Playful Math 179: Our Sweet Sixteen Carnival

Posted on by Denise Gaskins

Welcome to the sweet-16 birthday edition of the Playful Math Carnival. Originally called Math Teachers at Play, our first carnival was published in February 2009.

Each Playful Math Carnival offers 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.

There’s so much playful math to enjoy!

By tradition, we start the carnival with a math activity in honor of our 179th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

NOTE: Our wonderful volunteer hosts have kept the Playful Math Carnival going when so many other blog carnivals died off. If you’d like to sign up to host the carnival for a month, email Denise for information.

Try These Prime Puzzles

Did you know there are 179 even-numbered days this year?

  • How many even-numbered days will there be in a leap year?
  • But there are 365 days in a standard year and 366 in a leap year. Shouldn’t there be half that many even-numbered days?

179 is a prime number, and it’s also a knockout prime. You can knock out any of the digits, and what’s left is still prime: 17, 19, or 79.

  • Can you find another knockout prime number?

179 is a twin prime. That means that one of its odd-numbered neighbors is also prime.

  • Is the other twin 177 or 181? Can you tell without looking it up?
  • Why are twin primes limited to the odd numbers? That doesn’t seem fair!

179 is also an emirp. That’s a special kind of prime that forms a different prime number when you write it backwards: 971 is also prime.

  • How many emirps can you find?

“A palindrome is a word that when written in reverse results in the same word. for example, ‘racecar’ reversed is still ‘racecar’. Related to palindromes are semordnilaps. These are words that when written in reverse result in a distinct valid word. For example, ‘stressed’ written in reverse is ‘desserts’. Not all words are palindromes or semordnilaps.

    “While certainly not all numbers are palindromes, all non-palindromic numbers when written in reverse will form semordnilaps.

      “Narrowing to primes brings back the same trichotomy as with words: some numbers are emirps, some numbers are palindromic primes, but some are neither.”

      —The On-Line Encyclopedia of Integer Sequences A006567

      Click here for all the mathy goodness!

      Memories: The Oral Story Problem Game

      Posted on by Denise Gaskins
      photo of sheep in a field

      Homeschool Memories…

      Perhaps you’ve heard me mention the oral story problem game. It was one of my favorite ways to get my children thinking about math, back in our early days of homeschooling. We played in the car on the way to soccer practice, or while we washed dishes, or sitting in the lobby waiting for a doctor’s appointment.

      The rules are simple: I’ll make up a math problem for you to solve. And then you make up one for me.

      The kids always loved trying to stump me.

      This problem from Henry Ernest Dudeney’s Amusements in Mathematics reminded me of those days. This is exactly the way my eldest loved to torture me…

      Continue reading Memories: The Oral Story Problem Game

      Puzzle: Henry Dudeney’s Pebble Game

      Posted on by Denise Gaskins
      photo of girl playing with pebbles on the beach

      English mathematician and puzzle-meister Henry Ernest Dudeney once wrote:

      “It may be said generally that a game is a contest of skill for two or more persons, into which we enter either for amusement or to win a prize. A puzzle is something to be done or solved by the individual.

        “The example that I give here is apparently a game, but, as in every case one player may win if he only play correctly, it is in reality a puzzle. The interest, therefore, lies in attempting to discover the leading method of play.”

        Below is the puzzle game as Dudeney explained it.

        Play it for fun at first, then see if you can solve the puzzle.

        Continue reading Puzzle: Henry Dudeney’s Pebble Game

        The Rhythm of Math Puzzles

        Posted on by Denise Gaskins
        Father and son homeschooling math

        Homeschooling families naturally build patterns and routines that help us keep our sanity as we go through our homeschooling day.

        No matter what resources we choose or which curriculum packages we buy, we never end up following the book exactly as it is written. So don’t worry if you find yourself wandering away from the lesson plan. You’re not getting behind; you’re just discovering your family’s natural learning style.

        If you and your children have fallen into the rut of traditional math lessons, have patience. Give yourself time to adjust to a more relaxed mindset about math.

        And when you find the rhythm that fits your family, you’ll discover that math lessons flow so much more smoothly.

        Continue reading The Rhythm of Math Puzzles

        Learning Math with Puzzles

        Posted on by Denise Gaskins
        Mother and daughter homeschooling math

        Learning mathematics begins with puzzles. As stories are to history or science, puzzles are to math.

        In ancient times, math began with puzzles like:

        • How can we keep track of our herds, or predict the cycles of the moon, or figure out how much to pay for taxes?

        • How can we draw perfect right angles, or make beautifully symmetric designs?

        • What are the ratios of harp strings that create the most beautiful sounds?

        Math puzzles touch every area of life. Puzzles inspire curiosity and solving them brings joy.

        And we can enrich any homeschool math program with puzzles that invite children to think about mathematical concepts.

        Even those monster topics that often bring homeschooling families to tears, such as fractions.

        Continue reading Learning Math with Puzzles

        New Book: Farzanah and the 17 Camels

        Posted on by Denise Gaskins
        illustration from Farzanah and the 17 Camels

        Now’s your chance to promote creative math for kids, with Sue Looney’s new book on Kickstarter: Farzanah and the 17 Camels.

        You can order the book in digital or paperback format, get multiple copies for a classroom or book club, or just donate to support the project.

        Visit the Kickstarter

        Farzanah and the 17 Camels celebrates the excitement and the rewards of solving a challenging and intriguing math problem. Set against the backdrop of the ancient Silk Road, with bustling markets, stunning carpets, fun characters, and camels, the story draws readers into the magic of Farzanah’s surroundings. 

        As Farzanah searches for an unusual approach, a way of solving the problem that no one else could think of, she follows the wise advice of her mother: 

        “My dear Farzanah, don’t be discouraged,” said Mama. “Sometimes, being stuck is exactly where you need to be. I find the best thing I can do is to step away. I free my mind to think about other things. It is in that space that the magic happens. I am able to look at things from a different perspective. With wait time and wishful thinking comes the solution.”

        Farzanah embodies the joy of productive struggle in mathematical problem-solving. She is patient, persistent, and curious, using these qualities to tackle a perplexing dilemma that has troubled everyone.

        For a bonus math puzzle you can play today, based on Farzanah’s life, download Farzanah’s Sheep Dilemma.

        Looney’s earlier book, Ying and the Magic Turtle, is available on the Natural Math website. Or check out her Same But Different discussion prompts for all ages on her website.

        Visit the Kickstarter

         
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        Illustration above copyright © 2024 Noemi Sophia James, from the book Farzanah and the 17 Camels by Sue Looney.

        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!

        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!

        Can You Solve It? The Cyclists’ Feast

        Posted on by Denise Gaskins

        English mathematician Henry Ernest Dudeney wrote logic puzzles and mathematical games for several newspapers and magazines, later collected into books. This poem is from Amusements in Mathematics, published by Thomas Nelson and Sons, 1917.

        The numbers are simple enough that younger students can solve it by the guess-and-check method. Older students or adults may want to set up a quadratic equation.

        Historical Note: In the British currency of the time, there were 12 pennies to a shilling and 20 shillings to a pound (which was also called a sovereign).

        The Cyclists’ Feast

        ’Twas last Bank Holiday, so I’ve been told,
        Some cyclists rode abroad in glorious weather.
        Resting at noon within a tavern old,
        They all agreed to have a feast together.

        “Put it all in one bill, mine host,” they said,
        “For everyone an equal share will pay.”
        The bill was promptly on the table laid,
        And four pounds was the reckoning that day.

        But, sad to state, when they prepared to square,
        ’Twas found that two had sneaked outside and fled.
        So, for two shillings more than his due share
        Each honest friend who had remained was bled.

        They settled later with those rogues, no doubt.
        How many were they when they first set out?

        Did You Solve It?

        One fun thing about math is that you really don’t need the answer book. You can always check the math for yourself: Does your answer make sense? Does it fit the story?

        Would you like to write a math poem puzzle of your own? I’d love to hear it!

         
        * * *

        For more ideas on writing math poetry, check out Math Makers: Write a Poem.

        This blog is reader-supported.

        If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

        If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

        Which I am going to say right now. Thank you!

        “Can You Solve It? The Cyclists’ Feast” copyright © 2023 by Denise Gaskins. Image at the top of the post copyright © yanlev / Depositphotos.