martin gardner – celebration of mind

Martin Gardner was born on October 21, 1914. Each year on or around October 21, Celebrations of Mind are held to share the topics he wrote about in his Scientific American columns. Below are books and resources about hexaflexagons and other related topics:

hexaflexagoncover martingardner gardnersworkout

A brief video of Martin flexing a hexaflexagon:

And another video from Vi Hart:

Read more about Martin Gardner and Celebration of Mind.



Gardner, M. (2001). A gardner’s workout: Training the mind and entertaining the spirit. Natick, MA: A K Peters.

Gardner, M. (1988). Hexaflexagons and other mathematical diversions: The first scientific american book of puzzles and games. Chicago: The University of Chicago Press

Resources|Gathering for Gardner from Celebration of Mind http://celebrationofmind.org/resources Accessed October 21, 2013


wisdom of the crowd

The Wisdom of the Crowd is an excellent activity for students to work with data- mean, median, and mode. Below are photos of my students working with a project we co-created and carried out to test the wisdom of our classes. It encouraged students think about the differences between mean, median, and mode.

IMG_0903   IMG_0897   IMG_1039

IMG_1041   IMG_1040   IMG_1042

Below is a brief video giving the history of Wisom of the Crowd:

This video is what the students used as a framework for our version of Wisdom of the Crowd:

Before knowing the results, the students decided to use the mean to determine the wisdom of the crowd. The collective guess of the 80 participants (75 students and 5 teachers) was 539. There were 503 pieces of candy in the jar. How close were we?


NOVA | Wisdom of the Crowds from PBS http://www.pbs.org/wgbh/nova/physics/wisdom-crowds.html Accessed October 12, 2013

Wisdom of the Crowd from Wikipedia http://en.wikipedia.org/wiki/Wisdom_of_the_crowd Accessed October 12, 2013


a mix of gardner and tanton

Pictured below are a few of my favorite Martin Gardner books that I will share with friends and students on October 21 for a Celebration of Mind:

mmm  gardnersworkout  riddles

Motivating ideas are easy to find in any of Martin Gardner’s books.  A Gardner’s Workout: Training the Mind and Entertaining the Spirit has an item in the back of the book about a classic mixture puzzle.

The video below contains the classic puzzle involving a mixture of two different liquids, presented by James Tanton.  The video mentions the idea/how to (also found in A Gardner’s Workout) that you can accomplish with cards to work through the process of the puzzle.

Get a deck of cards, split them into piles of reds and blacks, and see how it works!  Also, consider following @jamestanton and @wwmgt on twitter for multiple ideas related to and demonstrating the richness of mathematics!


Gardner, M. (2001). A gardner’s workout: Training the mind and entertaining the spirit. Natick, MA: A K Peters.

J. Tanton, Milk and soda puzzle (video!) from Thinking Mathematics http://www.jamestanton.com/?p=991 Accessed 24 September 2013


Paul Erdős

After reading The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth this summer, I came across a fantastic children’s book about Paul Erdős.  The Boy Who Loved Math: The Improbable Life of Paul Erdős by Deborah Heiligman with pictures by LeUyen Pham is an excellent introduction to the man who is well-known for his collaboration in mathematics.  Below is a photo of the cover and my favorite illustration in the book:

IMG_1232   IMG_1236

Below is a short clip from N is a Number, which is a fantastic glimpse of Paul Erdős and his life of collaboration in mathematics:


Heiligman, D. (2013). The boy who loved math: The improbable life of Paul Erdős. New York: Roaring Brook Press.

Hoffman, P. (1998). The man who loved only numbers: The story of Paul Erdős and the search for mathematical truth. New York: Hyperion.


smith numbers

Prime numbers have been a popular topic in the news.  Below is a strip about working with composite and prime numbers, using what are called Smith Numbers.  Smith Numbers are composite, but identified when the sum of the individual digits in the number are equal to the sum of the prime factors!

Now let’s take a look at 27.  The number 27 is probably most easily identified by school children as being 9 • 3. However, 9 is composite, so instead let’s take the 9 and look at it as 3 • 3.  Now we have 27 taken as 2 + 7, which is 9, and 3 + 3 + 3, which is also 9.

For the number 27: 2 + 7 = 3 + 3 + 3

Can 71 be a Smith Number?


Caldwell, C. (2013). Smith number from The Prime Glossary http://primes.utm.edu/glossary/xpage/SmithNumber.html Accessed 11 June 2013.

Hoffman, P. (1998). The man who loved only numbers: The story of Paul Erdos and the search for mathematical truth. New York: Hyperion.

Weisstein, Eric W. “Smith Number.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/SmithNumber.html Accessed 11 June 2013.


the menger sponge with playing cards

An activity chosen by my students during the 2012-2013 school year was to build a level 2 Menger Sponge with playing cards.


The relevant mathematical concepts illustrated by the activity can be found in “Expectations from Principles and Standards for School Mathematics Content Standards: Grade 4.”  The three major relevant concepts included working with estimation and multiplication to determine how many cards and how many decks of cards would be needed for the level 2 Menger Sponge project, analyzing attributes of three-dimensional shapes and developing vocabulary to describe the attributes, and recognizing geometric ideas and applying them to problems in the classroom or real life.


When students decided they wanted to build a Menger Sponge, first I required them to figure out how many cards we would need.  Second, particularly during the build, students would refer to a “face” and or an edge or a vertex piece.  Third, students recognized that each cube needed to be comprised of “mostly” straight folds.  Otherwise, the cubes would not fit together to form a level 1 sponge without falling apart.  Most importantly, students collaborated at all stages of the project.







This activity was inspired by Dr. Jeanine Mosely’s work building a level 3 Menger Sponge with business cards.  The first time I saw the idea was during a presentation in Atlanta, Georgia at Gathering for Gardner 10.


At the end of our project, we used more than 2700 cards.

Find additional photos here.


Menger Sponge from The Institue for Figuring // Online Mathematical Paper Folding http://theiff.org/oexhibits/menger02.html Accessed 10 May 2013.

Menger Sponge from Wikipedia http://en.wikipedia.org/wiki/Menger_sponge Accessed 10 May 2013.

Menger Sponge from WolframAlpha http://www.wolframalpha.com/input/?i=Menger+sponge Accessed 10 May 2013.

Weisstein, Eric W. “Menger Sponge.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/MengerSponge.html Accessed 10 May 2013.

Pi Day

Pi Day Countdown


February 2015
« Oct