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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!

Middle School Math Proof

Posted on by Denise Gaskins

Homeschool Memories…

Kitten (my daughter) and I sat on the couch sharing a whiteboard, passing it back and forth as we took turns working through our prealgebra book together.

The chapter on number theory began with some puzzles about multiples and divisibility rules.

Continue reading Middle School Math Proof

Gameschooling Math

Posted on by Denise Gaskins

Games are fun, building a positive attitude toward math. They give students a refreshing break from textbook work and make kids willing to practice their math. Games make math practice enjoyable, something children want to do. We can happily work through many more calculations during a game than anyone would ever want to do on a homework page.

Benefits of Math Games

But more important than the fun, math games push children to think about what numbers mean and how they work. The numbers in a math game are not just meaningless abstractions, but tools that players can use to gain an advantage over their opponent.

A good math game reinforces the idea that math is about reasoning, using the things you know to figure out what you need. Math is not just about getting the right answer. It’s about what goes on in your head on the way to that answer. The answer itself is merely a side-effect. of what really matters, your thinking.

A good math game helps students develop flexibility, the ability to adapt, applying what they have learned to new situations, finding a way to work out the things they haven’t mastered yet. All these add up to a more robust type of mathematical fluency than what many people imagine possible.

Continue reading Gameschooling Math

Math Musings: When Should We Work on Memorization?

Posted on by Denise Gaskins

Having knowledge in long-term memory can be very helpful in solving problems.

But master problem-solver Sherlock Holmes was concerned that if he had too much knowledge in his mind, new facts would crowd out the old and cause him to forget something important:

Continue reading Math Musings: When Should We Work on Memorization?

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!

FAQ: The Necessity of Math Facts

Posted on by Denise Gaskins

Ah, math facts — the topic that just won’t stop giving grief to students and anxiety to their parents. So it happened that I got another question, but this one leaned in a more philosophical direction…

“I enjoyed your podcast interview on Cultivating Math Curiosity and Reasoning in Kids. I love the idea that we don’t have to make our children memorize everything in math. We can give them freedom to make mental connections for themselves.

    “But on the other hand, we don’t have unlimited time for them to figure things out on their own, do we? What about children who can’t make these connections for themselves?

      “For example, what about the math facts? If my kids aren’t picking them up, don’t they just have to memorize them?”

      Continue reading FAQ: The Necessity of Math Facts

      FAQ: Memorizing the Math Facts

      Posted on by Denise Gaskins

      It came up again this week, one of the most frequently asked questions about homeschooling math:

      “I believe it’s important for children to memorize the math facts, but my kids are struggling with mental math. How can I help them master these important number relationships?”

      We all want our children to own the math facts, those basic relationships between small numbers that form the foundation of all arithmetic.

      But I don’t think emphasizing memorization will develop the sort of fluency your children need.

      The human brain remembers what it thinks about, so we want children using their brains and thinking as deeply as possible about number relationships from as many different perspectives as we can get, noticing patterns, finding connections, making sense of the math.

      Continue reading FAQ: Memorizing the Math Facts

      Playful Math Carnival 169 via Math Hombre

      Posted on by Denise Gaskins

      If you’re into math education — or just curious about how learning math could possibly be fun — you’ll definitely want to check out the latest edition of the Playful Math Carnival.

      It’s a collection of awesome blog posts curated by John Golden and published on the Math Hombre website:

      The whole point of the carnival is to show that math doesn’t have to be tedious or repetitive. Through a bunch of fun and engaging posts, we celebrate math that’s playful, creative, and totally relevant to everyday life.

      Because what could be more relevant that having fun while we learn?

      In this edition, you’ll find everything from math puzzles and games to humor and much more — even a spooky monster escape room!

      So if you want to mix up your math teaching and make it more enjoyable for your students (and for you!), definitely check out the Playful Math Carnival. Happy reading!

      Go Visit the Carnival

      Wanted: Hosts for 2024

      The Playful Math Carnival is a joint effort. We depend on our volunteer hosts to collect blog posts and write the carnival each month.

      Putting together a blog carnival can be a lot of work, but it’s a great opportunity to share the work of bloggers you admire and to discover new math-friends online. I love that part of being a host!

      Classroom teachers, homeschoolers, college professors, unschoolers, or anyone who likes to play around with math — if you would like to take a turn hosting the carnival, please speak up.

      Check the details on the carnival’s home page, and then leave a comment here or email me directly to let me know which month fits your schedule.

      Playful Math Carnival Instructions

       
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      “Playful Math Carnival 169 via Math Hombre” copyright © 2023 by Denise Gaskins. Image at the top of the post copyright © Devon Rogers on Unsplash.

      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!

       
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      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.