Can You Do the Math Salute?

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How Is This Math?

The idea that math is only about numbers, calculations, and textbook exercises is one of the greatest lies we learn in school. Of course, nobody ever comes straight out and actually says that. But the whole system teaches us every day what counts for math and what doesn’t.

James Tanton’s math salute is a physical puzzle.

How in the world did he do that?

Physical puzzles don’t fit into our cultural understanding of math. But the process of figuring out the puzzle is the same problem-solving process we use to figure out other puzzles — including the puzzles we call math.

In fact, real mathematics is all about figuring out puzzles without a teacher showing you what to do. Problem-solving is a universally useful skill.

As master teacher W. W. Sawyer said:

“Everyone knows that it is easy to do a puzzle if someone has told you the answer. That is simply a test of memory. You can claim to be a mathematician only if you can solve puzzles that you have never studied before. That is the test of reasoning.”

—W. W. Sawyer, Mathematician’s Delight

So tackle the puzzle of the math salute. Show it to your kids. (And don’t be surprised if they figure it out before you do!)

[THE FINE PRINT: I am an Amazon affiliate. If you follow the link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

New Printable Puzzle Books: Diffy Inception

The best way to practice math is to play with it—to use the patterns and connections between math concepts in your pursuit of something fun or beautiful.

Diffy Inception puzzles have their own symmetric beauty, but mostly they are just plain fun. Students can practice subtraction and look for patterns in the difference layers.

I just published four new activity books to our online store:

Notes to the teacher include puzzle instructions, game variations, journaling prompts, and more. Plus answers for all puzzles.

Available with 8 1/2 by 11 (letter size) or A4 pages.

Click for a Preview

My publishing company runs this online store, so you can find all my playful math books there — including an exclusive pre-publication ebook edition of my newest title, Prealgebra & Geometry: Math Games for Middle School. Click here to browse the Tabletop Academy Press store.

The Value of Puzzles

I love puzzles. Don’t you?

Here are several examples of river-crossing puzzles you and your kids can try. They date back at least to the time of Alcuin, the famous scholar from the court of Charlemagne.

I wish someone would write a whole math curriculum devoted entirely to puzzles.

W.W. Sawyer on the Value of Puzzles

Master teacher W.W. Sawyer didn’t write a curriculum, but he often used puzzles in the classroom.

“It is quite possible to use simultaneous equations as an introduction to algebra. Within a single lesson, pupils who previously did not know what x meant can come not merely to see what simultaneous equtions are, but to have some competence in solving them.

“No rules need to be learnt; the work proceeds on a basis of common sense.

“The problems the pupils solve in such a first lesson will not be of any practical value. They will be in the nature of puzzles.

“Fortunately, nature has so arranged things that until the age of twelve years or so, children are more interested in puzzles than in realistic problems.”

—W. W. Sawyer, Vision in Elementary Mathematics

Then he gives this example:

“A man has two sons. The sons are twins; they are the same height. If we add the man’s height to the height of one son, we get 10 feet. The total height of the man and the two sons is 14 feet. What are the heights of the man and his sons?”

Try This at Home

Not only can children solve puzzles like this, but even better — they can make up story puzzles of their own. You could spend a whole week or more making up silly height puzzles for each other to solve. By the time you were done, your kids would have a great introduction to algebra!

Maybe I never grew up. Because I still prefer puzzles over “real world” math problems.

What are your favorite kinds of puzzles? Please share in the comments section.

CREDITS: “Boat puzzles” comic from
[THE FINE PRINT: I am an Amazon affiliate. If you follow the book link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

More Dover Samples

“Without mathematics you can’t do anything! Everything around you is mathematics. Everything around you is numbers.”

—Anna Claybourne, I Can Be a Math Magician

Dover Publications sent out a new email today with fun coloring and craft samples. And several puzzles from I Can Be a Math Magician: Fun STEM Activities for Kids by Anna Claybourne.


If you’d like to receive future Dover Sampler emails, you can sign up here.

THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).

Free Sample: The Bogotá Puzzles

“Mathematics, besides being beautiful and useful, is fun. I hope [my book] brings mathematical joy to many.”

—Bernardo Recamán, The Bogotá Puzzles

Dover Publications occasionally posts free samples from some of their wonderful collection of books. This month’s sampler includes several puzzles from The Bogotá Puzzles by Bernardo Recamán.

Inspired by such illustrious collections as The Canterbury Puzzles, The Moscow Puzzles, and The Tokyo Puzzles. Colombian mathematician and professor Bernardo Recamán assembled these 80 brainteasers, word problems, sudoku-style challenges, and other math-based diversions while living and working in Bogotá.


If you’d like to receive future Dover Sampler emails, you can sign up here.

THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).

The Gerrymander Math Project

With a big election on the horizon, now is a great time to talk about the math of politics.

Does “One person, one vote” make a fair democracy?

Or does it give the majority license to trample a minority?

How can planners arrange voting districts to give everyone the best representation? And is that really what politicians would do, if they had the choice?

Try the Gerrymander Project with your students to investigate these questions and spark real-world mathematical discussion.

First, Create a Map

[Or buy a copy of my printable activity guide, The Gerrymander Project: Math in the World of Politics, which includes a prepared city map with more detailed instructions, answers, and journaling prompts. My publisher has extended the 10% discount code TBLTOP10 through to Election Day, 3 November 2020.]

  • Print a blank hundred chart or outline a 10×10 square on grid paper. This represents your city. Give it a name.
  • Pull out your colored pencils. Choose one color for your city’s Majority Party and another for the Minority Party.
  • Color 10 squares in a neutral color for non-voting areas. These might be malls or parks or the downtown business district — your choice.
  • Color the remaining 90 blocks in a random distribution so that 60% are the Majority color and 40% the Minority. How will you choose which squares to make which colors? Can you think of a way to use dice or playing cards to make your choices random, yet still get the right proportion?

Slip your finished map into a clear page protector, so you can mark on it with dry-erase markers. Or make several copies, so you can write on them without destroying the original.

Then Gerrymander Your City

“Gerrymandering” is the American political tradition of adjusting the voting district boundaries to favor one’s own party at the expense of one’s opponents.

The city has hired you to mark out 10 new voting districts of 9 squares each (not counting the neutral squares, which can go in any district). The squares in each district must touch side-to-side, not just meet at a corner.

So now you get to play “political hack.”

First, see how fair you can make the map:

  • What happens if you ignore the party colors and make your districts as compact as possible, so the people living nearest to each other vote together? Will the Majority Party always win?
  • Can you give all your voters a proportional representation? Both parties should win the number of districts that most closely matches their percentage of the voting population.

Next, try your hand at gerrymandering, but make sure all the squares in each district stay connected. Can you create ten voting districts that will guarantee:

  • A come-from-behind triumph for the Minority Party? They need to carry at least six districts to wrest control of the City Council from their opponents.
  • The greatest possible margin of victory for the Majority Party? Can you keep the Minority from winning any districts at all?

Share Your Thoughts

I’d love to hear your students’ reaction to this project. Please share in the comments section below.

For myself, the more I play with this project, the more I admire the work done by the framers of the U.S. Constitution. Our Electoral College divides the country into “districts” based on state boundaries, giving each a vote roughly proportional to its population — but in a way that slightly strengthens the Minority Party. The system may not be perfect, but it’s done an amazing job through the centuries of maintaining a balance of power, making sure that neither major political party can destroy the other.

Which is NOT to say that our country always protects the rights of true minorities. Clearly, that’s an ongoing struggle.

But overall, the political parties stay relatively balanced, making for a stable government. After more than two centuries, we still have, as Ben Franklin said, “a republic, if you can keep it.”

Kenken is Mathematical Play

It’s back-to-school time here in the States. And that means it’s time for the Kenken Classroom Newsletter. Yay for math puzzles!

KenKen arithmetic puzzles build mental math skills, logical reasoning, persistence, and mathematical confidence.

Free via email every Friday during the school year.

What a great way to prepare your children for success in math!

Sign up anytime:

Click Here for KenKen Classroom Newsletter

Continue reading Kenken is Mathematical Play

2020 Mathematics Game — Join the Fun!

New Year’s Day

Now is the accepted time to make your regular annual good resolutions. Next week you can begin paving hell with them as usual.

Yesterday, everybody smoked his last cigar, took his last drink, and swore his last oath. Today, we are a pious and exemplary community. Thirty days from now, we shall have cast our reformation to the winds and gone to cutting our ancient shortcomings considerably shorter than ever. We shall also reflect pleasantly upon how we did the same old thing last year about this time.

However, go in, community. New Year’s is a harmless annual institution, of no particular use to anybody save as a scapegoat for promiscuous drunks, and friendly calls, and humbug resolutions, and we wish you to enjoy it with a looseness suited to the greatness of the occasion.

— Mark Twain
Letter to Virginia City Territorial Enterprise, Jan. 1863
quoted in Early Tales & Sketches, Vol. 1: 1851-1864 (affiliate link)

If you’d like to enjoy a mathematical New Year’s Resolution, may I recommend Evelyn Lamb’s Math Reading Challenge? I haven’t decided if I’m going to follow along, but it does look like fun.

Meanwhile, I do resolve to challenge myself with more math puzzles this year. Would you like to join me?

Here’s a great way to start: with the 2020 Mathematics Game!

Click here to continue reading.

Math That Is Beautiful

One of the sections in my book Let’s Play Math: How Families Can Learn Math Together — and Enjoy It encourages parents to make beautiful math with their children.

Do you have trouble believing that math can be beautiful?

In “Inspirations,” artist Cristóbal Vila creates a wonderful, imaginary work studio for the amazing M.C. Escher. You’ll want to view it in full-screen mode.

How many mathematical objects could you identify?

Vila offers a brief explanation of the history and significance of each item on his page Inspirations: A short movie inspired on Escher’s works.

Read about the inspirations, and then try making some math of your own.

“I looked into that enormous and inexhaustible source of inspiration that is Escher and tried to imagine how it could be his workplace, what things would surround an artist like him, so deeply interested in science in general and mathematics in particular. I imagined that these things could be his travel souvenirs, gifts from friends, sources of inspiration…”

—Cristóbal Vila
Inspirations: A short movie inspired on Escher’s works

Playful Math Education Carnival 130

Play. Learn. Enjoy!

Welcome to the 130th edition of the Playful Math Education Blog Carnival, a feast of delectable tidbits of mathy fun.

The Playful Math Carnival is like a free online magazine devoted to learning, teaching, and playing around with math. It’s back-to-school time in the U.S., so this month’s edition focuses on establishing a creative math mindset from preschool to high school.

You’re sure to find something that will delight both you and your child.

By tradition, we start the carnival with a puzzle in honor of our 130th edition. But if you would like to jump straight to our featured blog posts, use our handy Table of Contents.

Click here for all the mathy goodness!