#148 Playful Math Education Carnival

Magical math books are one of my favorite ways to share mathematics with children. Over the past 4 years, I’ve written about moments of math wonder and joy I’ve shared with my children through reading. There are of course many other paths for exploring math with children from problem solving to art projects. Starting January 2022, I am expanding this blog to share more math magic. The new blog (www.fairymathmother.com) will offer a curated list math art projects, problems, puzzles, games and, of course, books!

Fellow blogger, author, and educator Denise Gaskins knows all about the many magical paths for sharing math. I’ve learned so much from her on Twitter and her blog. Denise began a monthly traveling blog post series, The Playful Math Education Blog Carnival (formerly “Math Teachers at Play”), as a way to share math “tips, tidbits, games, activities, and more.” Check out the #146 Playful Math Carnival hosted by Iva Sallay for a treasure trove of magical math and #147 Playful Math Carnival hosted by Denise Gaskin for 12 archived posts to celebrate the 12th anniversary of The Playful Math Education Blog Carnival. I am thrilled to be hosting Carnival #148.

By tradition, we start the carnival with a bit of trivia in honor of our 148th edition. To be honest this had me a bit stumped. At first I went to a book I’ve owned for 20 years by David Wells called Curious and Interesting Numbers, but nothing was listed for 148.

Then, I turned to Wikipedia and found out 148 is the second number to be bothheptagonal number and a centered heptagonal number (the first is 1). I’m familiar with a few figurate number sequences. For example, the sequence of triangular numbers: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, … . (See green image below) and the sequence of square numbers: 1, 4, 9, 16, 25, 36,… . (See blue image below).

However, I was not familiar with figurate number sequence of heptagonal numbers (a 7-sided shape). Below is an image illustrating how the sequence of heptagonal numbers (1, 7, 18, 34, 55, 81, 112, 148, …) can be determined geometrically (Source: Public Domain image). Extend the figure below three more layers to get the number 148.

centered heptagonal number is “a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers”. (Source: Wikipedia) The sequence of centered heptagonal numbers is 1, 8, 22, 43, 71, 106, 148, 197, …. The image below illustrates the first four centered heptagonal numbers greater than one. The nth centered heptagonal number can be calculated by multiplying the triangular number for (n – 1) by 7, then adding 1. For example, to find the 7th centered heptagonal number, multiply the 6th triangular number 21 by 7 and add 1 to get 148. (Source: Image by Claudio Rocchini is licensed under CC by 2.5).

I guess I could have left it at that, but I really wanted to search for some more interesting facts about 148. I turned to the Carnival of Mathematics, another blog post series which is on their #196 blog post. On Carnival of Math post #148, I found this story on the Comfortably Numbered blog. In the story, a king poses a life-saving problem to a bad-tempered traveler.

“Now, if you can tell me how many ways there are to break a chessboard into (indistinguishable) square pieces, I shall spare your life.”

From Comfortably Numbered blog by Kartik Chandra.

At the end of the story, as if by some Ramanujan taxi cab magic, the traveler announces the answer to the king’s question: 148. What a curious answer to a curious question. I found myself in a state of wonder. How did the traveler know this? Or really, how did the storyteller know this? The story had me hooked, and after working the problem for a bit, I contacted blogger Kartik Chandra to find out more. Kartik kindly pointed me to this cool search engine, Online Encyclopedia of Integer Sequences and revealed this search engine to be the secret behind the magical connection of 148 to his story, The number of different ways to divide an 8 X 8 square into sub-squares, considering only the list of parts, is in fact 148 (See property AO34295) I also found this recent article featuring Kartik, an inspirational polymath studying for this doctorate at MIT this fall.


Now let’s get this Playful Math Education Carnival magic started. You can click on the list below to jump to each section.

Math Book Magic

Math Game Magic

Math Problem/Puzzle Magic

Math Art Magic

Mathematician Magic

Math Book Magic

Math Story Telling Day is September 25th, time to get your magical math book stack ready.

For the little ones, the new board book series by Grace Lin from Charlesbridge’s Storytelling Math series can’t be beat. Lin’s vibrant images and simple text provide the perfect launch into real-world exploration and math talk as children follow the experiences of three friends: Mei (inspired by Lin’s daughter), Olivia, and Alex. Here is a bit about the magic my children I found in these board books.

And here’s more from Charlesbridge’s Storytelling Math series which never disappoints.

  • Writer, illustrator and educator Jean Benton shares her interview with Art Coulson author of Look, Grandma! Ni, Elisi (illustrated by Madelyn Goodnight). Benton writes that how this picture book pulls “Cherokee traditions, high end math concepts, and story together in one amazing package!”. Look, Grandma! Ni, Elisi explores the concepts of volume, capacity AND area.
  • Ruth Coffey, who blogs at Books For Our Children, shares her review of Bracelets from Bina’s Brothers written by Rajani LaRocca and illustrated by Chaaya Prabhat. Coffey describes the book as “a glorious mix of story, siblings, and maths”. This book features mathematical patterns. [Aside: Author and medical doctor Rajani LaRocca is really on a roll this year in 2021 with 6 books as a debut kidlit author!. In particular, I adore her middle grade novel in verse Red, White and Whole and am in awe of this renaissance woman! (She is a mother, doctor, wonderer, writer and more. For more about this author go here. ]

Math educator and fellow picture book lover Lenny VerMaas shares his own magical book list for supporting a growth mindset. Click the link below for more ideas from Lenny.

Christopher Danielson tells us a bit about a new book created from children-generated solutions to a wonderful puzzle/challenge posed at Math-On-a Stick at the Minnesota State Fair: The Hexagon Challenge. Click the top of Christopher’s tweet to learn more about the magic of this book. You can find a template to create your own paper version of the Hexagon challenge at publicmath.com, here. Math-On-A-Stick is still looking for volunteers. If you are in the area, I highly recommend this opportunity to volunteer. It is a one-of-a kind experience. Find more info here.

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Math Game Magic

Denise Gaskins shares a new math game on her blog every week in her her series Math Game Monday Note: Be sure to check them out each week as they can only go live for one week exactly as they are excerpts from her published magical math books (and publisher request full excerpts not appear too long on websites). So if you like what you see, be sure to check out her list of playful math math resources. There are more games than you’ll have time to play for sure!

Have you seen the game Factris from Mathigon?! We discovered the game at our house and we are competing for the high score. I spent WAY too much time getting my score in the 7 millions, but my 11-year old is working on surpassing that soon (he was not happy when this happened recently in his quest to beat me). If you have a child learning multiplication, this is the game for you!

In their Making Math Moments that Matter podcast, Kyle Pierce and Jon Orr interview Dan Finkel in Episode #11: Play is the Engine of Learning. Dan Finkel is creator of thoughtfully constructed math games Prime Climb and Tiny Polka Dots and a new wonderful set of multiplication flashcards called Multiplication by Heart (which so happen to be also incorporated into an Mathigon activity!). Dan speaks about teaching with games in the math classroom and shares the three things he looks for when selecting games for use in the math classroom.

Love this game Kendra Lockman plays before bed with her child (Click tweet is see some examples).

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Math Puzzle/Problem Magic

In her blog post, K-8 math specialist Jenna Laib shares how mathematics of arrays came up in her daughter’s jigsaw puzzle play.

Some lovely math play on the beach from Charlotte Hawthorne with the Tower of Hanoi problem.

In this post containing her 1661th! puzzle (what?!), Iva Sallay invites readers to explore number palindromes and their factors. And in her 1660th puzzle she shares this mystery puzzle, go here for more info.

Shelby Strong recently blogged about a presentation she gave at Howie Hua‘s Math Summer 2021 conference where she combined her two of her favorite things, Desmos and Visual Patterns (visualpatterns.org). Check out her post about that work here.

Numberphile came up with a new video featuring Tom Crawford‘s favorite puzzle, an (old) Oxford Admissions problem, called A Problem with Rectangles.

If you are looking for geometric puzzles, Catriona Agg never disappoints. Here are a couple recent ones. Follow her on twitter for loads more!

Recently, Vincent Pantaloni tweeted about this match stick puzzle he created along with Ed Southall from their book Geometric Snacks.

Some number play surprises in this tweet from Berkley Everett (Click to read thread).

And if someone searching for math problems mentions the Thinking Classroom in a tweet, you know that list of comments are going to include some lovely problems to check out. The comments for Emma Vierheller‘s tweet here point you in lots of different directions if you’re in the market for some math magical problems.

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Math Art Magic

Diane Devine wrapped up the last #MathPhoto21 prompt with an invitation to share images of Math Play! Here is a beautiful illustration of #mathplay from @SACDavidson.

Check out the hashtags on Twitter: #MathPhoto21, #mathplay. And as Erick Lee mentions, keep adding your math photos on twitter for any of the week’s challenges (#mathsports or #lines). This fun co-sharing of math noticing and art does not expire.

For fans of Ramanujan, illustrator Daniel Miyares made a print of this beautiful illustration from the picture book, The Boy Who Dreamed of Infinity, written by Amy Alznauer. We wrote about the book here. I love this illustration so much, I immediately got a copy as soon as Daniel announced they were for sale on his website.

In a recent twitter poll, Sophia Wood asked others to vote on a muse for her next Math Bird creation. Math birds?! What could this be? I clicked on her website and was blown away. The kingfisher won the poll (see below) and you MUST check out all the birds here . It’s difficult to pick a favorite. I mean… Cardinality Cardinal and Mag-pi! Math Art Magic indeed.

Beautiful things always coming from Paual Beardell Krieg‘s twitter feed, from hexaflexagons and hexahexaflexagons to Kolam designs.

Also, if you want to create your own kolam designs on Mathigon‘s Polypad, you can go here, then click on Tiles–> Geometry–> Pattern and Art–> Kolam and create away!

Hanna Murphy is always posting the dreamiest pattern block creations.

Follow #MathsArtMonday on twitter for more math art magic.

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Mathematician Magic

Jose Vilson writes a touching tribute for math educator Bob Moses in his post titled Bob Moses and the Enduring Education of Injustice. Vilson shares how he wishes ” more people in the education field felt a similar possession about [Moses’] story” as he does.” In addition to reading Jose’s tribute, you can connect to Bob Moses’ story here in his book Radical Equations: Civil Rights from Mississippi to the Algebra Project by Bob Moses and Charles E. Cobb.

Sara Strong shared this Desmos activity, which seems like a wonderful way to learn more about your students’ mathematical experiences, beliefs, and dispositions. I plan to use it this fall in my classes.

Cyclist and mathematician Anna Kiesenhofer surprised many when she became an olympic champion. Kiesenhofer used her expertise in mathematical physics and problem solving in her approach to cycling.

And there are Howie Hua‘s magical TikTok videos.

Lastly, Dan Meyer‘s rounds up lots of mathematics educator wisdom in his post Back-to-School Resource Round-Up. Check out the link for advice from Fawn Nguyen, Howie Hua, Sarah Carter, Chanea Bond, Alex Shevrin Venet.

Alright, that’s all the magic I have time to post and surely you have time to read about if you’ve even made it this far and if you have, thanks for reading! I wish everyone a great school year (both those back in school already, those learning at home, and those gearing up to enter soon). Touch math magic, and pass it on!

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