More Math! Resources
For those of you who can't wait until the next National Math Festival, we invite you to explore the wonder and beauty of math with these puzzles, games, books, videos, and other mathy treats.
Resources are categorized by age level (All Ages, Kids and Families, Teens and Adults) as well as a selection of Featured Videos. New resources are added each month!
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What's New from Numberphile
Fun for All Ages
52 Master Pieces
An armchair treasure hunt puzzle contest overflowing with classic and original brainteasers, games, ciphers, puzzles, wordplay, and more. Free for everyone to enjoy!
All About Flexagons
Lots of activities here about folding these tricky paper puzzles. You can also try our 2017 National Math Festival flexagon print and play puzzle at home!
Dots & Boxes
Two players take turns drawing lines to connect dots, and whoever closes a square gets to put their initial inside, and the player with the most claimed squares wins! Sounds easy? This classic pen and paper game, beloved by children, gets new strategic insights in this video featuring Dr. Elwyn Berlekamp, a mathematician and expert in combinatorial games like chess and Go.
This low-cost book (under $5) is a great way to start learning origami skills! Try 32 simple projects using origami—clearly illustrated and with easy-to-follow instructions that even beginning papercrafters can follow with success.
NEW! Estimation 180
Teacher Andrew Statel has created these visual exercises to help his students build their number sense. Give them a try and maybe you’ll be a ringer the next time someone asks you to “guess the number of jellybeans in the jar”!
NEW! Find Your Pi Day
To celebrate Pi Day, Wolfram Alpha created this generator – enter your birth date, or any number sequence, and the system will find the same consecutive sequence within pi!
Free Math Printables: 3D Shapes
Create free printable patterns for common 3D shapes like pyramids, cubes, octahedrons, and more! You can add your own photos, textures, or clipart images to the faces to make them more colorful. Use these patterns to print and construct photo cubes, math models, and more.
How to Solve a Rubik’s Cube
This Think Maths guide to solving a Rubik’s Cube will take you through a simple method for solving a scrambled cube. Watching the videos will help you to learn a layer-by-layer solve, and the same solving method is outlined on the worksheets included, with appropriate diagrams. The method can be learned individually, or by whole class groups with teacher support.
NEW! Imbalance Problems
These puzzles are made of squares, triangles, and circles suspended by bars and wires from a center fulcrum. We can tell that the shapes don’t weigh the same when both sides don’t balance – but can you order them from heaviest to lightest just by looking at each puzzle? Use the pictures as your clues and try these fun brainteasers!
- More Imbalance Problems
These puzzles can be printed or drawn on paper for offline fun.
- Solve Me! Mobiles
More imbalance problems to solve online – or try your hand at building your own!
Large Birds, Hungry Tigers, and Other Logic Puzzles
Raymond M. Smullyan, a mathematician, often met people who said they hated math, and yet they loved his logic puzzles. Can you solve this sampling?
Match the Women Mathematicians
The Association for Women in Mathematics (AWM) created this game – can you match these women with their scientific accomplishments? (You can also find biographies of women mathematicians to learn more via Agnes Scott College!)
Math and Logic Puzzles by Martin Gardner
Martin Gardner (1914-2010) was an American popular mathematics and science writer, who shared his love of fun math and logic puzzles and magic tricks through decades of magazines and journal articles and books. For a taste of his work, try this collection of puzzles inspired by Gardner’s writings.
MathDice Daily Challenge
This mentally challenging and fun online dice game by ThinkFun helps players sharpen math skills by solving problems in a fun new way.
The connection between mathematics and art goes back thousands of years. Mathematicians and artists continue to create stunning works in all media, from computer graphics to origami, 3D printing, and LEGO sculptures!
NEW! The Mathematics of Juggling
Juggling has advanced enormously in recent decades, thanks in part to the mathematical study of possible patterns. The late computer scientist Claude Shannon was also an avid unicyclist, juggler and tinkerer. In the early 1980s, Shannon published the first formal mathematical theorem of juggling, and mathematicians have been fascinated ever since. You can find a great video about the math of juggling by National Math Festival presenter George Hart as well!
National Association of Math Circles
Math Circles bring K-12 students together to explore mathematical ideas, facilitated by professional mathematicians. Activities center around cooperative and playful experimentation, discussion, and solution of interesting, easily understood problems that offer many paths of attack, which can lead to harder and deeper problems that can be solved using the same methods. MSRI’s National Association of Math Circles can connect you with more than 180 Math Circles around the U.S.!
Navajo Math Circles
This inspiring documentary film, airing on PBS starting in September 2016, is a peek at the lives of the hundreds of Navajo children who in recent years have found themselves at the center of a lively collaboration with mathematicians from around the world, exploring the deep connections between math, nature, and Navajo culture.
Journalist Brady Haran makes fascinating videos starring mathematicians and others from around the world who are excited to share their favorite topics with you, whether it’s learning about curvature from eating a slice a pizza to picturing a number “so epic it will collapse your brain into a black hole”! Over 200 million viewers have joined the fun – there’s something for everyone here.
Origami and Math
How do origami and math relate to each other? Start by unfolding an origami model and find a complex geometric pattern, even in simple projects. Did you know that you were folding those angles or shapes? You can try to solve origami challenges, such as folding a piece of paper so that certain color patterns arise, or so that a shape of a certain area results.
Patterns of the Universe: A Coloring Adventure in Math and Beauty
Alex Bellos and Edmund Harriss have created a unique coloring and activity book showcasing the fascinating things math can be discovered in the universe, from 4D hypercubes to the infinite patterns of tessellations and more. For even more fun, check out the follow-up title, Visions of the Universe: A Coloring Journey Through Math’s Great Mysteries.
When you take a digital photo, your camera measures the amount of red, green and blue light hitting each pixel, ranks them on a scale from 0 to 255 and then records those values as a spreadsheet. 2017 Festival presenter Matt Parker found a way to actually open digital photos as spreadsheets in Microsoft Excel or similar programs. Upload a photo and instantly download it as a real spreadsheet, and learn from Matt’s experiments!
The Scale of the Universe
Zoom from the edge of the universe to the quantum foam of spacetime and learn the scale of things along the way!
SciStarter is the place to find, join, and contribute to science through more than 1,600 formal and informal research projects and events. Satisfy the urge to tinker, build, and explore through this database of research projects open to people of all ages to jump in and get their hands dirty with science!
Professor Tadashi Tokieda loves to share his toys: in this case, objects you can often make in a matter of minutes at home, which explore “pockets of mystery” in nature and physics. These videos come with lively animated guides to help illustrate the principles of mathematics at work.
Tessellations are symmetrical designs which can fit together in repetitive patterns like simple jigsaw puzzles. These fill a surface, usually a 2D plane, without gaps or overlaps. Brick walls, tiled floors, and the honeycomb in bee hives are all tessellations. You can learn about and see tessellations made by pros and amateurs, both adults and kids, or submit your own designs.
Vi Hart: Doodling in Math and more
Recreational mathematics and inspirational videos by Vi Hart, hosted by the free Khan Academy.
Mathematics is a creative subject, involving spotting patterns, making connections, finding new ways of looking at things and using what you already know in new contexts. Wild Maths has games, investigations, stories and spaces to explore, where there are discoveries to be made. Some have starting points, some a big question and others offer you a free space to investigate and develop as a mathematician.
Resources for Kids + Families
Calculus for Kids Activity Sparks
Natural Math has made these one-page activity guides for parents and kids to try activities that give insight into math concepts.
- How You Slice It: Use your X-Ray vision on different patterns to see how a whole is made of different parts. From this viewpoint you can see how different building blocks lead to different outcomes. Is one slicing technique simpler than others? More fair? More predictable? More fun? Let’s find out.
- Make Shapes with Sticks: Make models using integration, and learn to see flat 2D shapes as made from straight 1D lines. You can use craft sticks, matchsticks, toothpicks, or strips of paper to make your shapes. Can every shape be made from sticks? Are there hidden techniques to make complex shapes from simple lines?
- What would a 3D Printer Do? Choose any object and ask: How would a 3D printer build it? How would it grow in nature? How would you make it with crafts? We can train our skills in thinking with analogies. In music, we can play the same song in different styles (rock, jazz, classical, rap). Calculus lets us “remix” an object by building it different ways.
- Mosaics: 2D to 2D: Let’s learn how to approximate curves with straight lines, and try to fill and measure complex shapes. You can use anything that is flat enough: craft foam, construction paper, sticky notes, tiles, fusible beads, or LEGO bricks. How can small pieces come together to show a larger image? Do grids help or hurt your project? Can you make a circle out of squares? Let’s find out.
Games at PBS Kids
You can pair these online games with math activities for early childhood.
- Animal Lost and Found: Help owners find their lost pets! Count eyes, ears and other body parts in this match game for preschool and kindergarten.
- Building Sandcastles: Ready to play in the sand and practicing learning shapes for preschoolers and kindergartners? Match the shapes of wet sand with their outlines to build different sandcastles.
- Let’s Tessellate: Choose a shape and a color and then tessellate! See your shape repeat again and again to make a beautiful pattern in this fun tessellation math game.
- Pattern Matcher: In these fun pattern games for kindergarten and preschool, silly pictures make patterns that repeat. Can you find the patterns that repeat the same way?
- Time to Move: Help move these fish to their new homes with this measurement game for kids! Which fish move where? Catch and measure each fish to find out.
From how many teeth there are in the world to how long it would take an army of ants to carry you across the country, this free website and app gives kids something fun and mathy to think and talk about with their families every night before bed. (Lots of printable games and activities, too!)
Gracie and Friends Early Math Apps
2017 Festival presenter First 8 Studios™ at WGBH creates free Gracie and Friends series of mobile apps with titles like Birthday Café, Lemonade Stand, and Jungle Gym. Kids can explore games that teach two key concepts for early math learning: subitizing (learning to “see how many” objects without counting each one), and equipartitioning (learning how to divide objects into equal pieces).
How to Make Tessellations
This easy guide for elementary school students teaches how to design your own tessellation patterns using paper, scissors, and tape. What can you create?
Make your own Snowflakes (PDF)
Snowflakes are fun decorations this time of year. Many people like to make their own and display them on doors and in windows to celebrate winter. Snowflakes are both delicate and beautiful. Each real snowflake is a uniquely fashioned ice crystal with a symmetry that reflects the symmetry of water molecules. This six-fold symmetry is shared by all snowflakes and is easy to replicate by folding paper. This template will let you make your own paper snowflakes to observe symmetry and share your creation.
Mathical: Books for Kids from Tots to Teens
The Mathical Book Prize selects fiction and nonfiction stories for kids of all ages that make math visible in the world. From picture books to graphic novels, chapter books, and teen thrillers, there’s a story for everyone! Winners are selected by a nationwide committee of mathematicians, educators, librarians, and authors.
Sesame Street Math is Everywhere
Look around: Exciting math opportunities abound! Sesame Street Math Is Everywhere aims to help parents, caregivers, and educators help young children explore and understand math in the everyday world by focusing on the broad thinking and reasoning skills required to master mathematics.
Spark your child’s curiosity: connect to a STEM opportunity for your child. The Connectory is a free portal that helps parents and other caregivers find local STEM education opportunities for kids in their lives.
More Math! for Teens + Adults
A Dozen Hat Problems (PDF)
In each of these problems, hats of specified colors are placed on players’ heads. Each player can see the colors of some or all of the other player’s hats, but not his own. The goal is to come up with a strategy players can agree on before the game that will allow as many players as possible to correctly guess the colors of their hats. Some of these problems are psychological or philosophical and many are deeply mathematical. At the very least, they are fun to think about!
NEW! Adalogical AEnigmas
From The Guardian‘s Alex Bellos: Try your hand at these logic puzzles inspired by Ada Lovelace and designed by Pavel Curtis, a legend in the puzzle community who has a day job as a software architect at Microsoft. The grids are based on Japanese-style logic puzzles like Sudoku and Kakuro, and use similar deductions. Pavel has been releasing new puzzles every month, and you can find more at his website, along with gentle hints for first-time players.
Chevron STEM Zone
Lots of great PDF resources that can change the way you play sports or enjoy watching them by sharing the science and math behind golf, football, baseball, basketball, and ice hockey.
Solve is a weekly set of five thought-provoking and interactive math challenges produced by the makers of expii (including 2017 Festival presenter Dr. Po-Shen Loh!). These problems are about having fun and thinking creatively. Each set contains problems of varying difficulty, beginning with the most accessible and ending with the almost impossible. Explore and enjoy!
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Before John Glenn orbited the earth, or Neil Armstrong walked on the moon, a group of African-American female mathematicians known as “human computers” used pencils, slide rules and adding machines to calculate the numbers that would launch rockets, and astronauts, into space. The film adaptation of Margot Lee Shetterly’s book debuted in cinemas in January 2017, and you can preview an excerpt from the book.
International Mathematics of Planet Earth (MPE) Competition
How can mathematics be useful in explaining things happening on a global scale? From biodiversity and resource management to epidemics and climate change, Mathematics of Planet Earth (MPE) is a contest for individuals or groups of individuals, institutions, schools, or nonprofit organizations to develop modules for museums or the web to introduce people to these concepts.
The Manual of Mathematical Magic
Mathematics and magic may seem a strange combination, but many of the most powerful magical effects performed today have a mathematical basis. This free PDF booklet by the Faculty of Science and Engineering at Queen Mary University of London teaches the secrets behind street magic, explained clearly with instructions and videos to help you perform them perfectly. Learn about the math behind each trick and discover how that same mathematics is used to power our modern world!
The Math Inside the U.S. Highway System
Have you ever thought about why certain numbers are assigned to certain highway systems when you travel by car? Around Washington, D.C. you’ll see I-495, I-81, I-66.. but where did these numbers come from? Connecting patterns, associating properties of a number to those of a real world object — that’s what thinking mathematically is all about!
Mathematical Balloon Twisting (PDF)
This booklet by Vi Hart is for anyone interested in learning how to create mathematical shapes using the long tubular balloons designed for creating balloon animals and sculptures. It’s a tricky skill, but with a little practice you can be making your own masterpieces!
Moody’s Math Mega Challenge
Moody’s Mega Math Challenge is a mathematical modeling contest for U.S. high school juniors and seniors (for full eligibility rules, visit the site). Through participation, students gain the experience of working in teams to tackle a real-world problem under time and resource constraints akin to those faced by industrial applied mathematicians. The Challenge is sponsored by The Moody’s Foundation and organized by the Society for Industrial and Applied Mathematics (SIAM) and awards $150,000 in scholarships each year. Registration closes February 17, 2017.
This New York Times column by Gary Antonick and friends shares weekly math challenges on topics from pop culture to infinity.
The Parable of the Polygons
This game, created by Vi Hart and Nicky Case, is a simulation that shows how small individual bias can lead to large collective bias.
Phyllotactic Spirals and the Art of John Edmark
What do plants know about numbers? A certain spiral pattern commonly seen in sunflowers, pinecones, and many species of cacti contains some surprising numerical properties. In this video, Paul Dancstep of San Francisco’s Exploratorium investigates kinetic sculptures by artist John Edmark.
Mathematical Association of America (MAA)
The Mathematical Association of America (MAA) is the world’s largest community of mathematicians, students, and enthusiasts. MAA has a number of projects that may be of interest to members and the general public alike!
- Found Math: MAA’s website features a new math-related photo every week, where MAA members submit their images taken all over the world on a weekly basis. The deadline for submission is every Friday!
- Solving Real World Problems: Math students interested in industrial careers can learn from these case studies that come directly from the real world. Professional mathematicians talk about problems that have come up in their careers, from creating more realistic special effects with computer animation to storing nuclear waste, followed by videos which discuss ways you can use math techniques to tackle these real industrial problems.
- Math Horizon’s Aftermath: These editorial essays on a wide variety of subjects related to math have appeared in Math Horizons, an MAA publication. You can find more blog posts at Devin’s Angle as well!
Varsity Math is the weekly math puzzle column by the National Museum of Mathematics featured each weekend in the Wall Street Journal.
NEW! Visual Patterns
Click on any pattern to see a larger image and the answer to step 43. Can you figure out the equation? These are a great warm-up to problem solving!
Volumes: the MoMath Book Club
Love mathematics and books? This reading group (which meets in New York City) designed especially for those interested in mathematics and science and how it affects our lives. If you’re not in the New York City area, you can still enjoy their reading list of fiction and non-fiction books with math themes!
Why Do Math
Mathematical and computational analyses have proved to be uniquely insightful for solving problems in science, society and our everyday lives. The Society for Industrial and Applied Mathematics (SIAM) shares the stories of how math is being used in a wide variety of disciplines and career paths, from space travel to hearing implants and internet search engines.