Playful Math Education 162: The Math Games Carnival

Welcome to the 162nd edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

Bookmark this post, so you can take your time browsing.

There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle/activity in honor of our 162nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Try This Puzzle/Activity

The number 162 is a palindromic product:

162 = 3 x 3 x 2 x 3 x 3
and 162 = 9 x 2 x 9

  • How would you define palindromic products?
  • What other numbers can you find that are palindromic products?
  • What do you notice about palindromic products?
  • What questions can you ask?

Make a conjecture about palindromic products. (A conjecture is a statement you think might be true.)

Make another conjecture. How many can you make? Can you think of a way to investigate whether your conjectures are true or false?

Click here for all the mathy goodness!

Math Play for All Ages

Are you looking for new ways to explore math with your kids?

Would you like an easy, no-prep resource for creative problem-solving, number play, math art, word problems, mini-essays, math poetry, geometry investigations, research projects, and much more?

I’ve just launched a Kickstarter project for people to preorder my new book, 312 Things To Do with a Math Journal. It just might transform your child’s experience of math.

Visit the Playful Math Journaling Kickstarter

In a math journal, children explore their own ideas about numbers, shapes, and patterns through drawing or writing in response to a question. Journaling teaches them to see with mathematical eyes. Not just to remember what we adults tell them, but to create their own math.

Scroll down the Kickstarter project page to download the free 16-page printable “Math Journaling Sampler” file. It includes one of my all-time favorite math activities. [The Sampler will remain available after the Kickstarter campaign ends.]

If you like what you see, I’d love to have your support. Please help share the project and encourage everyone to play math with their kids!

For more math journaling tips and information, scroll through the Math Journals posts on my blog.

What Is Multiplication, Anyway?

At some point during the process of teaching multiplication to our children, we really need to come to terms with this question:

What IS multiplication?

Did your device hide the video? Find it on YouTube here.

“What’s my answer? It’s not one that society’s going to like. Because society expects — demands, even — that mathematics be concrete, real-world, absolute, having definitive answers.

    I can’t give a definitive answer.

      Multiplication manifests itself in different ways. So maybe the word ‘is’ there is just too absolute. And it’s actually at odds with what mathematicians do.

        Mathematicians do attend to real-world, practical scenarios — by stepping away from them, looking at a bigger picture.”

        —James Tanton, What is Multiplication?

        For Further Study

        You may also enjoy these posts from my blog archive:

        Memorizing the Times Table: A Life Skills Approach

        Continuing on my theme of times table facts, here’s the inimitable James Tanton:

        Did your device hide the video? Find it on YouTube here.

        “If our task is to memorize this table, please make it about mathematics — about thinking your way through a challenge, and what can I do to make my life easier.”

        —James Tanton, Making Memorising Multiplication Facts (if one really must) a meaningful Life Skill Lesson

        For Further Study

        You may also enjoy my blog post series about working through the times tables, paying attention to mathematical relationships (and a bit of prealgebra) along the way.

        Times Tables Series

        Click the button to see the whole series. Scroll down to the first post to go through it in order.

        What Are Mixed Numbers?

        I just discovered a fascinating fact: In some places in the world, mixed numbers apparently don’t exist.

        So that made me curious about my blog readers:

        • Did you learn about mixed numbers in school?
        • Do you ever use mixed numbers in daily life?
        • Are your children learning to work with them?

        And if you DO know mixed numbers, can you simplify this mess:

        [If you enjoy dry math humor, the answer is worth the work.]

        Continue reading What Are Mixed Numbers?

        Mathematical Days of Christmas

        Enjoy this bit of seasonal fidgeting from Vi Hart.

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

        Did your device hide the video? Find it on YouTube here.

        For More Holiday Math

        CREDITS: Lamppost photo (top) by Aaron Burden via

        Have a Mathematical Thanksgiving Dinner

        With the pandemic still raging, most of us will have to adapt our normal holiday traditions to fit the new reality. We may not be able to have a big family gathering (except over Zoom), but we can still enjoy great food.

        So for those of you who are planning ahead, here is a mathematician’s menu for next week’s Thanksgiving dinner.

        Optimal Potatoes

        Green Bean Matherole

        Borromean Onion Rings

        Thanksgiving Turduckenen-duckenen

        And for Dessert

        May I suggest some of Don Cohen’s Infinite Cake?

        Click here for cake

        CREDITS: “Thankful” photo (top) by Pro Church Media via Food videos by mathemusician/doodler Vi Hart.

        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