The Colors-of-Fall Carnival: Playful Math #160

Welcome to the 160th 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 160th 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

Appropriately for an October carnival, 160 is an evil number.

A number is evil if it has an even number of ones in binary form. Can you find the binary version of 160? (Hint: Exploding Dots.)

160 is also a polyiamond number. If you connect 9 equilateral triangles side-to-side, a complete set of 9-iamond shapes would have 160 pieces.

But sets that large can be overwhelming. Try playing with smaller sets of polyiamonds. Download some triangle-dot graph paper and see how many different polyiamond shapes you can make.

What do you notice? Does it make you wonder?

What designs can you create with your polyiamonds?

Photo by Daiga Ellaby on Unsplash

Click here for all the mathy goodness!

Parents: Math Is Figure-Out-Able

I love listening to podcasts during my morning walk with the dogs. One of my favorites over the past year has been Pam Harris and Kim Montague’s Math is Figure-Out-Able podcast.

Figure-out-able. What a great word!

Figure-out-able sums up what I mean when I tell parents that math is “applied common sense.” Kids can use the things they know to figure out things they don’t yet know.

And figuring things out like that is fun, like a mental game where we play with the ideas of numbers, shapes, and patterns.

Usually, the podcast targets teachers, and the hosts try to show how they can help students learn to mathematize — to think mathematically. Over the past few weeks, however, Pam and Kim have been talking directly to parents about how to help their children learn math.

Continue reading Parents: Math Is Figure-Out-Able

Podcast: Real Math and Family Fun

Christy Thomas interviewed me for her Keep Calm and Mother On podcast. We had a wonderful chat. I think you’ll enjoy it:

Real Math and Family Fun with Denise Gaskins

“School math sometimes is more stress-inducing. Real math is more freeing and more joyful, and just more interesting.

    “Real mathematics is basically applied common sense.

      “Real mathematics is noticing patterns, seeing connections, figuring things out.

        “These are all things that you can do. You do them in other areas of your life. Real mathematics draws on those same abilities and focuses those abilities on numbers, shapes, and patterns.

          “Real mathematics is about solving puzzles. It’s about creative reasoning. These are the things you want your child to understand.”

          —Denise Gaskins, Real Math and Family Fun

          Go Listen to the Interview

          CREDITS: Feature photo (top) by Bruno Nascimento via

          Podcast: Math as a Nature Walk

          Pam Barnhill interviewed me for the Your Morning Basket podcast. We had a great talk. I think you’ll enjoy it:

          YMB #94 Math in Morning Time: A Conversation with Denise Gaskins

          “Let me give you this new vision. I want you to think of math as a nature walk.

            “There’s this whole world of interesting things. More things, more concepts, more ideas than you and your children would ever have time to explore. And everywhere you look, there’s something cool to discover.

              “If you explore this world with your children, you’re not behind. Wherever you are, you’re not behind because there is no behind. There’s only, “We’re going this direction.” Or, “Let’s move that way.” Or, “Hey, look what I found over here!”

                “And as long as your children are thinking and wondering, and making sense of the math they find, they’re going to learn. They’re going to grow.

                  “So what you want to do is, you want to embrace this adventure of loving God with all your mind and approach math with an attitude of playful exploration.

                    “And you know, you’ll be surprised how much fun thinking hard can be.”

                    —Denise Gaskins, Math in Morning Time

                    Go Listen to the Interview

                    CREDITS: Feature photo (top) by Jessica Rockowitz via

                    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.

                          The Principality of Mathematics

                          Here’s the full quote:

                          “The Principality of Mathematics is a mountainous land, but the air is very fine and health-giving, though some people find it too rare for their breathing. People who seek their work or play in this principality find themselves braced by effort and satisfied with truth.”

                          — Charlotte Mason, Ourselves

                          Charlotte Mason and Math

                          Math was not one of Charlotte Mason’s primary interests. She didn’t think or write as deeply about it as she did other subjects.

                          She even wrote, “It is unnecessary to exhibit mathematical work done in the P.U.S. as it is on the same lines and reaches the same standard as in other schools.”

                          This leaves us modern parents and teachers having to read our own interpretations into her words. It should be no surprise when we come to different conclusions. Someday, perhaps, I’ll publish my own vision for a Charlotte Mason approach to homeschooling math.

                          In the meantime, the following articles describe a method that allows even the youngest children to explore the Principality of Mathematics:

                          In the years since writing those posts, Sonya and Lacy combined all their ideas into an easy-to-implement program that I think Mason herself would have enjoyed. Here’s my review:

                          CREDITS: Quote background photo (top) by Kalen Emsley via

                          Not Attained by Chance

                          I’ve been collecting quotes about life and learning. They make great discussion-starters or essay/journaling prompts.

                          This is one of my favorites.

                          “Learning is not attained by chance, it must be sought for with ardor and attended to with diligence.”

                          —Abigail Adams

                          [Aw, face it. They’re all my favorites. That’s why I collect them!]

                          If you like quotes, too, you might enjoy browsing my collection:

                          Math & Education Quotations

                          Math as a Verb

                          Here’s the full quote:

                          I like to play games. Almost any type of game.

                          I also like to play math.

                          If you’ve known enough mathematicians, you may have noticed that this isn’t unusual. I’m not sure if a love of games and puzzles among mathematicians exceeds a love of music among mathematicians, but both are strong and intersect.

                          Math in play is also a way of teaching mathematics. I think that as a metaphor, it best describes how I want to teach math.

                          I am constantly seeking ways to get my students thinking about math as a verb. It is about doing, not just about having right answers or the end product.

                          Games help set the culture I want to develop: Teaching students that multiple approaches and strategies are valued; trying is safe; and conversations about why, how, and discovery are the goals.

                          —John Golden
                          Yes, Playing Around

                          CREDITS: “Football outside Jakarta” photo by Robert Collins on Unsplash.

                          FAQ: Playful Math for Older Students

                          My students are so busy that time-consuming math projects are a luxury. How is it possible for older kids to play with mathematics?

                          Too often, the modern American school math curriculum is a relentless treadmill driving students toward calculus. (Does this happen in other countries, too?)

                          But that’s definitely not the only way to learn. For most students, it’s not the best way, either.

                          Here are a few ideas to get your older children playing with math…

                          Continue reading FAQ: Playful Math for Older Students