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!

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!

Math Game Monday: Operations

This game offers students in upper-elementary and beyond plenty of practice with mental math and the order of operations.

“Operations” is an excerpt from Prealgebra & Geometry: Math Games for Middle School, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

The Math Game Monday posts will be available for one week only. If you missed this one, explore the Topic Tag links in the sidebar. There are more than forty free games scattered around the blog. Have fun playing math with your kids!

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 ❯

Math Game Monday: Salute

Help children review times-table facts while they practice the inverse relationship between multiplication and division.

Salute may be the only game in my books where speed is a factor. Players should be closely matched in their skill level — or use the House Rule that calls for taking turns.

“Salute” is an excerpt from Multiplication & Fractions: Math Games for Tough Topics, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

The Math Game Monday posts will be available for one week only. If you missed this one, explore the Topic Tag links in the sidebar. There are more than forty free games scattered around the blog. Have fun playing math with your kids!

Limited Time Book Deals

Do you want to help your children master problem-solving skills?

Check out my temporary online store for anyone who missed the Kickstarter.

Through the end of September, you can place a preorder for the early-release edition of Word Problems from Literature, along with the Word Problems Student Workbook and exclusive Audio Commentary (or any of my other books or printable math activity guides).

I’ll lock down the preorder store when I’m ready to send the Kickstarter order to my printer.

Books will be delivered with the Kickstarter orders: Digital items in October, physical books by the end of December.

Shop Now ❯

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.

      Numberless Word Problems

      As I mentioned yesterday, my new book includes links to online resources to help you play with word problems. So this week, I’m sharing a few of my favorites.

      Visit the Kickstarter

      Today we examine a time-tested method to help kids reason about math: Leave out the numbers.

      First up, there’s Brian Bushart’s numberless problem bank for young students. Then we’ll look at Farrar Williams’s modern revision of a math teaching classic with problems for upper-elementary and middle school students.

      Have fun thinking math with your kids!

      Word Problem Bank

      Word problems are commonplace in mathematics classrooms, and yet they regularly confound students and lead to frustrated teachers saying things like:

      • “They just add all the numbers! It doesn’t matter what the problem says.”
      • “They don’t stop to think! They just start computing as soon as they’re done reading the problem.”

      Brian Bushart offers a collection of ready-to-go slide presentations that walk through the steps of making a word problem make sense.

      Visit the Site

      Math With No Numbers

      Discover Farrar Williams’s book Numberless Math Problems: A Modern Update of S.Y. Gillian’s Classic Problems Without Figures, available in ebook or paperback.

      Williams writes: “In order to answer the question, they’ll have to explain it, because the problem doesn’t give you anything to calculate with. The only way to answer is by explaining your process. See how sneaky a numberless problem is? It makes students really think about the process of solving the problem.”

      Find Out More

      “When students face a word problem, they often revert to pulling all the numbers out and “doing something” to them. They want to add, subtract, multiply, or divide them, without really considering which operation is the right one to perform or why.

        “When you don’t have numbers, it sidesteps that problem.

          “For students who freeze up when they see the numbers, this can be a really good way to get them to think about their process with math.”

          —Farrar Williams, Math With No Numbers

          CREDITS: Feature photo (top) by saeed karimi via Unsplash.com.

          Problem Solving with James Tanton

          At the back of my new Word Problems from Literature book, I’ve included an appendix with links to recommended online resources.

          Check in on the Kickstarter

          So I thought this week, I’d share some of my favorites with you. First up: Problem Solving Tips from James Tanton.

          You may know Tanton from the popular Exploding Dots and other activities at the Global Math Project website. But he’s been busy for decades sharing the delight and the beauty of the subject. He currently serves as the Mathematician-at-Large for the Mathematical Association of America.

          Read on to discover several of Tanton’s best problem-solving tips for middle school and older students.

          Have fun exploring math with your kids!

          How to Think like a School Math Genius

          In this 4-video series, Tanton presents five key principles for brilliant mathematical thinking, along with loads and loads of examples to explain what he means by each of them. A call for parents and teachers to be mindful of the life thinking we should foster, encourage, promote, embrace and reward — even in a math class!

          Watch the Videos

          Two Key — but Ignored —Steps to Solving Any Math Problem

          How many degrees in a Martian circle?
          Every challenge or problem we encounter in mathematics (or life!) elicits a human response. The dryness of textbooks and worksheets in the school world might suggest otherwise, but connecting with one’s emotions is fundamental and vital for success — and of course, joy — in doing mathematics.

          Read the Article

          MAA AMC Curriculum Inspirations

          Essays and videos showing how to approach math puzzles in a way that a) is relevant and connected to the curriculum, and b) revels in deep, joyous, mulling and flailing, reflection, intellectual play and extension, insight, and grand mathematical delight.

          Scroll down and start with the Ten Problem-Solving Strategies.

          Download the Puzzles

          Think Puzzles and Think Cool Math

          Here are some essays illustrating astounding tidbits of mathematical delight. And here are some purely visual puzzles to surprise.

          Explore and Enjoy

          “The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.

            “There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.

              “Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”

              —James Tanton

              CREDITS: Feature photo (top) by Ian Stauffer via Unsplash.com.

              6th Grade Minimalist Math Curriculum

              For details on using a Minimalist Math Curriculum, see my earlier post How To Make Time for Exploration.

              If you’re teaching or homeschooling students in 6th grade, here’s the new minimalist curriculum link:

              As I mentioned in my earlier post, a minimalist curriculum can be a great way to free up time for playing math games and exploring enrichment activities (like these).