Celebrating Spring with Playful Math Carnival 172

Posted on by Denise Gaskins
Playful Math Carnival 172

Welcome to the 172nd edition of the Playful Math Blog Carnival, a buffet 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.

The carnival went on hiatus for a couple of months due to unexpected life issues facing our volunteer hosts. But we’re back now, and ready to celebrate!

By tradition, we start the carnival with a puzzle in honor of our 172nd edition. But if you’d rather jump straight to our featured blog posts, click here for the Table of Contents.

Try This: Lazy Caterers and Clock-Binary Numbers

172 is a lazy caterer number: Imaging a caterer who brought a single large pie to serve the whole party. He needs to cut it into as many pieces as he can, using the fewest (straight) cuts he can get away with.

  • If each guest gets one piece of pie, what sizes of parties (numbers of people) can the lazy caterer serve?
  • Can you find a pattern in the lazy caterer sequence?

But for those of you who have followed the carnival for years, you may remember we played with the lazy caterer back in Playful Math 106. (That time, the caterer was serving pizza.) So here’s a bonus activity we’ve never done before…

The first several stages of a pattern are as follows:

Clock Binary pattern image

  • What do you notice about this pattern of shapes?
  • What is the next shape in the sequence?
  • Can you figure out how the shape below fits into the pattern?

Clock Binary puzzle image

This pattern sequence was named clock binary by its creator, noelements-setempty.

  • What questions can you ask about this sequence?
  • How are these shapes like the binary numbers?
  • How are they different?

Click here for all the mathy goodness!

Musings: A Common Misconception

Posted on by Denise Gaskins
Father and son thinking together about a math problem

One of my favorite podcasts to listen to is Pam Harris’s Math Is Figure-Out-Able because she puts so many of my thoughts into words.

For example:

“We have a misconception in math education that we think we need to teach methods so that kids can answer the craziest kind of a particular problem.

    “We would be far better served to teach kids to think about the most common kinds of questions WELL, and let the cranky ones go to ChatGPT. Because they’ll recognize the sense of the answer.

      “Let technology handle the crankiest, and REASON about the rest of them.”

      —Pam Harris,
      the Math is Figure-out-able Fractions Challenge

      Well, I do think she’s wrong about the AI chatbot, because ChatGPT comes up with the strangest bald-faced nonsense about math problems. Wolfram Alpha is a much more reliable resource.

      But Harris’s main point stands. This misconception, this math-education myth, drives much of what happens in our classrooms and home schools today.

      Continue reading Musings: A Common Misconception

      Musings: A Philosophy of Education

      Posted on by Denise Gaskins

      I’ve tried a few times over the years to express my philosophy of teaching math. Back when I first started doing workshops for homeschooling parents, I told them:

      “Instead of drudgery, mathematics should be a game of discovery. It should give children the same ‘Eureka!’ thrill that sent Archimedes running through town in his birthday suit. I call this the ‘Aha!’ factor, the delight in solving a challenging puzzle.”

      Years later, as the internet developed and much of life moved online, I started a blog about playing with math. And since all good blogs need an “About Me” page, I had another chance to sum up my thoughts:

      “Math is like ice cream, with more flavors than you can imagine — and if all your children ever see is textbook math, that’s like feeding them broccoli-flavored ice cream.”

      But over the years, some people got the impression that my goal was all about playing games. They asked, “How can we make math fun for our kids?” — as if gamification adds a candy coating to make the disgusting medicine more palatable.

      And of course, I do write a lot of books about games. I think games serve much better than worksheets for practicing basic math skills.

      Still, I wanted people to see that the ideas of math themselves are tasty tidbits worth playing with.

      Continue reading Musings: A Philosophy of Education

      Playful Math Education Carnival 171: Modern Math Artists

      Posted on by Denise Gaskins

      Welcome to the 171st 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 over the next week or so.

      There’s so much playful math to enjoy!

      By tradition, we start the carnival with a puzzle/activity in honor of our 171st 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

      171 is a triangular number, the sum of all the numbers from 1 to 18:

      • 1 + 2 + 3 + … + 17 + 18 = 171.
      • Can you think why a number like this is called “triangular”?
      • What other triangular numbers can you find?

      Also, 171 is a palindrome number, with the same digits forward and backward. It’s also a palindrome of powers:

      • 171 = 52 + 112 + 52
      • 171 = 23 + 43 + 33 + 43 + 23

      So in honor of our 171st Playful Math Carnival, here is a palindrome puzzle that leads to an unsolved question in math:

      • Does every number turn into a palindrome eventually?

      palindrome number activity

      Click here for all the mathy goodness!

      Carnival 170: A Plethora of Playful Math

      Posted on by Denise Gaskins

      Welcome to the 170th edition of the Playful Math Education 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 170th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

      Puzzle: Prime Permutations

      According to Tanya Khovanova’s Number Gossip, 170 is the smallest composite number where exactly four permutations of its digits make prime numbers.

      To find permutations, think of all the different ways you can arrange the digits 1, 7, 0 into three-digit numbers. (When the zero comes first, those permutations actually make two-digit numbers, which DO also count.)

      Can you figure out which permutations make prime numbers?

      Hint: The permutation that makes the number “170” is not prime, but it is the product of three prime numbers. Which ones?

      For Younger Children: The 170 Square

      A Latin square is a grid filled with permutations: letters, numbers, or other symbols so that no row or column contains more than one of any character. You’ve probably seen the popular Latin-square puzzle called Sudoku. A Graeco-Latin square (also called an Euler square) is two independent Latin squares overlapping each other.

      Can you complete this Euler square made by overlapping permutations of the digits of 170 with winter colors? Don’t repeat the same color OR the same number in any row or column.

      Click the picture to get a larger image you can print.

      Click here for all the mathy goodness!

      Living Books for Math

      Posted on by Denise Gaskins

      What is a “living book”? English education reformer Charlotte Mason introduced this term for any book that brings the reader directly into contact with the major ideas that have fascinated humans across the ages.

      We know that reading aloud helps build our children’s love for books. But did you know it works for math as well?

      And that it can transform the parent’s attitude as well as the child’s?

      A playful math book fleshes out the bones of abstract math,
      brings it alive,
      makes it human, relatable,
      interesting to readers of all ages,
      opening our eyes to the wonderful world of big ideas,
      where concepts meet and topics intertwine
      in a beautifully intricate dance
      of understanding.

      We live in an age of abundance, with more new creative math books being published every year, so many that I can’t keep track of them all, not to mention the older classics, some out of print, that can still be found in public libraries.

      Here are a few of my favorite books of playful, living math, both old and new:

      Continue reading Living Books for Math

      Podcast: Cultivating Math Curiosity and Reasoning in Kids

      Posted on by Denise Gaskins

      I have a new podcast interview, and I think you’ll enjoy it!

      Check out Learning Is Disruptable on your favorite podcast app, or listen on the website:

      Go to the podcast ❱

      Here’s an excerpt…

      “I think the most important thing that we need to change…we need to radically change what our idea is of what it means to learn math.

        “Our biggest failure, both in the classroom and in homeschool settings, is that we’ve given our children a totally wrong idea of what math is all about.

        Continue reading Podcast: Cultivating Math Curiosity and Reasoning in Kids

        Playful Math Education 162: The Math Games Carnival

        Posted on by Denise Gaskins

        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

        Posted on by Denise Gaskins

        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!

        Playful Math Carnival #154: The Math Journaling Edition

        Posted on by Denise Gaskins

        Welcome to the 154th 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 154th 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

        Since 154 is a nonagonal number, I think you might enjoy visiting some of my old “Adventures of Alexandria Jones” posts about figurate numbers:

        And then try this math journaling prompt: Build or draw your own nonagonal numbers — numbers built from 9-sided polygons.

        How many nonagonal numbers can you find? What do you notice? Does it make you wonder?

        Click here for all the mathy goodness!