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!

New Project: The Tabletop Math Games Collection

Coming Soon! On January 30th, I’ll be launching a brand new book series, the Tabletop Math Games Collection.

And the Kickstarter prelaunch page is now live. That means you can sign up to get an email from Kickstarter as soon as the campaign launches:

Visit the Prelaunch Page ❯
(free Kickstarter account required)

Test Out 4 Free Sample Games

Math games build mental flexibility and strategic reasoning in players of all ages. And even people who hated math in school can enjoy the friendly challenge of a game.

I’ve put together a free printable sampler file, with four ready-to-play card games you can enjoy today.

I think you’ll love it!

Download the Sample File ❯

Help Your Kids Learn Math the Playful Way

  • Are you a parent trying to help your child learn math?
  • Or a teacher looking for ways to encourage creative thinking?
  • Or a gamer ready to try something new with your friends?

Then the Tabletop Math Games Collection is perfect for you.

These are NOT the typical memory-and-speed-based math games you’ve probably seen online, but true battles of wit and skill (plus a bit of luck). Even the preschool games can be fun for adults, too.

Most of the games take only seconds to learn and less than 15 minutes to play, making them perfect ice-breakers for family gatherings, classroom warmups, or for launching a group game night.

Don’t miss the fun!

Hit the button to visit the prelaunch page and sign up for notifications:

Get Notified ❯

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!

Get a Weekly Dose of Playful Math

Our leaves haven’t started to turn yet, but summer’s on the wane, farmers are busy with harvest, and the back-to-school rush has calmed down into a daily routine.

But if you’re like me, you keep tweaking that routine, constantly looking for the perfect balance for your family or classroom. I especially love to discover easy ways to add more playful math to our schedule.

So here’s a collection of sites that offer fresh math resources on a weekly or monthly basis throughout the school year.

Which one will you try?

KenKen Classroom

Every week, they’ll email you a set of free KenKen arithmetic puzzles for all ages. As the challenge level subtly shifts week to week, students develop their math and logical thinking skills without even knowing it.

Subscribe ❯

#MathStratChat

Pose an interesting math problem. How can you figure it out? What else could you do? How many different ways can you find? Which strategy do you like best for this problem?

Follow Pam Harris on your favorite social media site to get a new problem every Wednesday.

Choose a Problem ❯

The Parallel Universe

Dr Simon Singh, author of the No. 1 bestseller Fermat’s Last Theorem and The Simpsons and Their Mathematical Secrets has created a set of weekly maths challenges – just 15-30 minutes of interesting, fun and challenging tidbits of mystery and history, activities and oddities, puzzles and problems.

Help students expand their mathematical horizons beyond the school curriculum and build strong mathematical thinking skills. Stretch your brain every week!

Learn More ❯

Playful Math: Getting Students To Write Their Own

To wrap up our week of exploring the resources from Word Problems from Literature, let’s talk about getting students to write their own math.

Check in on the Kickstarter

First up, I’m sharing an excerpt from the Word Problems Student Workbook. The “Story Problem Challenge” is one of my favorite math club activities.

Following that, you’ll find an amazing online mathemagical adventure for middle school: The Arithmetiquities. It’s great fun, and a great inspiration for students to create their own math stories.

Have fun writing math with your kids!

The Story Problem Challenge

What do you get when you cross a library book or favorite movie with a math worksheet? A great alternative to math homework!

The rules are simple:

(1) Choose a worksheet calculation to be the basis for your word problem.

(2) Solve the calculation.

(3) Consider where these numbers could make sense in your book or movie universe. How might the characters use math? What sort of things would they count or measure? Do they use money? Do they build things, or cook meals, or make crafts? Do they need to keep track of how far they have traveled? Or how long it takes to get there?

(4) Write your story problem.

To make the game easier, you may change the numbers to make a more realistic problem. But you must keep the same type of calculation. For example, if your worksheet problem was 18÷3, you could change it to 18÷6 or 24÷3 or even 119÷17 to fit your story, but you can’t make it something like 18−3.

Remember that some quantities are discrete and countable, such as hobbits and fireworks. Other quantities are continuous, such as a barrel of wine or a length of fabric. Be sure to consider both types when you are deciding what to use in your problem.

Then share your problem with friends, and you try their problems. Can you stump each other?

A Note about Copyright and Trademarks

Old books are in the public domain, so you can always use characters like Robin Hood, Sherlock Holmes, or Winnie-the-Pooh (but not the newer Disney version with the red jacket). But most books and movies are the protected intellectual property of their authors or estates, or of the company who bought those rights.

When you write problems for your own private use, feel free to use your favorite characters from any story. That’s like fan fiction, secret, just for your own pleasure.

But if you decide to share your creation beyond your own home or classroom, then be sure to “genericize” it first. Change or remove the proper names, using general descriptions instead.

For example, if you love the Harry Potter series, you might want to use Harry or Hermione in your story problems. Instead, write about “the boy wizard destined to fight an evil sorcerer.” Or “the bright young witch who can master any spell.”

Or if you like the Star Wars movies, you might write about “an interstellar justice warrior with an energy sword.” Or “an alien master of martial arts training a cocky but inexperienced apprentice.”

We’d love to add your story to the Student Math Makers Gallery.

The Arithmetiquities

When the world of Sfera is threatened by the machinations of a malevolent sorcerer, it will be up to a band of unlikely heroes to become the brightest light in the darkness.

The adventurers fan out across the land to find and retrieve the Arithmetiquities, a set of ancient mathemagical artifacts.

The Arithmetiquities is a fantasy adventure story told through a sequence of 36 mathematical puzzles.

Join the Adventure

“Though it is still before sunrise, Lumparland Harbor is already bustling. Sailing ships moor at the misty docks, bringing travelers and goods to the seaside town. Three dwarves disembark from different ships, each adventurer returning home from some faraway locale. The three women gather at the end of the pier.

    “The strangers discover that they all live along the main road that leads from the harbor, so they decide to split the cost of a wagon. Egga lives 10 miles away, Floora lives 20 miles away, and Greeta lives 30 miles away. The wagon ride costs $1.50 per mile regardless of the number of passengers.

      “How much should each of the adventurers pay so that each one has a fair fare?”

      —Jason Ermer, “Lumparland Harbor,” The Arithmetiquities Chapter I

      CREDITS: Feature photo (top) by Hannah Olinger via Unsplash.com.

      How To Make Time for Exploration

      Perhaps the most common objection I hear to using math games and enrichment activities is, “I don’t have the time. I can’t even get through our regular math book!”

      Well, here’s one possible solution: Use a “Minimalist Math” outline to guide your instruction, turning your regular textbook into a backup resource, teaching only the topics your children don’t already know, leaving more time free for exploration and playful discovery.

      Minimalist Math: Getting Down to Basics

      Michelle at ResearchParent.com condensed the elementary math curriculum down to 360 problems per year, just 10 per week.

      Take just a few puzzles each day, and talk math with your kids:

      • What do they notice in the problem?
      • Does it remind them of anything?
      • How might they try to figure it out?
      • Does it make them wonder about numbers, shapes, or patterns?

      Use colorful markers on a whiteboard for low-stress exploration. If your children can solve a problem and explain their reasoning, you don’t need to study that topic. When they get stuck, ask leading questions to help them think it through.

      If you’re both stymied, that’s when you pull out your regular textbook (or look the topic up online).

      Practice with Games

      Of course, children still need plenty of practice to master the math facts and solidify their knowledge.

      Since you’re not spending as much time on lessons and homework, you can plan on playing lots of math games. Games are a fun, low-stress way to firm up math skills.

      Check out My Best (Free) Math Games for All Ages, and follow the Math Game Monday posts on my blog.

      Read Library Books

      To enrich your child’s mind with the great ideas of mathematics and whet their appetite for learning, nothing beats a “living” math book.

      A living book is one that brings our minds into direct contact with the great ideas of life.

      Check out my Math with Living Books lists to get started, and ask your librarian for more suggestions.

      For Older Students

      Michelle’s Minimalist Math Curriculum goes through 6th grade (so far). But you could use the Corbettmaths 5-a-Day problems in the same way for older students.

      And for enrichment activities to fill up your free math time, I can’t think of a better resource for all ages than the NrichMaths website.

      “When I first started homeschooling, math became the most overwhelming, unpleasant part of our day. As someone who loves math, I didn’t want to continue on a path that was leading to such bad attitudes.

      “My Minimalist Math Curriculum covers the same breadth of topics as a traditional curriculum without all the repetition. You are welcome to use what I created in whatever way serves your family.”

      Michelle, Research Parent
      Mathematics Activities for Kids

      CREDITS: Photos by Aron Visuals, Andrew Ebrahim, and Melissa Askew via Unsplash.com.

      New to Playful Math? Start Here

      Do you want your children to enjoy learning math? Teach them how to play!

      After the troubles of recent years, it’s even more important for families to play together. So I’ve made the ebook version of Let’s Play Math Sampler: 10 Family-Favorite Games for Learning Math Through Play permanently free.

      What a great way to introduce your child to the joy of learning!

      With excerpts taken from my most popular books, the Let’s Play Math Sampler features ten kid-tested games covering math concepts from counting to prealgebra.

      Pick up a copy today, and make math a playful family adventure.

      Download Your FREE Copy

      Or Shop Your Favorite Online Store
      … or request a copy from your library or local bookshop.


      “Math is so many things — beauty, structure, problem solving, communication, language, creativity — but here’s what I’ve learned as I’ve tried to help my children develop positive relationships with math: It All Begins With Play. Anything by Denise Gaskins is a fantastic place to start. These books are filled with the perfect combination of perspective and practicality.”

      —Michele Johnson, Instagram post

      How To Respond to Your Child’s Math Writing

      In previous posts, I encouraged parents, homeschoolers, and teachers to explore the world of math and introduced one of my favorite learning tools, the math journal. Then I shared several of my favorite types of journaling prompts to get your kids started writing about math.

      Math journal prompts offer a wide range of options for students to explore. Most of the prompts do not have a “right” or “wrong” answer. Our goal is to root around in some small corner of the world of math, to lift a stone and peek underneath it, just to see what we can find.

      The idea that being good at math means finding the right answers is a huge myth. Of course, many problems in math do have a single right answer. But even for those problems, the answer is not the real math of the problem.

      Math is all about thinking.

      It’s like taking a road trip. You may have a destination, but there are many paths you could take to get there. Different students may take different paths — they may think about the problem in different ways.

      It’s this reasoning that is the real math, and the right answer is just a side effect of reasoning well.

      Continue reading How To Respond to Your Child’s Math Writing

      5 Ways To Enrich Your Student’s Experience of Math

      In previous posts, I encouraged parents, homeschoolers, and teachers to explore the world of math and introduced one of my favorite learning tools, the math journal.

      But you may be wondering, what can my students do with their journal? How do I find good math prompts?

      Here are five different ways your children can explore math through writing, classified by the type of reasoning involved.

      #1: Game Prompts

      Ask your children to play a number or strategy game and then write about it.

      Game prompts break through the idea that math is dull and boring. They help students develop a positive attitude toward math while practicing their number skills or strategic thinking.

      Continue reading 5 Ways To Enrich Your Student’s Experience of Math

      What Is a Math Journal?

      In my previous post, I encouraged parents, homeschoolers, and teachers to think of math as a nature walk through an infinite world of wonder.

      A math journal is a record of your child’s journey through this world of mathematics.

      In a math journal, children explore their own concepts 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.

      Journaling brings math back into the liberal arts. It makes abstract ideas accessible and stretches children’s understanding, building math fluency and creating a solid foundation for future learning.

      Continue reading What Is a Math Journal?