Tuesday, April 9, 2013

Math Teachers at Play 61

Researching 61 as a number tells us it's not just prime, but is a twin prime, a cuban prime, the 9th Mersenne prime exponent, and a Pillai prime. That's primo prime pedigree. It's a Keith number and thrice Fortunate. (Fortunate numbers are pretty interesting and the subject of an open conjecture.) It's a centered square number (1+4+8+12+16+20), a centered hexagonal number (1+6+12+18+24) and a centered decagonal number (1+10+20+30); mostly because it's neighbor 60 is so nice. (Did you see the 60th Math Teachers at Play?) Is there a reason that \( \sum 4n \), \( \sum 6n \) and \( \sum 10n \) overlap at 60? But the fact that really caught my eye was that 61 is an Euler Zig Zag number. How cool can a number get?

The Euler Zig Zag number for n is the number of alternating permutations (up-down-up-down arrangements) on n ordered objects.  For example 2 is the Euler Zig Zag number for a set of 3 objects. Désiré André was one of the first to study these, and I hadn't known about him before. He was a real leader of his mathematical community, serving as the president of a math lover society that exists to this day, the Société Philomathique de Paris. I want a t-shirt. How many elements are in the set for which there are 61 Zig Zags? Combinatorist Robert Dickaus has the answer and some great visualizations of these alternating permutations.

Early Learners
Preschool Math Ideas  from  Lilac at Learners in Bloom.   "Preschool math can be so creative and fun.  This post is a round-up of some of my favorite math activities from the past year (twins age 2.5-3.5)." Lots of fun kinesthetic number experiences shared here.

Make Me Dinner from Jennifer Bardsley at Teaching My Baby to Read.  "Here's a deceptively simple math game to play with little ones. It works on loads of math skills through pretend play." Working on cardinality and comparison.

Center Idea For Building Addition Fluency at Zoom Zoom Classroom.  "This blog post highlights a product I created.  The idea is to provide children with extra practice with solving addition facts in both vertical and horizontal form." CCSS.Math.Content.1.OA.C.6  There's velcro, but I'm not sure I understand the point of this center.

Skip-bo Addition Game (or The Funnest-est Bestest Math Game Ever) from Amy at Ita Vita.   "I wanted a fun way to practice addition with my son and came up with this one on the spur of the moment. It was such a hit. It can be modified to make it harder or easier, and variations could be invented for subtraction as well, or possibly even multiplication or division."

EDITOR'S SUBMISSION: Peeps Math with Tabitha from Christopher Danielson at Overthinking My Teaching. A slice of number thinking, representation and a teaching demonstration all rolled up in one.

Eva the Weaver
A Visual Approach to Simplying Radicals from Chris Hunter at Reflections in the Why.  "I'm submitting this blog post because I think the method discussed is bloody brilliant. I can get away with saying that because my colleague created it, not me. When you see it, you'll think 'Why haven't I seen this before?' " Perfectly fits his blog title!

Flippable Fun with Equations from Jennifer Smith-Sloane at 4mula Fun. Jennifer shares one of her Interactive Notebook (INB) on multistep equations.

If you like the INB approach, be sure to check out the resources at the Julie Reulbach's Math Wiki, too. (Among the many, many resources.)

Using the Area of a Rectangle to Derive the Area of a Triangle  from Guillermo Bautista, Jr  at Proofs from the Book poses some questions and shares some visualizations about the familiar triangle area formula.  He also shared Representing the Sum and Difference of Two Squares, another visual representation.
Understanding Slope  from Jamie Riggs at Miss Math Dork shares an early slope activity she did with her students in the resource room that seemed to help the idea develop for them.

Half-your-age-plus-seven Rule from John Chase at Random Walks.   "I saw this graph illustrating the half-your-age-plus-seven rule for dating ages  and I immediately thought about how this is both (1) a wonderful application of systems of inequalities, and (2) a wonderful application of inverse functions. It turns out that that 80-year-old has a *range* of datable ages from 47 at the lowest to 146 at the highest (good luck with that!). I had never thought of it that way."

EDITOR'S SUBMISSION: More Imbalance Problems from Paul Salomon at Lost in Recursion. I love these elegant and elemental problems for getting at some really powerful algebraic thinking. Plus he's hosting a contest. Check out the whole series.

Why is division of 0 Undefined? at Mathematization is a quick spreadsheet approach to divergence of 12/x at zero. 

Domain and Range  from Shaun at Math Concepts Explained. Shaun tries to explain these ideas in student friendly language.  (But be careful!) In a similar vein he steps through the procedure of Understanding Point Slope Form.

Squares at Five Triangles Mathematics.  "This is a middle school level problem that requires some visual and elementary math skills, but does not require the Pythagorean theorem." Good rearrangement problem with some room for generalization. What determines the size of the center square?

This actually inspired me to make a GeoGebra sketch to generalize this with a dynamic representation.  Download or mobile-ready applet. Thought this dissection was the essential idea in several proofs of the Pythagorean Theorem.

Speaking of inspiring me to do geometry, have you checked out the amazing art at Geometry Daily?

Oh, and what about the Pythagorean Theorem puzzle/proof Daniel Hardisky shared at Alexander Bogolmolny's Cut the Knot? He first posted it in Alexander's Facebook page for Interactive Mathematics Miscellany and Puzzles.  (I made a sketch for that, too. I may have a problem.)


Probability Tree Diagrams as Puzzles!  from Bon Crowder  at Math Four.  "I teach probabiity trees in Finite Math as well as Stats. And students either love them or hate them. Treating probability trees as puzzles helps them to practice and then see the value of them." Two free downloads with 11 probability tree puzzles.

Puzzle Break!

Quento is a fun sum and difference puzzle app for iOS or Android. Free trial version, 99¢ full.

Here's an example. The 2 number and 3 number paths are shown. No reusing a number. How would you make 8? I just discovered there's a 5 number option!

I made one for the carnival at right. My previous turns hosting were 47, 36, 26 and 22, so...

Thomas Hawk
Spot the mistake from Colleen Young at Mathematics, Leanring and Web 2.0.   "A collection of resources which allow students to mark work and correct errors. This is something they enjoy doing and can lead to some great discussions." Colleen highlights good TES resources for this idea, but I can't help linking Michael Pershan's Math Mistakes here also.

Start with One Straight Line  at Moebius Noodles.  A post in which Noodles contributor, Malke Rosenfeld, talks about using blue painters' tape to create an environment that fosters mathematical exploration.

EDITOR'S SUBMISSION: Speaking of Malke, do not miss her post at The Map Is Not the Territory on Adventurous Professional Learning, with a great video about what success looks like in her classroom.

What Goes Here? from David Coffey at DeltaScape shares an outstanding algebra lesson and teacher-thinking from one of our novice teachers, Alyssa Boike.

Mathematics: The Science of Patterns from Guillermo at Mathematics and Multimedia. "A post celebrating the beauty of mathematics through patterns."

This is where I'll throw in a plug for Fawn Nguyen's single serving Visual Patterns site. Many great problems.

On the theme 'Mathematicians Ask Questions', Denise Gaskins at Let's Play Math, the founder of this here carnival here, looks at questions for teachers or students to ask.

Subtraction with Borrowing: The Video  from Julie at Craft Knife.   "Faced with a kid unenthusiastic about learning subtraction with borrowing, I asked her to film a video tutorial to teach other kids how to do it. With that, I immediately found myself with an enthusiastic, highly engaged kiddo..." Julie then goes on to use the video for some analysis of the teacher's understanding.

Let's Get Talking  from Oluwasanya Awe at MatheMazier.   "I'm a student and I have worked as a tutor for about 3 years and I just thought I should 'pour out' some of the cries of people I have taught. I want this post to bring to mind, the problem children face in Mathematics and also to question teachers." A dozen short student complaints and misconceptions. He's also wondering about Points, Shapes and Space.

Morris Motorcycles
Math & Logic Puzzles from Sue VanHattum at Math Mama Writes.  "I went to a Pi Day Puzzle Party and had a blast. Here are the puzzles. (No pi involved.)" Very fun story from Sue.

10 Fun Parent-Tested Math Board Games from Caroline Mukisa at Maths Insider.  "Board games are a great way to make math practice painless. For those of you fellow board games fans, here are 10 recommended math board games, along with what parents have to say about them."

Math Game: Use Dominoes to Practice Number Bonds from Jeremy at Make Learning Fun.

Encouraging a Love of Math from Tricia Stohr-Hunt at Bookish Ways.   "I teach preservice teachers and spend a lot of time thinking about ways to get kids to love (or at least like) math. This post is about some of the things I suggest with links to additional resources." Puzzles, art, books and more, with loads of links.

How to Choose Your Marriageable Date from Yan Kow Cheong at Singapore Math: on numerical patterns in dates. (Reminded me of Dave Coffey's meditation on Pi Day - that every day should be a math day.)

Math Art - Geometry  from Julie at Highhill Homeschool: Many kids are very artistic and find learning geometry through art very rewarding. Geometric math art is always close to my heart. Julie is using activities from Mathematics in Space and Time by John Blackwood. Julie also shared Secret Codes    "Secret codes are really complicated patterns. They are fun to figure out and good for building creative math skills."

Basic operations worksheets generator UPDATED!  from Maria at Homeschool Math Blog. She's added more customizable features to their free random problem generator. (Please find a creative way to use such problems.)

Soggy Math from Ritsumei at Baby Steps.  "Wherein we have an impromptu math lesson in the swimming pool."

That brings MTAP61 to a close. I think we're still looking for a host for 62, and I highly recommend the opportunity. Just want to submit a post? Here's the link!

But I can't close without acknowledging that we all know the number 61 can really only mean one thing in the spring...

See Mid TN
Roger Maris hit the unimaginable 61st home run in 1961 to break Babe Ruth's single season record. Some people still consider it to be the record as those who have broken it were allegedly using chemical enhancements. I promise you a clean blog carnival with no unnatural math enhancing compounds. Of course, there's math in those stats: what portion of his hits were HR, how to compare his season of 61 to Ruth's season of 60 (in only 151 games), how do they compare to modern hitters, how hard is it to hit a home run... it could go on as long as the whole season. Maris even has some advice that's just as good in math as in baseball: "You hit home runs not by chance but by preparation."

Image credits: Flickr users noted on their photographs. I think I made all the other ones!

Then maybe you'd be kind enough to try the adding and subtracting integers game I made in Scratch? And give me feedback?

Here's the game, and here's the post about it.


  1. What a great collection, thanks! (I've bookmarked the post on encouraging a love of math and the mistakes collection post.) And I hope to find time later to do the puzzle you created.

  2. Fantastic collection and I learned a heap about the number 61. I was especially glad to find the post about math board games.

  3. Thank you for including me in your collection!

  4. Thanks for including "Marriageable Dates," too. May I take this opportunity to invite "Math Hombre" readers to visit my recently set-up "Yan's One Minute Math Blog," which aims to focus on some problem-solving strategies commonly used among Singapore math students?

  5. Really mind refreshing collection and useful for students to get their brain into it and solve. Math games are great for students to learn math.

  6. As I'm writing the May carnival, I read back through yours to make sure I wasn't duplicating any posts. I noticed a glitch in your post: half a paragraph is missing, where you had linked to my post.