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

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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:

Arithmetic

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.

Art

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.

Displays

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.

Games

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.

Geometry

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?

Money

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.

Posters

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.

Puzzles

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

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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!

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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!

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65 is the Magic Sum of a 5 x 5 Magic Square

65 = (1 + 2 + 3 +. . . + 23 + 24 + 25)/5 so it is the magic sum of a 5 × 5 magic square. I solved this 5×5 magic square game using a time-honored algorithm. Notice that 11, 12, 13, 14, and 15 are on a diagonal. Actually, all of the numbers are sort of on a diagonal if you follow the instructions given here. Also notice that the first number, 1, is in the center of the top row and the last number, 25, is in the center of the bottom row.

You can try to solve the square, too. Just click on the magic square image above to go to a website where you can try these or other combinations of numbers. You will know you have solved the magic square when the sum of each row, column, and diagonal totals 65.

65 is also the sum of two squares two different ways:

  • 8² + 1² = 65
  • 7² + 4² = 65

That makes 65 the hypotenuse of FOUR Pythagorean triples:

  • 16-63-65 which was calculated from 2(8)(1), 8² – 1², 8² + 1²
  • 25-60-65 which is 5 times 5-12-13
  • 33-56-65 which was calculated from 7² – 4², 2(7)(4), 7² + 4²
  • 39-52-65 which is 13 times 3-4-5

65 is a composite number. 65 = 1 x 65 or 5 x 13. Factors of 65: 1, 5, 13, 65. Prime factorization: 65 = 5 x 13.

65 – 56 = 9, a square number and 65+56 = 121, another square number. Stetson.edu informs us that 65 and 56 are the smallest pair of mirror image numbers that produce a square number when either added or subtracted.

 

 

7 Spaghetti and Meatballs for All!

  • 7 is a prime number.
  • Prime factorization: 7 is prime.
  • The exponent of prime number 7 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 7 has exactly 2 factors.
  • Factors of 7: 1, 7
  • Factor pairs: 7 = 1 x 7
  • 7 has no square factors that allow its square root to be simplified. √7 ≈ 2.64575.

How do we know that 7 is a prime number? If 7 were not a prime number, then it would be divisible by at least one prime number less than or equal to √7 ≈ 2.6. Since 7 cannot be divided evenly by 2, we know that 7 is a prime number.

When 7 is a clue in the FIND THE FACTORS puzzles, one factor will be 7 and the other will be 1.

Spaghetti and Meatballs for All! by Marilyn Burns is a delightful story, the kind that children enjoy hearing over and over again.

I work at a Leader in Me school, where we promote the Seven Habits. I used this book when I taught about habit 4, think win-win. When we think win-win, we do not allow someone to “step on us’ to give them a win. Mrs. Comfort’s relatives stepped on her over and over again, and they didn’t even realize it. Finally, she cried, “I give up!” and planted herself on a chair. She definitely felt like she was losing. The class listened to the story intently trying to identify places where the Seven Habits were used or could have been used. We had a great discussion afterward. Also since the book did not use the words, “area” or “perimeter” at all, the class hardly realized that the story was also about those concepts. When we followed the suggestions at the back of the book, the class was able to learn about perimeter and area as we had a great discussion about those topics as well. 

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