August 21

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Playful Math Carnival 167

Welcome to the 167th Playful Math Blog Carnival, except it's not really a blog carnival because blogs are a dying breed. It's more of a internet/social media carnival. That's not the point really, it's about playful math and there is still plenty of that on the web. 

Last month, the carnival was hosted by Sue at Math Mama. If you missed it, you should check it out.

The Number 167

It's traditional to start the carnival with a discussion on the carnival number: 167. Number 167 is a Happy Number. I know, I know - what in the world is a happy number? Does the existence of happy numbers mean there are sad numbers? Yes, sad numbers do exist. According to Wikipedia, "In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit."   Let's try this, I'm a bit skeptical but off we go:


Just being honest here. This isn't looking like we are going to get to one, but let's try it again.


Nearly done. I can see the end! One more time. 

That was a delightful surprise.  Sad or unhappy numbers don't offer this little surprise.  167 is full of surprises. 

For instance, we can insert a couple of symbols and get a correct equation: 1 + 6 = 7. Isn't that fun? This would make a great exploration for learners: Using only complements inside of and including 10, how many of these types of numbers could you create? How would you know when you had them all?

167 is a strictly non-palindromic number, which means it can't be written the same forward and backwards in any base between 2 & 165.  The reason we stop at 165 is because every number n  (in this case 167) is the palindrome 11 in the base n-1 (so 167 - 1 = 166). 

Not only is 167 prime, but it is a safe prime. That means it is the sum of a doubled prime plus 1 or 2(133) + 1. Not sure what this has to do with qualities of safeness, but if you do, let me know in the comments section. 

It is also a full reptend prime. Not sure I've wrapped my head around full reptend primes and Fermat's Quotient. But this I get: 7 is also full reptend prime. That means there is a 6-digit number such that when you multiply it by any other integer, the digits are exactly the same and in the same order but start in a different place. The number for 7 is 142,857. Now go ahead and multiply it by integers 1 - 9. Notice what happens. This is the stuff that makes math cool. 

The same thing is true for 167 - but the number is 166 digits long and I don't know what it is, nor can I get my head wrapped around that. 

On To Other Mathy Goodness

While #MTBOS (MathTwitterBlogOSphere) isn't what it used to be, there is plenty of great stuff to be found on social media. Though the write ups are a bit shorter these days. 

This is just some of the fun, playful math stuff I found from the August 2023 chit chat across the web.

There was a lot of buzz on what's left of the #MTBOS on Twitter about this game Chris Hogbin created called Number Hive. This is a seriously addictive game. It's free and no ads. Yeah. I dropped Sudoku on my phone for this little gem. It's math facts meets the game 'GO' or '4 in a Row' but requires a lot more strategy. There's an app, however you can also buy a full set of game boards (super cheap) to do in-person, 2-player games. And there's even Number Hive Tournament Rules. The Number Hive boards mean the game can be played at math clubs, classrooms, homeschool co-ops, and family game nights.  Just warning you now, you'll be fighting with your kids over the app.


This is a different version of "4 in a Row" created by Joe Swartz at  Exit10A. I learned about it because Robert Kaplinski is playing this with his elementary students. 

 Sam Shah went to the movies with his Alamo Movie Pass and discusses the intersection of math, impulse purchases, entertainment and self-deception.

 Tim Brzezinski posted this on Twitter and Ticktock. It's a fascinating look at #Pythagoras and left me wondering about other shapes.

It seems like it's the season for new math books on math play. There are so many inexpensive resources to add to the curriculum to make math playful. This is just what I found posted online in August.

This wasn't exactly in August, but it's close. Ben Orlin, from Math with Bad Drawings, has published a free companion to his book Math Games with Bad Drawings, called Solo Flights. It's all about how to turn the games in his book into games you can play alone. If you aren't following Ben Orlin, you should be.

This post isn't from August either, but the sale on the Super Tangrams ends in August (so I think that counts) on Henri Picciotto's Mathed site. Since there is no other place to get Super Tangrams, you might want to check it out and all of the other tangram material that he's published - much of it free. Tangrams are fabulous math fun and depending on the puzzle, can be both simple and quite challenging. Excellent spatial problem-solving activity and, of course, play.

Super Tangrams:

There's a lot of buzz surrounding the book Math Play by Libo Valencia and I'll probably be picking it up - because you just can't have enough books on playing math and this looks interesting. 

The folks over at Abacus created the very best recipe for a bubble mixture. There are still enough humid days to make it worth putting the recipe together plus winter is coming. Plus, according to them, this recipe consistenly makes large, long lasting bubbles (one lasting 24 hours). How is that for the intersection of math, science and play?

Over on Twitter, Abacus also dropped this mesmerizing video. Geometry and music. You can't avert your eyes. 

Speaking of geometry, Karen Campe wrote an excellent article on using the area model for working out hard to grasp math ideas. We are big fans of the area model. The post does a great job of using both a drawn model and one that uses manipulatives. For those of you who've seen those YouTube videos making fun of the area model as if it's this weird thing common core dreamed up - you'll find it in Ray's Arithmetic published 1885.  Did you ever wonder where we got the long division symbol? 

If you don't have enough to explore and need some more, James Myklebust-Hampshire tweeted about the sembl app. It's a free app that contains over 500 tasks that are designed to provoke thinking. 

We're nearly done with our August Playful Math Blog Carnival. Before you go, check out Denise Gaskins' Math Monday Game  Strike Out. Denise is the one who started this carnival and keeps it going. You can subscribe and get all kinds of playful math activities in your inbox or get one of her highly recommended playful math books.  Also, let her know if you'd be interested in hosting a Playful Math Blog Carnival.

Oh, before we go, The International Day of Mathematics is March 14th, 2024. What does that have to do with August this year? Well, they just announced next year's theme. It's Playing with Math. Thought I'd let you know since this is the Playful Math Blog Carnival and all. 



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Caleb Gattegno

Educator, Mathematician 

โ Only awareness is educable. . ."

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