discusses how teachers should approach a new curriculum in FAQ: What Can We Change?

- Mike (@mikeandallie) wonders about the best way to help when his son is Struggling through an AMC 8 problem. You may also enjoy the challenge of Counting paths in a lattice.

- Paula (@PaulaKrieg) explores some beautiful angle relationships in Pentagons, Paper Folding, Stars & Origami. And did you see her amazing crowd-sourced math art? Ta- Dah! I wish I’d remembered this post sooner, so I could try something similar with my co-op classes.

- Michael (@mpershan) and his students struggle with geometry proofs in Study an example, see the world. And he shares his thoughts on Teaching, in General.

- Rupesh’s (rupesh.s.gesota) students reason their way through a Geometry problem, finding several ways to solve it. The next day, they tackle an Extension of the problem and prove the general case.

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- Shaun (@theshauncarter) focuses on parent functions to give students a solid understanding: My most used notebook template this year. And check out his wife Sarah’s (@mathequalslove) Two Truths and a Lie: Parent Functions game.

- I like David’s (@DavidKButlerUoA) common-sense approach to Finding an inverse function. But his series of posts exploring Where the complex points are really blew my mind.

- Gary (~antonick) celebrates the U.S. Team Wins First Place at International Math Olympiad with sample problems and an interview. And explores the different ways people approach problem-solving in A Numberplay Farewell.

- Keith (@profkeithdevlin) examines the problem of Mathematics and the Supreme Court. And takes on a classic — and surprisingly difficult — puzzle in Monty Hall may now rest in peace, but his problem will continue to frustrate.

- And don’t miss the fun at our sister blog carnival: 151st Carnival of Mathematics. Update: the 152nd Carnival of Mathematics is now up, too.

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- Play is the heart of recreational math, leading to connections between deep ideas. See Simon’s (@Simon_Gregg) post about Arranging things, and about the relationship between Play and Manipulatives.

- Which reminds me of Sara’s (@saravdwerf) post You need a play table in your math classroom! — recently updated with printable play posters. You may also enjoy Even if they say they don’t like doing math, they secretly do. An Experiment you should try.

- Sasha (@aofradkin) shares a delightful math-inspired love story in verse. And check out the fun her students have exploring pentacubes.

- Dan (@MathforLove) collects a series of symmetrical investigations to show how interaction between teachers Makes Teachers Better. And explores how recreational math puzzles can help students learn to think in Overcoming Confirmation Bias with the 2, 4, 6 Puzzle.

- David (@DavidKButlerUoA) demonstrates a cool topology game called Home in One Piece with printable game board and dice. And a giant, printable version of Body-Scale Prime Climb.

- Christy (@housefulofchaos) invents an even-more-ultimate variation on Ultimate Tic-Tac-Toe. And explores graph theory relationships in her Logical Graph Game, too. So creative!

- James (@JimPropp) examines a classic brain-teaser with many implications: Impaled on a Fencepost. And have you ever wondered How Do You Write One Hundred in Base 3/2?

- If I end up with Christmas money to spend, I think I’ll buy myself a gift from Shecky’s (@SheckyR) list of Math Books… Year-end Review. Oh, and be sure to check out his Math Frolic Interviews. What a treat!

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- Mark (@MarkChubb3) investigates the different ways we might look at an elementary geometry worksheet and discusses how to encourage student thinking. How Many Do You See? (Part 2 of 2) You may also enjoy A few of my favourite blog posts – to read… or inspire writing.

- John (@Jstevens009) considers how to present a textbook lesson that encourages student talk and perseverance. Back To School: The Textbook Teacher. And if you haven’t subscribed to his Tabletalk Math newsletter — what are you waiting for?

- Kristin (@MathMinds) ponders the many ways we can think about Fraction Division and Complex Fractions — and how much all of us can learn from other teachers across the K–12 spectrum. And if you missed it back in May, be sure to read her post Today’s Number: Making Connections.

- My daughter is struggling with online homework in her calculus class — not because the math is too hard, but because the interface is anti-intuitive. So David’s (@davidwees) post resonates with me: Online Practice is Terrible Practice. And I love his challenge to find and teach to the Big Ideas of math.

- Michael (@mpershan) stirs up controversy with A typically wishy-washy take on discovery in math class. And the follow-up post, Addendum: On Discovery and Inquiry.

- I’d like to wrap up the carnival with an article you may have seen before. If you haven’t read it, you’re in for a treat. And if you have, well, it’s very much worth re-reading. Annually. As we wrap up the old year and prepare for the new … Francis’s (@mathyawp) Mathematics for Human Flourishing.

“Shalom and salaam, my friends. Grace and peace to you. May you and all your students flourish.”

— Francis Su

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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 January 22–26, 2018, at … well, we don’t know!

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.

To share your favorite blog post with the carnival, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Older-but-still-relevant posts are welcome, as long as they haven’t been published in past editions of this carnival (at least, not in recent memory).

Past posts and future hosts can be found on our blog carnival information page.

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Including an especially-tough Advent meta-puzzle for truly determined problem-solvers…

Click the images below to visit the corresponding December Math Calendar home pages.

Easier activities for elementary and middle school.

Math puzzle fun, plus a printable coloring page.

When you get to the Nrich website, click a number to go to that day’s math.

Activities for middle and high school.

Each day features a challenge from the Short Problems Collection.

2017 Secondary Advent Calendar

When you get to the Nrich website, click a number to go to that day’s math.

“This year we’ve decided to bring you some of our favourite *Plus* videos. There’s nothing more soothing that a bit of fascinating maths, explained by a fascinating mathematician, that doesn’t even require you to read stuff. Happy watching!”

When you get to the *+Plus Magazine* website, you can tell which links are live because they jump to a larger size when you tap or mouse over the picture.

One link becomes live each day — so come back tomorrow and discover something new!

Or try your hand at the biggest mathematical mystery of them all — and save Christmas for Alex, Ben, and Carol!

Santa’s lost his memory, and the elves are cursed to alternate between lying and truth-telling. It’s up to you to piece together the clues and figure out which presents go where.

If you solve all the clues and enter the answer on Christmas day, you may win a present for yourself, too.

“Peanuts Christmas Panorama” photo [top] by Kevin Dooley via Flicker. (CCBY2.0)

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You get math journaling pages, games, creative task cards, thought-provoking worksheets, and video training resources to help you build your child’s understanding of math from arithmetic to early algebra. Wow!

These activities are perfect for homeschooling families or anyone looking to supplement their child’s current math curriculum with effective discovery-based activities. If you’ve ever wondered what to do with those Cuisenaire rods you picked up on sale way back when, this bundle is for you.

I’m so looking forward to using some of these ideas with my elementary homeschool co-op kids next year!

Sale price is $30 from December 2-15.

Cuisenaire Rod Activities Blowout Bundle

If you’ve been reading my blog for very long, you’ve probably seen how much I love the blog, books, and classes available from the Natural Math folks.

Their newest book is just off the presses — *Funville Adventures,* a math adventure chapter book.

And until December 20, they’re having a holiday sale. Make your own bundle of any Natural Math books. Playful algebra, calculus for 5-year-olds, inquiry problems and more: Great deal!

Finally, if you’ve been wanting to pick up a paperback copy of *Let’s Play Math* or some of my game books, or maybe a set of dot-grid math journals, I’m currently offering a discount on bulk orders.

Bundle ANY assortment of titles. Stock up on books for your family, friends, or homeschool group.

- 2–4 books: 15% discount off retail prices
- 5–9 books: 25% discount
- 10–19 books: 35% discount
- 20+ books: 35% discount, and free Continental U.S. standard shipping or the equivalent discount off other shipping options

Bulk Order Playful Math Paperbacks

(US customers only: We’re sorry we can’t offer bulk discounts for our international readers, but the complexities of international duties and tax laws are too much for this very small family business.)

If you’ve seen a great deal or holiday price on a math resource you love, please share!

Add your deal to the comment section below, so we can all take advantage of the math joy this season.

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