Playing Math with Michael and Nash

Michael and Nash have been creating and posting new math games with astonishing regularity throughout the pandemic. Their YouTube channel is a great resource for parents who want to play math with elementary-age children.

Today’s entry: Closest to Ten, a quick game for addition and subtraction fluency with a tiny bit of multiplication potential.

And here’s one of my favorites for older players: Factor Triangles, a card game for 2-digit multiplication.

Check out their channel, and have fun playing math with your kids!

Visit Michael and Nash on YouTube

That’s Mathematics

Here’s a bit of fun I found on YouTube. Happy Friday!

Mathematicians and maths educators in order of appearance:

Eddie Woo @misterwootube
Hannah Fry @FryRSquared
James Tanton @jamestanton
Chris Smith @aap03102
Bobby Seagull @Bobby_Seagull
Jo Morgan @mathsjem
David Wees @DavidWees
Matt Parker @standupmaths
Michael Stevens @tweetsauce
Lieven Schiere @lievenscheire
Ben Sparks @SparksMaths
Rob Eastaway @robeastaway
Nira Chamberlain @ch_nira
Ed Southall @edsouthall
Steven Strogatz @stevenstrogatz
Simon Pampena @mathemaniac
Rachel Riley @RachelRileyRR
Alex Bellos @alexbellos
Simon Singh @SLSingh
Katie Steckles @stecks
Craig Barton @mrbartonmaths
Kyle Evans @kyledevans

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

Math Makes Sense — Let’s Teach It That Way

I had forgotten this video, and then rediscovered it yesterday and loved it just as much as ever. Perhaps you’ll enjoy it, too — especially if you think of yourself as “not a math person.”

Annie Fetter is talking to classroom teachers, but her message is just as important for homeschoolers. Math is all about making sense. Let’s help our kids see it that way.

“Sense-making is the first mathematical practice for a reason. If we don’t do this one, the rest of them don’t matter. If we’re not doing this, our children are not going to learn mathematics.”

—Annie Fetter
Sense Making: It isn’t Just for Literacy Anymore

You can download the notes for Fetter’s updated session on sense-making and find several links to wonderful, thought-provoking posts on her blog:

How Can We Encourage Sense-Making?

Here are some ideas from Fetter’s updated notes, which expand on her comments in the video above:

  • Get rid of the question. Literally.
  • Ask students “What could the question be?”
  • Get rid of the question and the numbers.
  • Give the answer.
  • Or give several answers.
  • Ask about ideas, not answers.
  • Ask “Why?” or “How did you know?” or “How did you decide that?” or “Tell me more about that.”
  • Use active reading strategies.

Get this free downloadable poster from Teacher Trap via Teachers Pay Teachers.

A Few Resources to Practice Sense-Making

In no particular order…

“I implore you, stop ‘cracking the math code.’ Make sense-making the focus of every single thing you do in your math classroom.”

—Annie Fetter
Sense Making: It isn’t Just for Literacy Anymore

And if you haven’t seen it before, don’t miss Annie Fetter’s classic video “Ever Wonder What They’d Notice?”

CREDITS: “Building a rocket ship” photo by Kelly Sikkema via Unsplash. “Reading is thinking” poster by Teacher Trap via Teachers Pay Teachers.

Mathematics Is Worthy

“When I began my college education, I still had many doubts about whether I was good enough for mathematics. Then a colleague said the decisive words to me: it is not that I am worthy to occupy myself with mathematics, but rather that mathematics is worthy for one to occupy oneself with.”

Rózsa Péter
Mathematics is beautiful
essay in The Mathematical Intelligencer

Rózsa Péter and the Curious Students

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.
The schoolchildren that I have taught in the past were always attuned to this, and so I have also learned much from them.
It never would have occurred to me, for instance, to talk about the Euclidean Algorithm in a class with twelve-year-old girls, but my students led me to do it.
I would like to recount this lesson.
What we were busy with was that I would name two numbers, and the students would figure out their greatest common divisor. For small numbers this went quickly. Gradually, I named larger and larger numbers so that the students would experience difficulty and would want to have a procedure.
I thought that the procedure would be factorization into primes.
They had still easily figured out the greatest common divisor of 60 and 48: “Twelve!”
But a girl remarked: “Well, that’s just the same as the difference of 60 and 48.”

“That’s a coincidence,” I said and wanted to go on.
But they would not let me go on: “Please name us numbers where it isn’t like that.”
“Fine. 60 and 36 also have 12 as their greatest common divisor, and their difference is 24.”

Another interruption: “Here the difference is twice as big as the greatest common divisor.”
“All right, if this will satisfy all of you, it is in fact no coincidence: the difference of two numbers is always divisible by all their common divisors. And so is their sum.”
Certainly that needed to be stated in full, but having done so, I really did want to move on.
However, I still could not do that.
A girl asked: “Couldn’t they discover a procedure to find the greatest common divisor just from that?”

They certainly could! But that is precisely the basic idea behind the Euclidean Algorithm!
So I abandoned my plan and went the way that my students led me.

— Rózsa Péter
quoted at the MacTutor History of Mathematics Archive

For Further Exploration

Note: When the video narrator says “Greatest Common Denominator,” he really means “Greatest Common Divisor.”

CREDITS: “Pink toned thoughts on a hike” photo courtesy of Simon Matzinger on Unsplash.

Mindset for Learning Math

Playing with a new image editor, I came across this Winston Churchill quote. What a great description of how it feels to learn math!

If you have a student who struggles with math or is suffering from a loss of enthusiasm, check out Jo Boaler’s free online course on developing a mathematical mindset:

Or explore some of the playful activity ideas for all ages in her Week of Inspirational Math.

How to Talk Math With Your Kids

A friend shared this video, and I loved it! From Kent Haines, a father who happens to also be a math teacher…

“I hope that this video helps parents find new ways of interacting with their kids on math topics.”

Kent Haines

More from Kent Haines

Advice and Examples of Talking Math with Kids

Danielson-Talking Math

If you enjoyed Kent’s video, you’ll love Christopher Danielson’s book and blog.

It’s a short book with plenty of great stories, advice, and conversation-starters. While Danielson writes directly to parents, the book will also interest grandparents, aunts & uncles, teachers, and anyone else who wants to help children notice and think about math in daily life.

“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.
“You don’t need to love math. You don’t need to have been particularly successful in school mathematics. You just need to notice when your children are being curious about math, and you need some ideas for turning that curiosity into a conversation.
“In nearly all circumstances, our conversations grow organically out of our everyday activity. We have not scheduled “talking math time” in our household. Instead, we talk about these things when it seems natural to do so, when the things we are doing (reading books, making lunch, riding in the car, etc) bump up against important mathematical ideas.
“The dialogues in this book are intended to open your eyes to these opportunities in your own family’s life.”

— Christopher Danielson
Talking Math with Your Kids

CREDITS: “Kids Talk” photo (top) by Victoria Harjadi via Flickr (CC BY 2.0). “Parent Rules” by Kent Haines.

There Ain’t No Free Candy

Ah, the infinite chocolate bar. If only it could work in real life! But can your children find the mistake? Where does the extra chocolate come from?

Here’s a hint: It’s related to this classic brainteaser. And here’s a video from Christopher Danielson (, showing how the chocolate bar dissection really works.

Happy munchings!

CREDITS: Feature photo (top) by Yoori Koo via Unsplash. “Hershey Bar Math” video by Christopher Danielson via YouTube. The infinite chocolate gif went viral long ago, and I have no idea who was the original artist.

How to Break In Your New Math Journal

I love my new paperback math journal series. The books are sturdy, inexpensive, and fit nicely in my purse.

But as with any paperback book, these have one problem. How do I use them without cracking the spine?

When we exercise, we need to warm up our bodies with a bit of stretching to prevent injury. In the same way, we need to warm up a new book to protect it. The process is called “breaking it in.”

It only takes a few minutes to break in a paperback book:

Step by Step

Never force the book but help it limber up gradually, and it will serve you well.

Because my journals are working books, I take the breaking-in process a bit further than shown in the video:

(1) Set the book on its back and follow the process above. Press down each cover, but not completely flat — let it bend at the fold line, about 1 cm from the actual spine. Then press a couple pages at a time, alternating front and back, down flat on each cover.

(2) Flip through the pages of the book forward and backward to limber them up.

(3) Repeat the steps of the video. This time, gently lean the main part of the book away from the part you are pressing down. Aim for a 130–140 degree angle.

(4) Flip through the pages again. Even roll the book back and forth a bit — curving the cover and pages as if you’re trying to fold the book in half — to encourage flexibility.

(5) Repeat the breaking-in process one more time. This time, fold each section back as close to 180 degrees as it will go.

And you’re done!

The pages will still curve in at the fold line, where they connect to the spine of the book. You want that because it makes the book strong. But now they’ll also open up to provide a nice, wide area for writing or math doodling.

Beauty in Math: A Fable

Have you ever wondered what mathematicians mean when they talk about a “beautiful” math proof?

“Beauty in mathematics is seeing the truth without effort.”

George Pólya

“There’s something striking about the economy of the counselor’s construction. He drew a single line, and that totally changed one’s vision of the geometry involved.

“Very often, there’s a simple introduction of something that’s not logically within the framework of the question — and it can be very simple — and it utterly changes your view of what the question really is about.”

Barry Mazur
The Moral of the Scale Fable

CREDITS: Castle photo (top) by Rachel Davis via Unsplash. “A Mathematical Fable” via YouTube. Story told by Barry Mazur. Animation by Pete McPartlan. Video by Brady Haran for Numberphile.