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Math Teachers at Play: Three-Cubed Edition

June 19, 2010

Magic Squares Rubik's Cube Puzzle

Photo Credit: Colin Hall

Welcome to the Blog Carnival:

Math Teachers at Play!

Twenty-seven is one of my favorite numbers, so I was excited to find that “my” edition of the carnival would be number 27.

Some fun facts via Wikipedia (click the link for even more):

  • 27 is a perfect cube: 3³ = 3 × 3 × 3 = 27.
  • 27 can also be written as 23 using the notation of tetration, which means that it is 3 taken to the power of itself, 2 times:

{^{n}a} =  \underbrace{a^{a^{\cdot^{\cdot^{a}}}}}_n

a exponentiated by itself, n times.
  • 27  is the twenty-eighth (and twenty-ninth) digit in π. (3.141592653589793238462643383279…). If you start counting with 0 it is considered one of few Self-Locating strings in pi.
  • 27  is the first composite number not evenly divisible by any of its digits.

I don’t know what I was thinking, agreeing to do a blog carnival in the middle of June!  So please accept my apologies for the tardiness of this post, and the lack of creativity in presenting the posts!

Without further ado, the posts:

We’ll start the carnival with a little humor as Patrick Vennebush presents Cats and Dogs math jokes at Math Jokes 4 Mathy Folks.

I always love the way Denise at Let’s Play Math! makes word problems fun by her choices of literary themes, as well as providing excellent explanations of to approach them.  Hobbit Math: Elementary Problem Solving 5th Grade is a fantastic example of her wonderful style.

Imagine discussing the Fundamental Theorem of Calculus to a very gifted eight-year-old.  Sue VanHattum provides a peek into her work with Artemis in Sneaking Up On the Fundamental Theorem of Calculus at Math Mama Writes….

What happens to the American flag if Puerto Rico becomes the 51st state?  Read A mathematician figures out the best way to jam an extra star onto the American flag by Chris Wilson at Slate Magazine to find out!  There’s also a fun widget provided so you can see what the flag might look like with an arbitrary number of stars, using a variety of different types of pattern.

Check out Caroline Mukisa’s brief interview with a UK-trained Maths tutor in A Maths Tutor Reveals All! at Maths Insider.

David Ginsburg tackles a huge pet peeve of mine — the lack of “sanity checking” of answers among math students — in Estimation Before Computation at Coach G’s Teaching Tips.  (I posted a related rant — my Calculator Rant here a few years ago.)

Teachers stuck with silly word problems provided in the officially sanctioned textbooks will appreciate the ideas in One word problem – many word problems at CTK Insights.  (This expands on a related post from Dan Meyer a few months back on his blog dy/dan.)

Tracy Beach presents New Teacher Downloadable: Give Parents Ideas to Avoid the “Summer Slide” posted at Math Learning, Fun & Education Blog : Dreambox Learning. (Note that the handout also contains an advertisement encouraging parents to purchase a subscription to their website. I don’t know enough about their subscription service to offer an opinion as to quality or value.)

C heck out Guillermo P. Bautista Jr.’s presentation of Rational and Irrational Numbers at Mathematics and Multimedia for clear explanations and diagrams illustrating that the real numbers are divided into rationals and irrationals.

Shana Donohue presents two zero-based posts at her appropriately-named blog The ZeroSum RulerTo the Zero! [power] and Dividing by Zero Blows up the Universe!. The middle school students I work with seem to think that the rules about zero are mostly arbitrary. (I kind of agree with them on 0! — 1 is the value that makes all the combinatorial formulas work out cleanly, but I’ve never heard an actual good argument for it otherwise.) But these posts show why and how the rules make perfect sense when it comes to division by zero and raising numbers to the zeroth power!  The “to the zero” lesson also extends gracefully into explaining how negative exponents work, and showing that they just keep following the same pattern. :)

Pat Ballew stumps his pre-calc students by asking the simple question, “Given two points, write the equation of a line containing the two points,” in Given Two Points???? at Pat’sBlog.  Why are these bright honors students stumped?  Because the points given are in three dimensions rather than two!

Jason Dyer offers his take on Dan Meyer’s “Be Less Helpful” TEDx speech in The varieties of Be Less Helpful at The Number Warrior.

At the intersection of Math and Computer Science, John Cook talks about what goes wrong when computations with large numbers must be carried out on computers with limited precision in What’s so hard about finding a hypotenuse? posted at The Endeavour.

And finally I decided to share some of my student’s responses to the prompt “Write the biggest number you can in this box” — an idea I got from Dr. Mike’s Math Games For Kids (check it out!)

For more Math Blog Carnival fun, check out the 66th Carnival of Mathematics posted at Wild About Math.


I missed tagging an incoming carnival post, so this one got accidentally overlooked when I put it together.  So now you get an extra bonus post:

John Golden presents a great game to practice ordering decimals in Decimal Point Pickle at Math Hombre.  It’s too late for this school year, but I’ll have to bookmark it for next year.  Thanks John and sorry for forgetting your submission in my original  post!

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34 Comments leave one →
  1. June 19, 2010 5:55 pm

    Thank you for hosting! Now I’m off to browse the entries…

  2. June 19, 2010 6:04 pm


    I love your blog about the #27 and a cube. I didn’t realize you could get a #27 on a cube until I read your blog. Also, the way you came up with different math equations for the #27 was really unique.

  3. shana donohue permalink
    June 19, 2010 8:27 pm

    Thank you so much for including me and my posts! I look forward to your calls to write about other topics! Thank you!

  4. June 20, 2010 6:37 am

    Wonderful job! Great variety!

  5. June 20, 2010 8:43 am

    On 0! (zero-factorial), if you think about n! as the number of choices in the ways you can arrange n objects, then there is exactly one way to arrange zero objects. In other words, there is only one way you can do nothing.

    • November 5, 2012 8:47 pm

      Not true! I can do nothing by watching TV, drinking a beer, or reading a Twilight novel. :-)

      My favorite prolem related to this… What’s the product of the single-digit prime factors of 143?

  6. David Ginsburg permalink
    June 20, 2010 9:20 am

    Lots of great posts–thanks for including mine among them!!

  7. June 20, 2010 9:53 am

    @EastwoodDC — I agree that 0! “makes sense” in the combinatorial formulas, but I’ve never seen n! defined in terms of permutations of n items — I’ve always thought of it as just a convenient notation for writing out what that formula works out to be. If it’s defined as the product of the first n counting numbers (or the equivalent in more formal pi notation) then 0! is nonsensical.

    • July 3, 2010 7:49 pm

      Actually, 0!=1 makes perfect sense when viewed as the product of no numbers. Just as the sum of no numbers is the identity value for addition (0), the empty product is the identity value for multiplication (1). This is a general property of the Pi notation: the empty product is always 1.

  8. shana donohue permalink
    June 20, 2010 7:13 pm

    yes! math Hombre is the man!

  9. June 20, 2010 7:48 pm

    can’t wait to read the entries.

  10. July 12, 2010 3:06 pm

    I am new to blogs and am trying to learn math from whomever I can. I will soon be going into computer programming and I thought that this site would help prepare my mind.

    Thank you for the post. Thank you for helping my mind think more of math. I look forward to more posts!

    math games for the classroom

  11. September 25, 2010 9:24 pm

    Fabulously thorough list! Thank you for this post.

  12. October 29, 2010 9:35 am

    Great list of articles and information. I am always impressed by the knowledge people are able to share. If you do not mind me asking what blog carnival is this information coming from? I want to make sure I never miss it. Thanks again.

  13. Karen Olsen permalink
    January 24, 2011 5:06 pm

    Hi Everyone!
    Loved this post (and many of the others) – helps me keep math ideas flowing through my brain. I’ve other helpful blogs to keep up to date with math info, such as , they kind of hit on everything from exercises to info for school math teachers. All this info is making me want to go back to school and get a math degree!

  14. August 30, 2011 3:24 pm

    Hi Math Mom,
    I am just wondering what the education pundits make of the recent math scores in which Asian Americans score almost to the levels of the top countries in the world.

    Is this from home tutoring, cultural bias, or Tiger Mom parenting? I am wondering what people make of this.

  15. October 24, 2011 2:13 pm

    Simply wanna say that this is very beneficial, Thanks for taking your time to write this.

  16. January 2, 2012 8:24 pm

    I was reading throught some of the posts and i locate them to be altogether attention-grabbing. sorry my english is not exaclty the actually best. would there be anyway to transalte this into my vernacular, spanish. it would in reality better me a lot. since i could compare the english lingo to the spanish language.

  17. April 9, 2012 7:18 pm

    I just couldn’t go away your website before suggesting that I extremely enjoyed the standard information a person supply to your visitors? Is going to be again frequently to check out new posts

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