Welcome to the 140th Playful Math Education Blog Carnival!

What’s Special about 140?

Ladies and Gentlemen, welcome to the 140th Playful Math Education Blog Carnival! Feast your eyes on the number, 140, the 7th member of the famous Square Pyramidal Number family. Watch as 140 performs these amazing feats:

140 is the 7th square pyramidal number because
(7³/3) +(7²/2) + (7/6) = 140.

140 has twelve factors and will now use them to make a lovely factor rainbow:

For140’s next trick, see what happens when it is divided by six of its non-factors:

Finally, 140 is the fourth harmonic divisor number, and Wolfram Math World even uses 140 to explain what a harmonic divisor number is.

Now let’s move on to the blog entries for this month’s carnival:

Children’s Literature and Math

Kelly Darke of Math Book Magic wrote a post about a brand new entry in children’s literature, The Boy Who Dreamed of Infinity.  This is the story of the great Indian mathematician, Ramanujan. The book is available for us to read now, but Kelly was able to read it for the first time last year. I felt so much joy inside of me as I read first her reaction to the description of the book and later to the book itself. I am grateful that the mere idea of that book prompted Kelly to create a blog to share the magic of good mathematical children’s literature.

Rhapsody in Books Weblog tells us about, Raye Montague, an African-American girl born in 1935. She was told repeatedly that her race and her gender would prevent her from becoming the mathematician that she dreamed of becoming. She didn’t heed her naysayers. The Girl with a Mind for Math: The Story of Raye Montague tells her inspiring story.

On world Tessellation Day, TheKittyCats blog introduced us to Tessellations!  Children will enjoy looking at the illustrations in the book and won’t even realize they are learning some math in the process unless someone shares that secret.

Games and Math

Alan Parr of Established 1962 explains how to play Dotty Six, a game played with a tic tac toe grid and a die. Because he asked himself, “What If Not?”, he was able to suggest some mathematically interesting variations of the game as well.

Mrs. O’Brien started her blog, Math Epiphany, very recently-in May 2020. She has written two posts about using games to learn mathematics. She writes about card games in Summer Math Fun: Math Games, and about board games in Summer Math Fun: Good Old Fashioned Games.

Denise Gaskins shares a math game that lets children complexify expressions or equations rather than simplify them. Making the expression or equation a little more complex than it was before can be great fun and wonderfully educational. Check out The Best Math Game Ever!

Do you know how to play Dara, Five Field Kono, Mu Torere, Pong Hau K’I, Shisima, or Triangle Peg Solitaire? I’ve never even heard of these games before. Mark Chubb of Thinking Mathematically introduces all of these games in Math Games-building a foundation for mathematical reasoning. One of the games is illustrated in the tweet below.

Math and Paper-Folding

How is making a pouch out of a newspaper doing math? Paula Krieg and John Golden explain that it can be more than simply taking measurements and using rulers in Pouch: Something from Almost Nothing #3.

Did you know that paper folding can help kids understand systems of linear equations?

Or paper folding can even help kids understand Knot Theory or Topology?

Math and Art

What creatures can be seen in these numbers? Click on the video to find out what one artist saw!

We can always count on Robert Loves Pi to create dazzling and beautiful geometric art. Here he tells us how relaxing it is to produce it:

Photographer Ming Thein shares 13 discussion-evoking photos in Photo essay: The texture of geometry. I’d love to hear some of those discussions!

Quilts can be stunning examples of mathematical art. Aby Dolinger of Abyquilts has created a quilt pattern she calls “Math Whiz,” and this mathy quilt was featured on the July/August 2020 COVER of Quiltmaker magazine! Congratulations Aby!

Geometry and Trigonometry

Laura of Mathsux² has written an explanation and created a video to take the mystery out of trigonometric ratios in How to Use SOHCAHTOA.

Jo Morgan’s website is filled with resources to make teaching and learning math more effective, and yet she always finds room for more ideas! She recently created her 133rd Maths Gems Post that included some playful ways to look at angles in a circle and areas of rectangles inside of a larger rectangle. . . Now to segway into word problems. . . If Jo writes two Maths Gems a month and her July 30th post was number 133, and the Playful Math Blog Carnival comes out ten times a year and this is the 140th post, when will the Maths Gems number and the Playful Math Blog number be the same number?

Word Problems

I love the giant Sequoia Trees. This blog post has story problem suggestions about Sequoia Trees for every age group:

A-Hundred-Years-Ago Blog explores some Hundred-year-old Food-related Math Problems when large oranges were only 60 cents a dozen. Go back in time and enjoy solving these with your students! Let them compare them with word problems from the 21st century.

Puzzles

Alan Paar of established1962 shares his last experience helping kids play with math before the lockdown. It was a series of puzzles that made A Lesson That Will Stay With Me. He has used these adventures for 30 years and kids enjoy them so much. He was especially glad that these puzzle adventures will be their last memories of attending primary school. They was so much better than Key Stage 2 SATs.

The Find the Factors puzzles I create are a playful way to get to know the multiplication table better. This level 3 puzzle can be solved by considering the factors of 30 and 90 where only factor pairs with numbers from 1 to 10 are used. After those factors are found, write them in the appropriate cells then work your way down the puzzle row by row using logic until all of the factors are found.

Singapore Maths Tuition shares an “average” math puzzle with a twist that might baffle all but those kids who enjoy math but find little challenge in traditional math work. No worries for the rest of us; a good explanation is also included.

Mathematical Humor

Emily’s Post tells a timely math joke about three ducks that will teach while it delights children in Modern Math.

Joseph Nebus has a humor blog in which he wrote a humorous post he titled What your Favorite Polygon Says about You. I’m not sure what my favorite polygon is, but I will carefully consider all the possibilities.

The Bored Side of the Phone shares a couple of stand-up-comedy-worthy jokes about Mathematics in The Truth About Maths.

Numbers

Natural Numbers:

The counting numbers/whole number set has been further categorized! Can you imagine how? Read all about it in Publications de BOULAY’s New Whole Numbers classification. As you learned about the set of ultimate numbers, how well did your imagination serve you?

Rational and Irrational Numbers: Mike of Mike’s Math Page gives us a front-row seat observing how he teaches his sons about mathematics in Sharing John Urschel’s great video on rational and irrational numbers with my son.

Imaginary Numbers: Every year Joseph Nebus lets his readers chose mathematical topics for each letter of the alphabet, and then he writes a post about each of those A to Z topics. For 2020 he wrote a serious essay on imaginary numbers that playfully included some comics about some numbers that you can imagine.

Life skills and Math

Ladybugs or ladybirds want to teach you some math concepts. Come out in the garden with the lesson plans provided by DogwoodDays in Garden Schooling: Ladybird Maths and see what you learn!

Cooking is an important life skill and a fun way to learn about fractions and other math concepts. The For-Health blog featured a post kids and adults can enjoy together: How to Cut Down Recipes: What’s Half of ½ cup, ¾ cup, 2/3 cup and More. Verifying the given measurement equivalents can be great fun for kids so do let that happen!

How can we make our lives be as well-balanced as an equation? That’s a good question for high school students to consider. A life coach’s advice on how to find success in life is given using mathematical symbols and vocabulary in Mathematics of Life, Learn from Math symbols.

Corona Virus Math

In Wheel of Theodorus – Distance Learning Edition, MrJoyce180’s shares his students’ work creating their own, and I do mean their own, Wheels of Theodorus. All of this creating occurred virtually during the lockdown. He shares both the successes and the failures. This was one of my favorite discoveries while I created this carnival.

I didn’t have my glasses on questions Cosco’s mathematical reasoning of cake buying and serving in Let (a few of) them eat cake! Can you formulate a word problem from this post?

Statistics

When Disney produces a direct to video sequel, will a Roman numeral, an Arabic numeral, or neither most likely appear in the title? Even young children will be able to explore that topic with Joseph Nebus in this Statistics Saturday Post.

World Affairs uses cleverly represented graphs to help us understand The Math of How China Surpasses USA in 5 Years. Understanding the math behind the graphs could help us improve our situation.

Poetry and Math

Beginning with irrational numbers, Prerna’s Blog uses mathematical and poetic language to describe the Mathematics of My Mind.

Math+Life connects math with life by writing poetry. After you read Set in Stone the mathematics of sets is explained followed by how they relate to life. Do we place limits on children or adults when we categorize them into sets of different types of people?

Making Math More Inclusive

Please read Sunil Singh’s powerful and thought-provoking post, How to Begin Bringing Rich and Inclusive Math History Resources Inside K to 12 Classrooms.

I am also pleased to introduce you to the brand-new BlackWomenRockMath Blog. Their first post is The Brilliance Hiding in Plain Sight in which three women share their sobering math stories. Thankfully, they each were able to overcome negative early experiences in learning mathematics to make worthwhile contributions to mathematics education today.

Mathematics Carnivals and Amusements:

Every Monday Denise Gaskins invites you over for a Morning Coffee. There she will direct you to other mathematics blogs for your edification and amusement.

There is also a Carnival of Mathematics that may interest you. The current (184th) Carnival is hosted at Tom Rocks Maths.

I really liked putting this month’s carnival together, and I hope you have enjoyed reading it as well. Feel free to stop by and hang out whenever you’d like.

The previous Playful Math Education Blog Carnival #139 was hosted by Math Mama Writes. Be sure to check it out if you haven’t already.

I am already looking forward to the next Playful Math Education Blog Carnival which will be hosted by Joseph Nebus of Nebus Research.

Perhaps you would like to volunteer to host one of the carnivals? Contact Denise Gaskins to get on the carnival calendar! I can’t wait to see what you put together!

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:

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!

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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