131 Playful Math Carnival

Welcome to the Playful Math Education Blog Carnival featuring the amazing prime number 131, whose digits can mutate into other prime numbers right before your eyes!

131, a permutable prime number

make science GIFs like this at MakeaGif
Yessiree, 131 is prime, and so is 113 and 331. Do I need to mention that 3, 11, 13, and 31 are also prime numbers?
131’s next trick happens when you add up all the 2-digit PRIMES that begin with a 4:
41 + 43 + 47 = 131.
Because 131is a palindrome, it reads the same forwards and backward. Here’s another trick: 131 is 65 in BASE 21 and 56 in BASE 25.


We have many different attractions this month. You can go to any category quickly here:

Carnival Attractions:


You’ve heard of the three R’s, reading, and writing and ‘rithmetic, but what is arithmetic? Joseph Nebus shares a few comics about basic arithmetic and explains what they mean:

Arithmetic is also television’s Lisa Simpson’s favorite subject in school and she will miss it greatly as she recovers from the mumps. In this blog post, Safi explains Dr. Hibbert’s comforting words to her about polygons, hypotenuses, and Euclidean algorithms.


You can always count on Robert Loves Pi to produce a beautiful and complex geometric design. This one he calls Two Rhombic Polyhedra with Tessellated Faces. Here’s another one:

Paula Beardell Krieg helped students create big, beautiful geometric artwork and origami in Summer Projects with Teens.

Also, check out Paula’s Paper, Books, and Math Workshop for many more ways to learn math through art.

Big Prize, Little Chance of Winning

Several years ago Mental Floss wrote about carnival games that offer big prizes but have very little chance of being won. This carnival has a couple of those as well. They are called unsolved math problems. Even if winning probably isn’t going to happen, that doesn’t mean the games and activities aren’t fun. Explaining Science updates us on a very famous unsolved problem, The Goldbach’s Conjecture. Supercomputers have worked on it, but we are no closer to a solution.

In A Neat Unsolved Problem in Number Theory That Kids Can Explore, Mike’s Math Page explores the new-to-me Collatz conjecture that for every positive n, the sum 3 + 8n will equal a perfect square plus an even number. It’s a simple enough conjecture for kids to understand and it is fascinating, yet mathematicians have not been able to prove or disprove it yet!

Creative Writing

Subha laxmi Moharana (Angel Subu) writes creatively about some tough topics in high school mathematics in Math Poem. I think her words could be turned into a rap.

Poetrywithmathematics shares Doug Norton’s lovely mathematical poem Take a Chance on Me.

What if graphs were self-conscious about their looks? High School aged students can consider that thought as they read the imaginative blog post, To Infinity and Beyond.


There’s a cozy classroom place that promotes mathematics in Our New Math Space. It was designed for older students by Continuous Everywhere But Differentiable Nowhere and includes many pictures.

Have you considered displaying a weekly math joke? MathEqualsLove shares a fun joke and a puzzle for kids to gather around and enjoy.

Factoring Quadratics

Super Safi uses another episode from the Simpsons to teach about the quadratic formula.

Food for Thought

Anybody can cook or do math. Really? What does that even mean? Math4Love explains both in What We Mean When We Say, “Anyone Can Do Math.”
Math with Bad Drawings makes a similar point in The Adventures of Captain Math.


Joyful Parenting made a simple kindergarten-age counting game and called it Snack Math, but even older kids might enjoy figuring out exactly how many crackers are required to play the game.

How many are in the jar. What is a good estimate? Add Steve Wyborney’s clues one by one to get an even better estimate. He has 51 New Esti-Mysteries that also happen to teach several different math concepts.

For older students, Kent Haines a free game he calls Last Factor Loses. I played it a few times with a student. Making prime factorization a game really did make it more fun.


Bn11nb enjoys the geometry of architecture. The pictures in this post are worth a look and could be an inspiration to your students.

House of Mirrors (Reflecting on Mathematics Teaching)

We often reflect on the effectiveness of our teaching methods. Sometimes we are advised to require students to use more strategies. We might ask them to notice or wonder about a concept. These two thoughtful posts will certainly give you cause for reflection:

“The More Strategies, the Better?

Noticing and Wondering: A powerful tool for assessment


Robert Kaplinsky shares ten things he’s embarrassed to tell you. Has he been reading your mind and mine?


What is your favorite part of a cupcake? What if you could buy just that part? What if you wanted to put a whole cupcake together? How much would that cost? Your child can learn about money and decimals exploring those answers with Mathgeekmama’s  Money Math Problems.

Museum of Mathematics

Beads can be a fun manipulative when learning mathematics. Joseph Nebus has begun his 2019 Mathematics A-Z series by writing about the Japanese abacus. He compares it to a slide rule and the Chinese abacus. He also describes how to use it to add, subtract, and multiply numbers. Students could have some fun using it to understand place value, too.

Life Through a Mathematician’s Eyes is giving museum tours in A History of Mathematics-August. K-12 students could be fascinated by the mathematical relics from the Smithsonian founded in August 1846 as well as the Seven Bridges of Königsberg solved by Euler in August 1735.

Pumpkin Patch

Erin of Sixth Bloom’s Pumpkin Math-Preschool Activity will engage your little ones as they learn to count and sort pumpkin-shaped macaroni or candies.

They will also love decomposing numbers using pumpkin seeds and  Mathgeekmama’s cute Pumpkin cards.


Digital Educators Alliance offers free posters of admirable women in math and related fields:

While Sara Van Derwerf set of 112 New Math Fail Posters will delight students as they notice and wonder about and LEARN from grown-ups’ computing mistakes.


7Puzzle gives some clues about a 3-digit number. Can you figure out what it is?



Alan Parr writes about a newspaper puzzle called Evens Puzzles. He suggests that students can make their own and hints that he has thought up several variations of it. I look forward to reading about those!



American Calendars for September had more than a week’s worth of palindromes. Would palindromes make a good puzzle? Yes! Print off a 100 chart and try Denise Gaskins’s A Puzzle for Palindromes. Also, check out her new Morning Coffee feature each week for more math teaching tips.

Next Month’s Carnival

That’s it for this month’s Math Education Blog Carnival. The 132nd Carnival will be next month at Arithmophobia No More. Would you like to share a post or host the carnival? Go to Let’s Play Math for details!


127th Playful Math Education Blog Carnival






Art and Mathematics


Classwork/Homework that is enjoyable


Creative Writing




Desmos First Aid Station?


Eggstraordinary Mathematical Easter Egg Hunt from Twitter

  7. And these Eggsponenential eggs created by Traci Jackson!

Exponents and Exponential Functions




Games and Educational Toys




Giving Back


Linear Equations


Literature and Mathematics


Museum of Mathematics


Number Theory


Optical Illusions




Statistics and Probability


Telling Time







1371 Today is a Good Day to Review Proof by Induction

0² = 0
1²  = 1








Now I’ll write a little bit about the number 1371:

  • 1371 is a composite number.
  • Prime factorization: 1371 = 3 × 457

1371 is the hypotenuse of a Pythagorean triple:


1366 Fractions Acting Improperly





Now I’ll write a little bit about the number 1366:

  • 1366 is a composite number.
  • Prime factorization: 1366 = 2 × 683
  • Factors of 1366: 1, 2, 683, 1366


1350 Logic is at the Heart of This Puzzle

By simply changing two clues of that recently published puzzle that I rejected, I was able to create a love-ly puzzle that can be solved entirely by logic. Can you figure out where to put the numbers from 1 to 12 in each of the four outlined areas that divide the puzzle into four equal sections? If you can, my heart might just skip a beat!

If you need some tips on how to get started on this puzzle, check out this video:

Now I’ll tell you a few things about the number 1350:

  • 1350 is a composite number.
  • Prime factorization: 1350 = 2 × 3 × 3 × 3 × 5 × 5, which can be written 1350 = 2 × 3³ × 5²
  • The exponents in the prime factorization are 1, 3 and 2. Adding one to each and multiplying we get (1 + 1)(3 + 1)(2 + 1) = 2 × 4 × 3 = 24. Therefore 1350 has exactly 24 factors.
  • Factors of 1350: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350
  • Factor pairs: 1350 = 1 × 1350, 2 × 675, 3 × 450, 5 × 270, 6 × 225, 9 × 150, 10 × 135, 15 × 90, 18 × 75, 25 × 54, 27 × 50 or 30 × 45
  • Taking the factor pair with the largest square number factor, we get √1350 = (√225)(√6) = 15√6 ≈ 36.74235

1350 is the sum of consecutive prime numbers two ways:
It is the sum of the fourteen prime numbers from 67 to 131, and
673 + 677 = 1350

1350 is the hypotenuse of two Pythagorean triples:
810-1080-1350 which is (3-4-5) times 270
378-1296-1350 which is (7-24-25) times 54

1350 is also the 20th nonagonal number because 20(7 · 20 – 5)/2 = 1350

Facts about and Factors of 2019

Here’s a countdown you can use to ring in the New Year:

Countdown to 2019

make science GIFs like this at MakeaGif

2019 is the sum of consecutive numbers three different ways:
1009 + 1010 = 2019
672 + 673 + 674 = 2019
334 + 335 + 336 + 337 + 338 + 339 = 2019

There is one way that 2019 is the sum of consecutive odd numbers:
671 + 673 + 675 = 2019

2019 is the difference of two squares two different ways:
338² – 335² = 2019
1010² – 1009² = 2019

2019 is the sum of three squares nine different ways:
43² + 13² + 1² = 2019
43² + 11² + 7² = 2019
41² + 17² + 7² = 2019
41² + 13² + 13² = 2019
37² + 25² + 5² = 2019
37² + 23² + 11² = 2019
37² + 19² + 17² = 2019
35² + 25² + 13² = 2019
31² + 23² + 23² = 2019

2019 is the hypotenuse of a Pythagorean triple:
1155-1656-2019 so 1155² + 1656² = 2019²

2¹⁰ + 2⁹ + 2⁸ + 2⁷ + 2⁶ + 2⁵ + 2¹ + 2⁰ = 2019

2019 is a palindrome in a couple of bases:
It’s 5B5 in BASE 19 (B is 11 base 10) because 5(19²) + 11(19) + 5(1) = 2019,
and 3C3 in BASE 24 (C is 12 base 10) because 3(24²) + 12(24) + 3(1) = 2019

Every year has factors that often catch people by surprise. Today I would like to give you my predictions for the factors of 2019:
2019 will have four positive factors: 1, 3, 673, and 2019
However, 2019 will also have four negative factors: -1, -3, -673, and -2019

Which factors, positive or negative, will be your focus in the coming year?

Finally, I’ll share some mathematics-related 2019 and New Year tweets that I’ve seen on twitter. Some of these tweets have links that contain even more facts about the number 2019.

That tweet inspired me to make my own 3 × 3 Magic Square where every number is different but every row, column and diagonal totals the same number:



And finally, here is my contribution to 2019 twitter:


810 Stick and Stone











The sixth graders were delighted with the answer.











  • 810 is a composite number.






  • 810 is 30222 BASE 4
  • 810 is 11220 BASE 5
  • 810 is 3430 BASE 6 and so forth.




807 and Level 1

What can I say about the number 807?

807 is palindrome 151 in BASE 26 because 1(26²) + 5(26) + 1(1) = 807.

Anything else? Well, I can figure out a few other things because 807’s has two prime factors, 3 and 269:

We can write ANY number (unless it’s a power of 2) as the sum of consecutive numbers in at least one way. 807 has three different ways to do that:

  • 403 + 404 = 807 because 807 isn’t divisible by 2.
  • 268 + 269 + 270 = 807 because it is divisible by 3.
  • 132 + 133 + 134 + 135 + 136 + 137 = 807 since it is divisible by 3 but not by 6.

I know that one of 807’s factors, 269, is a hypotenuse of a Pythagorean triple, so 807 is also. Thus. . .

  • (3·69)² + (3·260)² = (3·269)², or in other words, 207² + 780² = 807²

Since 807 has two odd sets of factor pairs, I know that 807 can be written as the difference of two squares two different ways:

  • 136² – 133² = 807
  • 404² – 403² = 807

I don’t usually do this, but today’s puzzle has something in common with 807. Can you tell what it is?


  • 807 is a composite number.
  • Prime factorization: 807 = 3 x 269
  • Factors of 807: 1, 3, 269, 807
  • Factor pairs: 807 = 1 x 807 or 3 x 269
  • 807 has no square factors that allow its square root to be simplified. √807 ≈ 28.4077454






572 and Level 1

72 can be evenly divided by 4 so 572 is divisible by 4.

5 – 7 + 2 = 0, which can be evenly divided by 11, so 11 is a factor of 572.

572 is the hypotenuse of the Pythagorean triple 220-528-572. Which factor of 572 is the greatest common factor of those three numbers?

572 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2015-08-03


  • 572 is a composite number.
  • Prime factorization: 572 = 2 x 2 x 11 x 13, which can be written 572 = (2^2) x 11 x 13
  • The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 572 has exactly 12 factors.
  • Factors of 572: 1, 2, 4, 11, 13, 22, 26, 44, 52, 143, 286, 572
  • Factor pairs: 572 = 1 x 572, 2 x 286, 4 x 143, 11 x 52, 13 x 44, or 22 x 26
  • Taking the factor pair with the largest square number factor, we get √572 = (√4)(√143) = 2√143 ≈ 23.91652


572 Factors

564 and Level 6

Consecutive primes 281 and 283 add up to 564.

564 is made from three consecutive numbers so it can be evenly divided by 3. If the middle number is divisible by 3, then a number made from three consecutive numbers will also be divisible by 9. Is 564 divisible by 9? Why or why not?

564 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2015-07-20


  • 564 is a composite number.
  • Prime factorization: 564 = 2 x 2 x 3 x 47, which can be written 564 = (2^2) x 3 x 47
  • Factors of 564: 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
  • Factor pairs: 564 = 1 x 564, 2 x 282, 3 x 188, 4 x 141, 6 x 94, or 12 x 47
  • Taking the factor pair with the largest square number factor, we get √564 = (√4)(√141) = 2√141 ≈ 23.74868


564 Logic