Recreational Math

resources useful for nurturing a 'math mindset'in math classrooms, math clubs, math fairs, and math circles

see also: Geometry Wonderland, Puzzles (Mechanical & Non-Mechanical)

"The element of play, which makes recreational mathematics 'recreational', may take many forms: a puzzle to be solved, a competitive game, a magic trick, paradox, fallacy, or simply mathematics with any sort of curious or amusing fillip.... Perhaps this need for play is behind even pure mathematics. There is not much difference between the delight a novice experiences in cracking a clever brain teaser and the delight a mathematician experiences in mastering a more advanced problem. Both look on beauty bare -- that clean, sharply defined, mysterious, entrancing order that underlies all structure."


Martin Gardner (1914-2010), father of recreational mathematics

Curiosity Shoppe

'The Research Behind' Guides
Mechanical Puzzles & ManipulativesBooks: Math & Logic Puzzle CollectionsBooks: Math Analysis of Games & PuzzlesBooks: Illusions & AmbigramsBooks: Math PedagogyBooks: Research & Professional Development

Curiosity Shoppe

'A First Look At' Guides

Links

for Math Educators & Recreationalists

Recreational Mathematics Magazine2014-Present

The Games & Puzzles JournalVol. 1: 1-12 (1987-89), Vol. 2: 13-18 (1996-2000)Online Journal for Mathematical RecreationsIssues 19-45 (2001-2006)

Recreational Math Video Channels


Organizations & Conferences

G4G Celebration of MindAnnual World Events
Celebration of Mind events bring people of all ages together to share and delight in playing with puzzles, games, math and magic. As Martin Gardner said, you can learn more when you’re in a state of entrancement and that’s our guiding principle.
Large and small, formal and informal, CoM events are happening around the world.
Need help planning your event? We have a growing list of resources including puzzles, games, magic tricks, illusions and crafts that are free to download and use. We also have a list of talented presenters who are happy to enliven your CoM event.
Bridges
An annual conference to foster research, practice, and new interests in the mathematical connections in art, architecture, education, and culture
2019 Bridges Conference
past conferences
Global Math Project
"A global community of mathematics teachers and supporters who want all learners across the globe to experience joy and wonder in school-relevant mathematics"
Exploding Dots Lessons
Bacche, K. A., & Tanton, J. (2018). The joy of exploding dots: A revolutionary concept that changes the way we learn and teach mathematics.
Math Pickle
A free online resource of original mathematical puzzles, games and unsolved problems for K-12 teachers. It is supported by the American Institute of Mathematics.
Its visually compelling puzzles and games engage students in tough problem solving. Its puzzles are organized by grade and subject – each designed for a 45-60 minute period. They engage struggling students in curricular skill acquisition, and deflect top students into tenacity-building challenges.

MathsJam
A monthly opportunity for math enthusiasts held in pubs & restaurants throughout the world. Activities include puzzles, games, problems or anything about math.
National Association of Math Circles
An organization that provides resourses to build and sustain successful 'math circles'
National Museum of Mathematics
The National Museum of Mathematics (MoMath) is an award-winning museum that highlights the role of mathematics in illuminating the patterns and structures all around us. Its dynamic exhibits, gallery, and programs are designed to stimulate inquiry, spark curiosity, and reveal the wonders of mathematics.
National Math Festival
The National Math Festival brings together some of the most fascinating mathematicians of our time to inspire and challenge all ages to see math in new and unexpected ways.
2019 National Math Festival
This free and public celebration returns to Washington, D.C. in 2019, with program tracks for adults, middle and high schoolers, as well as elementary schoolers and the very young.
SNAP Math Fairs
SNAP Math Fairs are student-centered, non-competitive, all-inclusive, problem-based. Students present become experts on a particular math puzzle and act as facilitators to help visitors solve them.
Math Fairs problems from Galileo.org

Gathering 4 Gardner


Gathering 4 Gardner

Biennial Conference
Martin Gardner’s mathemagical life. Recreational Mathematics Magazine, 2, 21-40. .pdf format
Mulcahy, C., & Goetz, A. (2014, October). The best friend mathematics ever had: A tip of the hat to the popular mathematics writer Martin Gardner. Mathematics Teacher, 108(3), pp. 194-199.

Berlekamp, E. R., & Rodgers, T. (1999). The mathemagician and pied piper puzzler: A collection in tribute to Martin Gardner.

Cipra, B., Demaine, E. D., Demaine, M. L., & Rodgers, T. (Eds.) (2004). Tribute to a mathemagician..

Scott Kim, Puzzle Master



Math Mondayan elementary school initiative

Math Circles

Archive of math circle activities from 1998-present, including handouts
Archive of math circle activities from 2007-present, differentiated by level, including handouts
No longer updated but contains a wealth of 'timeless' resources for math circles

A math circle is a social structure where participants engage in the depths and intricacies of mathematical thinking, propagate the culture of doing mathematics, and create knowledge. To reach these goals, participants partake in problem-solving, mathematical modeling, the practice of art, and philosophical discourse. Some circles involve competition, others do not; all promote camaraderie. wikipedia

Vandervelde, S. (2007). Circle in a box. MSRI.
Pre-Schoolers
Zvonkin, A. (2011). Math from three to seven. The story of a mathematical circle for preschoolers. American Mathematical Society.
Grades 1-6
Rozhkovskaya, N. (2014). Math circles for elementary school students: Berkeley 2009 and Manhattan 2011. American Mathematical Society.
Grades 5-7
Burago, A. (2012). Mathematical circles diaries, Year 1: Complete curriculum for grades 5 to 7. American Mathematical Society.
Grades 6-8
Burago, A. (2018). Mathematical circles diaries, Year 2: Complete curriculum for grades 6 to 8. American Mathematical Society.
Grades 7-10
Dorichenko, S. (2011). Moscow math circle: Week-by-week problem sets. American Mathematical Society.
Grades 7-12 (Top Tier)
Stankova, Z., & Rike, T. (Eds.) (2015). A decade of the Berkeley math circle: The American experience - vplume 1. American Mathematical Society.

Some Other Resources for Math Circles

Puzzling Math Problems
see also the following collections: Brian Bolt Martin Gardner Dick Hess Ivan Moscovich Raymond Smullyan
Garibi, I., Goodman, D. H., & Elran, Y. (2018). The paper puzzle book: All you need is paper. World Scientific Publishing
(middle/high school)
Kordemsky, B. A. (1992). The Moscow puzzles: 359 mathematical recreations. Dover
(middle/high school)
Pappas, T. (1997). The adventures of Penrose the mathematical cat. Wide World Publishing.
(elementary school)
Pappas, T. (2004). The further adventures of Penrose the mathematical cat. Wide World Publishing.
(elementary school)
Southall, E. (2017). Geometry snacks: Bite size problems and multiple ways to solve them. Tarquin
(middle/high school)
Southall, E. (2018). More geometry snacks: Bite size problems and multiple ways to solve them. Tarquin
(middle/high school)
Wells, D. (1992). The Penguin dictionary of curious and interesting geometry. Penguin.
Wells, D. (1998). The Penguin book of curious and interesting numbers (Revised Ed.)

Math Mindset Movement

inspired by the work of Carol Dweckadapted for math education at Stanford's 'YouCubed'
A Stanford organization to support innovative math teaching & formation of a math 'growth mindset' for students
free 6-lesson (1.5 hour) course from Stanford University's 'YouCubed" organization
Boaler, J., & Dweck, C. (2015). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching.
Boaler, J. Munson, J., & Williams, C. (2018) Mindset mathematics: Visualizing and investigating big ideas - grade 5.
Boaler, J. Munson, J., & Williams, C. (2019) Mindset mathematics: Visualizing and investigating big ideas - grade 6.
Boaler, J. Munson, J., & Williams, C. (2019) Mindset mathematics: Visualizing and investigating big ideas - grade 7.

Natural Math Community

publishers of math books for 'math mindset' environments: schools, homeschools, math circles)
(released under a Creative Commons license)
A 'math mindset' website that includes free books, an online camp for children (ages 9-15), a blog, a newsletter, and a discussion forum.
Ages: Under 3-8
McManaman, Y., & Droujkova, M. (2013). Moebius noodles.
(released under Creative Commons)
Ages; 3-8
Rosenfeld, R., & Hamilton, G. (2016). Socks are like pants, cats are like dogs: Games, puzzles, and activities for choosing, identifying, and sorting math.
(released under Creative Commons)
Ages: 3-8
Brodsky, J. (2015). Bright, brave, open minds: Engaging young children in math inquiry.
(released under Creative Commons)
Ages; 3-10
Tanton, J., & McManaman, Y. (2016). Avoid hard work!: ...And other encouraging problem-solving solving tips for the young, the very young, and the young at heart.
(released under Creative Commons)
Ages; 5-10
Fradkin, A. O., & Bishop, A. B. (2017). Funville adventures.
(released under Creative Commons)
Grades 2-8
Saul, M., & Zelbo, S. (2015). Camp logic: A week of logic games and activities for young people.
(released under Creative Commons)
Grades 2-8
Steining, R. & Steinig, R. (2018). Math renaissance: Growing math circles, changing classrooms, and creating sustainable math education.
(released under Creative Commons)
Grades 2-8
VanHattum, S. (Ed.) (2015). Playing with math: Stories from math circles, homeschoolers, and passionate teachers. Natural Math.
(released under Creative Commons.

Mathematical Reasoning & Problem Solving

Averbach, B., & Chein, O. (2000). Problem solving through recreational mathematics.
Bransford, J. D. &, Stein, B. S. (1993). The ideal problem solver: A guide to improving thinking, learning, and creativity (2nd ed.)
Michalewicz, Z. & Michalewicz, M. (2014). Puzzle-Based learning: An introduction to critical thinking and problem solving (3rd ed.).
Note: 3rd ed. is only available on Kindle.
Polya, G. (1990). Mathematics and plausible reasoning, Volume 1: Induction and analogy in mathematics.

A Playful Approach to Math Instruction

(Books)
Dacey, L., Gartland, K., & Lynch, J. B. (2017). Well Played, 6-8: Building mathematical thinking through number and algebraic games and puzzles.
Gaskins, D. (2016). Let’s play math: How families can learn math together -- and enjoy it (Version 1.3).
(cross-listed in "Pedagogy & Reform' because it provides pedagogical justification for this approach)
Singh, S., & Brownell, C. (2019). Math recess: Playful learning in an age of disruption.
(cross-listed in "Pedagogy & Reform' because it provides pedagogical justification for this approach)
Smith Jr., S. E. , & Backman C. A. (1975). Games and elementary and middle school mathematics: Readings from the arithmetic teachers. NCTM.
Positive Engagement Project
A collection of games to teach basic mathematics skills.
Gaskins, D. (2016). Let’s play math: How families can learn math together -- and enjoy it (Version 1.3).

Math Analysis of Games & Puzzles



Berkman, R. M. (2004, January). The chess and mathematics connection: More than just a game. Mathematics Teaching in the Middle School, 9(5), pp. 246-250.
Evered, L. J. (2001, April). Riddles, puzzles, and paradoxes: Having fun with serious mathematics. Mathematics Teaching in the Middle School 6(8), pp. 458-461.
Jackson, C., Cynthia, T., & Burchheister, K. (2013, March). Bingo! Select games for mathematical thinking. Mathematics Teaching in the Middle School, 18(7), pp. 424-429.
Kulig, C. J. (1996, May). Winning at QUARTO! Mathematics Teacher, 89(5), pp. 374-375.
Lach, T. & Sakshaug, L. (2015, November). Let's Do Math: Wanna Play? Mathematics Teaching in the Middle School, 11(4), pp. 172-176.
McFeetors, P. J., & Mason, R. (2009). Learning deductive reasoning through games of logic. Mathematics Teacher, 103(4), pp. 284-290.
McFeetors, P. J., & Paify, K. (2017, May) . We're in math class playing games, not playing games in math class. Mathematics Teaching in the Middle School, 22(9), pp. 534- 544.
Shaw, D. J., & Miller, C. M. (2015, August). The prisoner's dilemma: Introducing game theory. Mathematics Teacher, 109(1), pp. 29-33.
Shockey, T. L., & Bradley, D. M. (2006, April). An engaging puzzle to explore algebraic generalization. Mathematics Teacher, 99(8) pp. 532-536.
Staples, S. G. (2004, November). Patterns jumping out of a simple checker puzzle. Mathematics Teacher, 98(4), pp. 224-227.
Swetz F. (2001, September). The most magical of all magical squares. Mathematics Teacher, 94(6), pp. 458-463.
Wanko, J. J. (2017). Teaching inductive reasoning with puzzles. Mathematics Teacher, 110(7), pp. 514-519.
Watson, G. A. (2003, January). The versatile magic square. Mathematics Teaching in the Middle School, 8(5), pp. 252-255.
The books in this section are generally aimed at professional development for mathematicians, recreational math enthusiasts, or serious gamers/puzzlers. Some of the topics covered could be worked into middle/high school math with more or less effort by a teacher. See the bibliography above for articles from National Council of Teachers of Mathematics publications that cover the use of puzzles & games in a more K-12 friendly manner.
Albert, M. H., Nowakowski, R. J., & Wolfe, D. (2019). Lessons in play: An introduction to combinatorial game theory (2nd Ed.). A. K. Peters.
Beasley, J. D. (1985). The ins and outs of peg solitaire. Oxford
Beasley, J. D. (2006). The mathematics of games. Dover.
Browne, C. (2005). Connection games: Variations on a theme. A. K. Peters.
Browne, C. (Ed.)(2018). Game & puzzle design compendium: Issues 1-6.
Coffin, S. (2007). Geometric puzzle design. A. K. Peters.
Knizia, R. (2010). Dice games properly explained. Blue Terrier Press
(general public)
Levitin, A., & Levitin, M. (2011). Algorithmic puzzles. Oxford.
Neto, J. P., & Silva, J. N. (2013). Mathematical games, abstract games. Dover.
Nowakowski, R. (Ed.) (1996). Games of no chance. Cambridge
Petkovic, M, (2009). Famous puzzles of great mathematicians (New Ed.). American Mathematical Society.
Rubik, E., Varga, T., Gerzson, K., Marx, G., & Vekerdy, T. (1988). Rubik's cubic compendium. Oxford
Schuh, F. (2015). The master book of mathematical recreations.
Teixeira, R. V., & Park J.-W. (2018). Mathemagic: A magical journey through advanced math.
Fraenkel, A. S. (2012). Combinatorial games: Selected bibliography with a succinct gourmet introduction. The Electronic Journal of Combinatorics, #DS2, 1-109.

Math Games

Albert's Insomnia Homeschool Kit
Players use a common pool of cards (each containing math operations and a number) to create an equation that equals a target number. For the basic game, the target number for the first player is 1, for the secon player 2, etc. The player that solves the highest value target number is the winner. The game can be differentiated for K-12 by including/excluding various operations, e.g. addition, multiplcation, factorials, exponents).
Got It! + ‘Math Geek’ Expansionby Tom Jolly
Ages: 6+2-8 players, 30 mins.
A 6x6 grid of cards is placed randomly checkerboard-style on the table with numbers (1-14) and mathematical operators adjacent to one another. Everyone plays simultaneously, with players trying to find a five-card formula that results in the number shown on a goal card (ranging from 1-40). The solution must consist of horizontal or vertically adjacent cards, though not necessarily in a straight line. Players can mentally insert parentheses into a formula.
An easier version of Got It! can be set up for younger players, with a 5x5 grid that contains only the numbers 1-9 and only addition and subtraction as math operators.
Got It! ‘Math Geek’ Expansionby Tom Jolly

"Math Geek" is an expansion set for "Got It!" consisting of 12 cards with exponentiation, concatenation, factorial, and modulo operators, as well as the numbers 15-20.
[ NOTE: Not Currently For Sale ]
Now and VennThe Gamecrafter
Ages: 12+, 2-4 players, 30 mins.,
An abstract board game where players explore the vocabulary and formulas of five basic Venn diagram relationships.
how to play (vimeo video)
Now and Venn rules
Points of Interest (school edition)The Gamecrafter
Ages: 12+2-4 players, <30 mins.
Points of Interest is a fast-paced, point gathering game that teaches the basics of transformation movement in 2-dimentional space. Cards allow movement using motion equations.


Math DiceThinkFun
Ages: 8+1 player
Roll the two 12-sided target dice and multiply them to get a target number. Roll the three scoring dice and combine these numbers using addition, subtraction, multiplication, division, or even powers to build an equation that is closest, or equal to, the target.
Math Dice rules


Math DicePowers Practice EditionThinkFun
Ages: 10+Multiple players
Math Dice Powers includes dice specially designed to encourage the use of exponents and build advanced mental math skills. To play, roll the two 12-Sided Target Dice and calculate the Target Number by using the blue die as the base and the red die as the exponent. Roll the three 6-Sided Scoring Dice and combine their numbers using mathematical operations to match, or come closest to, the Target Number.
Math Dice - Powers Practice Edition rules
Prime ClimbMath for Love
Ages: 10+2-4 players, <45 mins.
A math game highlighting the power of the prime numbers. Each player controls two pawns that start at the 0 circle. Players take turns rolling two 10-sided dice and applying the values to their two pawns using any of the four basic arithmetic operations: addition, subtraction, multiplication, and division. The first to get both pawns into the 101 circle exactly wins the game! The color coding allows players a way to quickly analyze the factors and multiples of the numbers on the board.
Totally RadicalThe Gamecrafter
Designed to teach how to simplify radicals through factoring.
Totally Radical rules

'Accelerated Learning Foundation'

CONFIGURATIONSGeometric Number Puzzles for All AgesAccelerated Learning Foundation

CONFIGURATIONS is a series of geometric puzzles based on Harold L. Dorwart's book, "The Geometry of Incidence". It is a solitaire game involving careful reasoning providing "a simple yet elegant road through geometry country that is rich in rewards of beauty, excitement, surprise, amusement, delight and illumination".
CONFIGURATIONS - What's it all about? (1 min.)
EQUATIONSAccelerated Learning Foundation
Forty years of research and testing have extended the range of this joyful learning tool to become the centerpiece of the Instructional Gaming Program in schools.
Research demonstrates that EQUATIONS develops skills far beyond “drill and practice” computation. It cultivates the critical problem-solving abilities needed to recognize and apply fundamental concepts. It creates a rich problem-solving interaction filled with complex strategy, bluffing and intrigue. The basic game can be taught to eight-year olds using simple arithmetic. As players develop skill, the game becomes more sophisticated exploring a broad range of math topics: addition, subtraction, multiplication, division, exponentiation, root operations, logarithms, fractions, decimals, percents, variables, algebra, functions.
EQUATIONS: The Game of creative Mathematics: What's it all about? (4 mins.)
Instructional Math Play (IMP) KitsAccelerated Learning Foundation
Each of these 21 “kits” is an individual EQUATIONS match designed to teach one powerful concept dealing with the fundamental relationships between the arithmetic operations (addition, subtraction, multiplication, exponentiation, and root operation). The pamphlet responds to all possible moves that the user can make in a manner that focuses the match on the targeted idea. IMP Kits are useful for home or class situations where computers are not always available.
REAL NUMBERSAccelerated Learning Foundation
REAL NUMBERS is a game that involves rolling 5 'math dice' (numbers 0-9, +, -, /, *, root, and exponentiation). The roller of the dice then declares a type of number: natural, integer, rational, irrational, real.Players (or teams) then come up with as many solutions (values) as possible by combining the dice faces that were rolled (within the constraints of the declared criterion). One point is scored for each correct answer and one is deducted for each incorrect answer. A bonus is earned by declaring and successfully defending claim that one has found all possible solutions.
REAL NUMBERS - What's it all about? (1 min.)

'24 Game' Series

by Suntex International
Double Digits(48-card travel set)
Fractions & Decimals96-card class set
Integers ( + / - )(96-card classr set)
Variables(96-card class set)
Algebra/Exponents(96-card class set)

Math Manipulatives


Canada, D. L., Ciancetta, M. A., & Blair, S. D. (2014, December ). Going-off-the-pegs: Revisiting geoboard squares. Mathematics Teaching in the Middle School, 20(5) pp. 286-292.
Growne, I., Browne, M., Draghicescu, M., Draghicescu, C., and Ionescu, C. (2013). A fun approach to teaching geometry and inspiring creativity. In G. W. Hart, & R. Sarhangi (Eds.), Proceedings of Bridges 2013: Mathematics, art, music, architecture, eduction, culture (pp. 587-592). Phoenix, AZ: Tessleations Publishing. Retrieved from: http://archive.bridgesmathart.org/2013/bridges2013-587.pdf
Hart, V. (2010). Mathematical balloon twisting for education. In G. W. Hart, & R. Sarhangi (Eds.), Proceedings of Bridges 2017: Mathematics, art, music, architecture, education, culture (pp. 515-522). Phoenix, AZ: Tesselations Publishing. Retrieved from http://archive.bridgesmathart.org/2010/bridges2010-515.pdf
Wheeler, A., & Champion (2016, February). Stretching probability explorations with geoboards. Mathematics Teaching in the Middle School, 21(6), pp. 332-337.
Math Manipulatives(HTML5 format)by Jonathans Hall
Henri Picciotto, “Manipulatives”(web article)
Napier's BonesCreative Crafthouse
Invented in 1617 by John Napier, this device is referred to as the ‘first calculator’ and was in common use for nearly 300 years. This set of rods was capable of doing long division and square roots.
Genaille-Lucas Rods for MultiplicationCreative Crafthouse
In 1891 Henri Genaille invented these rods as an improvement to Napier’s Bones/ These rods allowed the user to read off the results of simple multiplicaiton problems with no mental calculations.
The Irrational PuzzleMathArtFun
Four cubes are dissected in 4 different ways to form 11 geometric solids. The puzzle introduces students to the concept of irrational numbers and the Pythagorean Theorem.
ITSPHUN: Geometric Construction Kit - Pologons
A 104-piece system (36 triangles, 36 square, 12 pentagons, 20 hexagons) of interlocking shapes that can be used to create free form creations or the ones specified on 28-double-sided cards.
Pythagorean Theorem PuzzleCreative Crafthouse
Use the provided pieces (4 triangles of sides a-b-c, 4 squares of size 'a', 'b', 'c', and 'a-b') to prove the Pythagorean theorem. The documentation provides 3 ways.

Algebra Lab Gear

by Henri Picciotto
Algebra Lab Gear(2 student set)Henri PicciottoDidax
Picciotto, H. (2016). Algebra Lab Gear: Algebra 1 (Grades 7-10).
Picciotto, H. (2016). Algebra Lab Gear: Basic Algebra (Grades 6-9).
Picciotto, H. (1990). The Algebra Lab: High School.
free online access
free PDF access

Math Jokes & Poetry

Pappas, T. (1993). Math talk: mathematical ideas in poems for two voices.
Vennebush, G. P. (2010). Math jokes 4 mathy folks.
Vennebush, G. P. (2017). More jokes 4 mathy folks.

Math History

Dunham, W. (1991). Journey through genius: The great theorems of mathematics.
Jackson, T. (2017). Mathematics: An illustrated history of numbers -- 100 breakthroughs that changed history. (Revised and Updated Ed.).
Pickover, C. A. (2012). The math book: From Pythagoras to the 57th dimension, 250 milestones in the history of mathematics.

Math Awareness & Appreciation

Discovering mathematical wonder in Nature, Culture, and Human Creations
Bellos, A. (2011). Here' looking at Euclid: From counting ants to games of chance - an awe-inspiring journey through the world of numbers.
Bellos, A. (2015). The grapes of math: How life reflects number and numbers reflect life.
Orlin, B. (2018). Math with bad drawings: Illuminating the ideas that shape our reality. New York, NY: Black Dog & Leventhal.
Pappas, T. (1994). The magic of mathematics: Discovering the spell of mathematics.
Parker, M. (2015). Things to make and do in the fourth dimension: A mathematician's journey through narcissistic numbers, optimal dating algorithms, at least two kinds of infinity, and more.
[Math with comedic elements perfect to lure a middle/high schooler into serious math thinking.
For a similar perfect 'science' book, see "what If?" by Randall Munroe in the 'Citizen Science' section of this website.]
Parker, M. (2019). Humble Pi: A comedy of math errors.
[Math with dark comedic elements perfect to lure a middle/high schooler into serious math thinking.]

Cryptography


Avila, C. L., & Ortiz, E. (2012, November). Produce intrigue with Crypto! Mathematics Teaching in the Middle School, 18(4), pp. 212–20.
Bachman, D. J., Brown, E. A., Norton, A. H. (2010, September). Chocolate key cryptography. Mathematics Teacher, 104(2), pp. 100-104.
Paoletti, T. J. (2013, November). Cracking codes and launching rockets. Mathematics Teacher, 107(4), pp. 266-270.
American Cryptogram Association
A non-profit organization dedicated to promoting the hobby and art of cryptanalysis.
Cipher Types
The ACA's guide to over 60 cipher types based on several hundred years of cryptography developments.
Beissinger, J. & Pless, V. (2006). Crytoclub: Using mathematics to make and break secrets codes.
Workbook available in print& as a free PDF file. Grades: 6-8
(Highly recommended for middle school math enrichment and STEM clubs)
Dunin, E. (2006). The mammoth book of secret codes and cryptograms: Over 600 mystery codes to be cracked!
Gaines, H. (1989). Cyrptanalysis: A study of ciphers and their solution.
Gardner, M. (1984). Codes, ciphers and secret writing.
Grade Level: 4-7
Holden, J. (2018). The mathematics of secrets: Cryptography from caesar ciphers to digital encryption.
Janeczko, P. B. (2006). Top secret: A handbook of codes, ciphers, and secret writing.
Grade Level: 4-7
Johnson, B. (2013). Break the code: Cryptography for beginners.
Grade Level: 3-12
Singh, S. (2000). The code book: The science of secrecy from ancient Egypt to quantum cryptography.
Sweigart, A. (2018). Cracking codes with Python: An introduction to building and breaking ciphers.
Civil WarConfederate ArmyCreative Crafthouse
Civil WarUnion ArmyCreative Crafthouse
Mexican Army c.1900Creative Crafthouse
Vietnam EraDiana Cryptosystem(US Army Special Forces)Creative Crafthouse
Mexican Army Cipher WheelMiniEscapeGames
Do-It-Yourself downloadable .PDFapprox. $3unlimited prints
Pigpen Cipher WheelMiniEscapegames
Do-It-Yoursefdownloadable .PDFapprox. $2.50unlimited prints

Mathematics of Origami

and other foldings

Cipoletti, B., & Wilson, N. (2004, August). Turning origami into the language of mathematics. Mathematics Teaching in the Middle School, 10(1), pp. 26-31.
Garibi, I., Goodman, D., & Elran, Y. (2018). The paper puzzle book: All you need is paper!
Jenkins, G., & Wild, A. (1999). Make shapes 1: 19 mathematical models to cut out, glue and decorate.
Jenkins, G., & Wild, A. (1999). Make shapes 2: 8 mathematical models to cut out, glue and decorate.
Maekawa, J. (2007) Genuine origami: 43 Mathematically-based models, from simple to complex.
Mitchell, D. (1997). Mathematical origamia: Geometrical shapes by paper folding.
Pearl, B. (2008). Math in motion: Origami in the classroom K-8 (7th ed.).
Sarcone, G. A., & Waeber, M. (2014). Impossible folding puzzles and other mathematical paradoxes.
FOLD!Ivan Moscovichpublisher: Fat Brain
Ivan's HingeIvan Moscovichpublisher: Fat Brain
Manifold : The Origami Mind Bender Puzzlepublisher: Brainwright
Robinson, , N. (2017). Fantastic flexagons: Hexaflexagons and other flexible folds to twist and turn.
How to make a hexaflexagon:The definitive guideVi Hart
HexaflexaflakesVi Hart
Flex MexVi Hart

Exploring Knots

and other Tanglements
Adams, C. C. (2004). The knot book: An elementary introduction to the mathematical theory of knots.
Petit, P. (2013). Why knot?: How to tie more than sixty ingenious, useful, beautiful, lifesaving and secure knots!
KnoTiles MathArtFun
A collection of puzzles introducting the math of knots and the symmetry of knot designs. All of the knots through seven crossings can be formed with the set of 105 tiles
KnotRobotPUZZLaTOMicDouglas Engel
instructions


HoudiniMaster of EscapeThinkFunNicholas Cravotta & Rebecca Bleau
Knot So FastBrain Fitness SeriesThinkFun


Celtic!by Cameron Browne (2009)nestorgames
Celtic! rules

Exploring Symmetry


Swart, D. (2015). Soccer ball symmetry. In K. Delp, C. S. Kaplan, D. McKenna, & R. Sarhangi (Eds.), Proceedings of Bridges 2015: Mathematics, art, music, architecture, education, culture (pp. 151-158). Phoenix, AZ: Tessellations Publishing. Retrieved from http://archive.bridgesmathart.org/2015/bridges2015-151.pdf
Farmer, D. W. (1996). Groups and symmetry: A guide to discovering mathematics.
Holden, A. (2012). Shapes, space, and symmetry.
Weyl, H. (2016). Symmetry.
Walter, M. (1985). The mirror puzzle book.
Hexellation by Nestor Romeral Andresnestorgames
Hexellation rules
AstraVladimir Krasnoukhov
Make symmetrical shapes using a combination of elements. The difficulty level depends on the number of elements used. Two types of symmetry can be applied: mirror and rotational symmetry.
Bitten BiscuitJin-Hoo Ahn
Make a shape of mirrored symmetry.
DreiecksbeziehungenJean-Claude Constantin
Given nine identical equilateral triangles, fit the required number of triangles into each of the boxes.
SymmetrickProblem BodenVesa Timonen
Make a symmetric shape from the two wooden pieces. Both pieces must be flat on the table.
T-Shirt PuzzlePuzzleMistWilliam Waite
The collar is given, so how hard can it be to make a nice symmetrical short-sleeved T-shirt? Most people that have tried it so far have given up without solving it! One person solved it immediately.

Mathematics of Magic

Mathemagic, Impossible Objects
Blasco, F. (2011). Performing mathematical magic. In R. Sarhangi. & C. H. Sequin (Eds.), Proceedings of Bridges 2011: Mathematics, art, music, architecture, education, culture (pp. 351-356). Retrieved from http://archive.bridgesmathart.org/2011/bridges2011-351.pdf
Koirala, H. P., & Goodwin, P. M. (2000, May). Teaching algebra in the middle grades using mathmagic. Mathematics Teaching in the Middle School, 5(9), pp. 562-566.
Matthews, M. (2008, September). Selecting and using mathemagic tricks in the classroom. Mathematics Teacher, 102(2), pp. 98-101.
Morgan, J. L., & Ginther, J. L. (1994). Magic of mathematics. Mathematics Teacher 87(3), pp. 150-153.
Mulligan, C H. (1989, February). Interest in mathematics-It's in the cards. Mathematics Teacher, 82(2). pp. 100-103.
Benjamin, A., & Shermer, M. (2006). Secrets of mental math: The mathemagicians guide to lightning calculation and amazing math tricks.
Colgan, L., & Kurisu, J. (2011). Mathemagic!: Number tricks.
Diaconis, P., & Graham, R. (2011). Magical mathematics: The mathematical ideas that animate great magic tricks.
(advanced)
Gardner, M. (1956). Mathematics, magic, and mystery
Ho, O. (2002). Amazing math magic.
Simon, W. (2012). Mathematical magic. (Original work published 1964).
Brainiac 12 Math MagicCreative Crafthouse
Heath's Decipering Dice (expanded 8 dice version)Royal Heath (1927)Creative Crafthouse
Impossible Shape 1Creative Crafthouse
Impossible Shape 2Creative Crafthouse
Magic Math CandlesCreative Crafthouse
Magic Mentalist CardsCreative Crafthouse
Mind Reader Animal AlphaCreative Crafthouse
Mysterious Mind Reader Cards(1-60 version)Creative Crafthouse
Swords of TruthCreative Crafthouse
Vanishing LineCreative Crafthouse
Wizards Math Magic CardsCreative Crafthouse

Illusions

wikipedia
Website featuring videos of the top 10 finalists for "Illusion of the Year" (2005-present)
a puzzle site featuring a collection of 192 optical illusions & 39 autostereograms
an optical illusions gallery with explanations
'This 3D Optical Illusion Will Make You Question The Shape of Reality' - a Science Alert blog article by Peter Dockrill about the optical illusion explorations of Japanese mathematician Kokichi Sugihara.
Ausbourne, R. (2007). How to understand, enjoy, and drawn optical illusions: 37 illustrated projects.
Honeycutt, B. (2014). The art of deception: Illusions to challenge the eye and the mind.
Sarcone, G. A. (2012). Eye bogglers: A mesmerizing mass of amazing illusions.
Seckel, A. (2006). The ultimate book of optical illusions.
Stickels, T., & Honeycutt, B.(2012). The art of the illusion: Deceptions to challenge the eye and the mind.

Ambigrams

wikipedia
Kim, S. (1981). Inversions: A catalog of calligraphic cartwheels. (2nd printing ed.) BYTE Books.
Note: a more difficult to obtain 'revised edition was published in 1989.
Langdon, J. (2005). Wordplay: The philosophy, art, and science of ambigrams.
Polster, B. (2008). Eye twisters: Ambigrams & other visual puzzles to amaze and entertain.

Topsys and Turvys

Newell, P. (1991). Tupsys & Turvys, Number 1.
Created over 100 years ago by the children's author, Peter Newell, these are cartoons that appear as something else when turned 'upside down' (hence the different captions on the top & bottom of each page.
Martin Gardner mentions these books. They are important for illustrating 'pictoral' symmetry and for creating intellectual empathy -- the realization that different people looking at the same things from different perspectives can have justifiably different interpretations.
It is tragic that so many mistaught students and their teachers subscribe to the notion that the defining virtue of math is that there is one and only one correct answer to every problem. Compiance-centered instruction aimed at passing end-of-year multiple choice tests reinforces this untruth.
"Topsys and Turvys" and the "Illusions" sections are good, playful pedagogical experiences for developing intellectual empathy & humility that are important attitudes for critical thinking (whether applied to math, science, civic life, or oral/written communication).
Newell, P. (2017). Tupsys & Turvys, Number 2.

Brian Bolt Collection

(Cambridge University Press)
a selection of books within the Curiosity Shoppe
Bolt, B. (1982). Mathematical activities: A resource book for teachers. (Grades 2-6)
Bolt, B. (1984). The amazing mathematical amusement arcade. (Grades 2-6)
Bolt, B. (1985). More mathematical activities: A resource book for teachers. (Grades 2-6)
Bolt, B. (1989). Mathemtical funfair. (Grades 2-6)
Bolt, B. (1992). Mathematical cavalcade. (Grades 2-6)
Bolt, B. (1993). A mathematical Pandora's box. (Grades 6-9)
Bolt, B. (1995). A mathematical jamboree.

Martin Gardner Collection

a selection of books within the Curiosity Shoppe(see also Citizen Science & Mathemagic)
Gardner, M. (Ed.) (1959). Mathematical puzzles of Sam Loyd.
Gardner, M. (Ed.) (1960). More mathematical puzzles of Sam Loyd.
Gardner, M. (1986). Entertaining mathematical puzzles.
Gardner, M. (1988). Perplexing puzzles and tantalizing teasers: Two volumes bound as one.
Gardner, M. (2006). The colossal book of short puzzles and problems.
The New Martin Gardner Mathematical LibraryCambridge University Press
Gardner, M. (2008). Hexaflexagons, probability paradoxes, and the Tower of Hanoi: Martin Gardner's first book of mathematical puzzles and games. (Book 1)
Gardner, M. (2008). Origami, eleusis, and the soma cube: Martin Gardner's mathematical diversions. (Book 2)
Gardner, M. (2009). Sphere packing, Lewis Carroll, and reversi. (Book 3)
Gardner, M. (2014). Knots, and borromean rings, rep-tiles, and eight queens. (Book 4)

Dick Hess Collection

a selection of books within the Curiosity Shoppe

Hess, D. (2009). All-Star Mathlete Puzzles (Mensa Series).

Hess, D. (2013). Number-crunching math puzzles.

Hess, D. (2014). Golf on the moon: Entertaining mathematical paradoxes and puzzles.

Hess, D. (2016). Population explosion and other mathematical puzzles.

Ivan Moscovich Collection

a selection of books within the Curiosity Shoppe


Moscovich, I. (2005). Cunning combination problems & other puzzles.
Moscovich, I. (2005). The hinged square & other puzzles.
Moscovich, I. (2005). Perplexing pattern problems & other puzzles.
Moscovich, I. (2005). Sensational shape & problems & other puzzles.
Moscovich, I. (2006). The big book of brain games: 1,000 PlayThinks of art, mathematics & science.
Moscovich, I. (2006). Brain-flexing balance problems & other puzzles.
Moscovich, I. (2006). Magic arrow tile puzzles.
Moscovich, I. (2006). Peerless probability problems & other puzzles.
Moscovich, I. (2006). Tough topology & other puzzles.
Moscovich, I. (2011). Leonardo’s mirror & other puzzles.
Moscovich, I. (2011). The Monty Hall problem and other puzzles.
Moscovich, I. (2015). The puzzle universe: A history of mathematics in 315 puzzles.

Raymond Smullyan Collection

a selection of books within the Curiosity Shoppe
Smullyan, R. M. (2000). To mock a mockingbird.
Smullyan, R. M. (2009). The lady or the tiger?: And other logic puzzles.
Smullyan, R. M. (2009). Satan, Cantor, and infinity: Mind-boggling puzzles.
Smullyan, R. M. (2010). King Arthur in search of his dog and other curious puzzles,
Smullyan, R. M. (2011). Alice in puzzle-Land: A Carrollian tale for children under eighty.
Smullyan, R. M. (2011). What is the name of this Book?: The riddle of Dracula and other logical puzzles.