Books, Color, Chance

_mur0006The next time you see a telephone book, look beyond the phone numbers, advertisements, thin pages, and wobbly covers. Philadelphia artist Katie Murken did exactly that when she created Continua, a work that combines recycled phone books, color dye, math, elements of chance, and sculpture.

Gathering scores of old and surplus phone books, Katie stripped off their covers and dipped the 3 outer edges into dye. In total, she dyed approximately 1,560,000 sheets of paper with 24 different colors.

dye_readybooks_dryingThen she stacked the altered books into columns. However, the colors she used were determined by a customized color wheel and a pair of dice. A dice roll determined how she would stack the books.

murken_continua_2The result was 24 tall columns of vibrantly colored, gently wavy books pages, arranged completely by chance. And the color! The color! Katie used non-toxic dyes from a small company in California.

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Walking among the stacked pages was incredibly calming, yet energizing. It was also validating. To me, it felt like confirmation of what the knowledge inside books really looks like.

_mur0019If you’d like to see more images of Continua, or read interviews about Katie and her fascinating process, you will find numerous links on Katie Murken’s site.

Photographs courtesy of Katie Murken

Race Around the Clock

race around the clockGo beyond Hickory Dickory Dock with this clever crank clock!  Turn the handle on the back to send the characters dashing around the numbers and through the big red barn (scroll to the bottom of the post to see it in action)!

We read The Clock Struck One, written by Trudy Harris, and illustrated by Carrie Hartman (Millbrook Press, 2009). It’s 1pm and a mouse makes an untimely dash at just the wrong moment, catching the attention of the cat. A chase ensues that involves the mouse, the cat, the dog, some bees, the hen, the farmer’s wife, the farmer’s son, and the farmer! By 11pm, everyone is exhausted. By midnight, everyone is asleep. But at 1am, the clock strikes, and guess who’s in the wrong place at the wrong time again?

Kids loved this clock project, but parents were especially thrilled. Many sought me out after story time to thank me for such a fun introduction to numbers, clocks, and time.

You’ll need:

Begin by stacking both circles on top of one another, and using a box cutter to cut a slit in the middle of both. The top cardboard circle is the clock face. The bottom cardboard circle is the back of the clock.

First, the clock face! Cut, color, and glue (or tape) the numbers from the clock numbers template to the first cardboard circle. You can use markers to add flourishes to the clock face as well (we, for example, added a striped border). Next, trace the barn shape from the clock pieces template onto red poster board. Use markers to add outlines to the barn.

clock barnAttach the barn to the back of the clock face, right above the number 12. I highly recommend attaching the barn with hot glue. You really want the barn to stick because later, it can be used as a carrying handle for your clock! Here’s what the finished clock face looks like:

finished clock faceSet the finished clock face aside for a moment. Cut four, 1.5″ tabs in the end of a toilet paper tube. Then bend the tabs outward and hot glue the toilet paper tube to the back of the second cardboard circle:

clock handleYou’ll notice that the toilet paper handle gets glued on the perimeter of the cardboard circle. We experimented and found that was the best handle position for cranking the clock.

clock handle placementCut and color the animals from the template, and tape (or glue) them onto the ends of the craft sticks. Make sure there’s plenty of room at the bottom of the craft sticks – you’ll need some space to attach the sticks to the clock.

finished clock animalsTape the craft sticks to the cardboard circle. Note – the craft sticks need to be on the same side as the toilet paper tube handle. If the sticks are taped on the opposite side, they will rub and bump into your hand while you’re operating the clock. If you want to follow the order of the characters in the book, the mouse should go first, followed by the cat, dog, bees, and hen.

attached animalsThe back is done, time to put two clock circles together! Push a brass fastener through the clock face’s slit (you might need to enlarge the slit a little with a pair of scissors). Thread 2 foam beads on the fastener’s prongs:

clock tack step 1Push the prongs through the second circle’s slit, then unfold the prongs and secure in place with tape. Depending on your cardboard, foam beads, and brass fastener, you might have to do a little adjusting to get the circles to rotate smoothly.

clock tack step 2

Cut the minute and hour hands from the clock pieces template, then trace them onto red poster board. Arrange the hands to your preferred time, then attach them to the head of the brass fastener with a glob of hot glue. I say “glob of hot glue” because you want the hands to rest on the glob, slightly above the head of the brass fastener. If the hands are pressed flat to the head, they’ll get snagged on the clock numbers later. We stuck green mini dot sticker at the intersection of the clock hands. Done!

finished clockTo operate the clock, grip the clock face firmly at the bottom. Use your other hand to crank the toilet paper tube handle. You might have to adjust the animals a little, or bend the clock hands upward a bit, if they snag on the barn door or the numbers. But eventually, you’ll have a smooth race around the clock!

A quick word about a construction issue. You definitely need a 1.5″ brass fastener and foam spacers to get this project to work. You need that space in between the two cardboard circles in order to grip the clock, turn it, and have it operate smoothly. If the circles are too close together, animals repeatedly knock against your hand while the clock is turning. We experimented with shorter brass tacks, fewer foam beads, handles made out of 8″ craft sticks. Nope. The 1.5″ brass fastener with the 2 foam bead spacers is the combination that worked best!

Want to see my favorite project involving a brass fastener? Check out this little carousel!

A Day in Digitopolis, Part II

Radiance by Matt ElsonWho knew infinity could be so beautiful? I’ve returned with Part II of the Digitopolis event post (Part I can be found here) and thought I would start it off with one of the stars of the show! The above image was taken inside an Infinity Box, one of multiple creations by Los Angeles-based artist, Matt Elson. Matt’s boxes have been exhibited at colleges, science centers, festivals, and museums. He generously loaned us two (titled Radiance, and You & Me Together) for our math event.

You and Me Together by Matt ElsonThe boxes are designed to be infinite, interactive environments that play with your perception and inspire inquisitiveness and wonder. They were in constant use during the event, and there were lots of shrieks of amazement, enthusiastic explosions of “Cool!” and long, drown out utterances of “Woooooow…”

infinity marissaDigitopolis was not without its celebrities too, including the King of Numbers himself. I speak, of course, of the Mathamagician.

mathamagiciansThat’s real-life mathamagician Brent Ferguson on the right, grinning away under the pointy hat covered with equations. He’s math faculty at the Lawrenceville School, and in 2013, he was awarded the National Museum of Mathamatics’ Rosenthal Prize for innovation in math teaching. On the left is Dr. Dan Fishman, a high school math teacher, who, like Brent, has unbridled enthusiasm for all things math.

Together, Brent and Dan staffed the “Ask the Mathamagician” table. Kids could walk up and ask them any question they could possibly think of involving math. We had prompt cards on the table to get things started:

Why do you like math?
What’s an irrational number?
What’s the biggest number there is?
Why is math important?
Why does a negative times a negative equal a positive?
Is zero a number?
What’s a perfect number?
What’s that crazy math thing with the exclamation point?
What’s an imaginary number?
Know any good math jokes?
What’s your favorite equation?

Brent and Dan also brought a whole bunch of math toys and puzzles with them. It was an irresistible treasure trove of numerical goodies.

mathamagician 2Also at the Mathamagican’s table were three Digitopolis “tourism” posters for families to take home (the posters were inspired by this fantastic NASA concept). The first two posters are by Princeton University senior, Aliisa Lee. The third poster is by freshman Demi Zhang.

city poster by aliisa leemines poster by aliisa leeevent poster by demi zhangA quick word about the Mathamagician’s costume. The robes and hat were made by freshman James Jared, who ingeniously modified this Jedi robe. Then Casandra used silver and gold metallic fabric markers to draw real, honest-to-goodness math equations on them. We snapped a couple shots so you can get the full effect!

robes 2robes 1The Mathamagician wasn’t the only celebrity in Digitopolis that day. Does this gentleman look familiar to you?

albert einsteinYup, it’s Albert Einstein. Or rather, professional reenactor Bill Agress playing Albert Einstein. Mr. Einstein circulated the event floor, chatted with kids, answered questions about his life and work, tried an activity or two, and posed for pictures. And yes – he wasn’t wearing any socks.

In addition to being one of world’s most famous theoretical physicists (and no slouch at mathematics either), did you know that Einstein was a resident of Princeton? He emigrated here in 1933 to join the faculty of at the newly-created Institute for Advanced Study.

The Historical Society of Princeton put together a terrific mini-exhibit on Einstein in Princeton (my favorite is that photo of him wearing the fuzzy slippers). Families were invited to take home a map of notable Einstein haunts around town as well.

historical societyThey also whipped up an Einstein quiz for kids to try (the answers, by the way are B, A, B, C, B, C). The prize was a cool little puzzle. I found some terrific ones at Oriental Trading Company (the ones below are from the “Mind Teaser Game Assortment”).

maze prizesElsewhere in Digitopolis, another math wizard was hard at work. This is Emile Oshima, a junior at Princeton and master of the Japanese abacus. Next to him is senior Rei Mastsuura.

abacus races 1In addition to having Emile and Rei teaching kids how to use an abacus, Emile raced kids (and parents!) armed with electronic calculators to see who could reach the product of 3 x 3 multiplication problem faster. Emile always won. He was lightning fast!

abacus races 2Meanwhile, at another event table, another calculator was keeping kids busy. But this calculator was rather…odd.

crazy calculator 1The “Crazy Calculator” was designed by the Princeton Society of Women Engineers using 2 Makey Makey sets. Have you seen Makey Makey? It’s pretty awesome. Each set consists of wired alligator clips, a small central board, and computer software.

Attach the alligator clip to anything that conducts electricity, and you can do all sorts of crazy things. Turn bananas into a keyboard, or use Play-doe like a video game controller. The Women Engineers used all sorts of things to build their calculator – tin foil, wet sponges, water, metal objects, shaving cream, flowers, even high fives!

crazy calculator 2Interspersed with the other event tables were 5 “Pop Up History” activities that tied together math and history. These tables were designed to be simple, stand-alone, and un-staffed.

global counting 1At “Global Counting,” kids could see diverse numerical systems on a big display board (the book Go Figure: A Totally Cool Book About Numbers (DK, 2005) was very helpful in this regard). Then, kids copied their favorite number system on a 3.5″ x 17″ strip of paper, and used yarn to turn it into a little scroll.

global counting 2At another table were Möbius strips, a must-have for any hands-on math event. Discovered in 1858 by German mathematician August Ferdinand Möbius, the strip demonstrates how a piece of paper can have only one side! All it takes is a 2.5″ x 28″ piece of poster board, tape, and some instructions.

mobius stripsAnother hands-on math must-have? Tangram puzzles. Originating in China, tangram puzzles were first introduced to Europe in the 19th century. There are plenty of inexpensive tabletop tangrams out there, but we decided to splurge on some giant foam floor size versions (thinner ones purchased from SimplyFun, chunkier ones from Fat Brain Toys). Later, these were donated to a local non-profit family shelter.

tangram puzzlesThe fourth Pop Up History table was called “Tally Hides.” Some American Indian tribes kept track of important things by making tally marks on animal hides and tree bark. Definitely a cool way to count!

tally hides 1Before the event, we cut 9″ x 12″ pieces of brown paper into the shape of a hide. During the event, kids wrinkled the paper, flattened it out, and used markers to draw the wildlife they’ve seen around their homes and town. Then, they estimated how many times they’d seen each critter, and made a tally mark next to it. The project is originally from The Secret Life of Math (Williamson Books, 2005).

tally hides 2The final history table was called “Tile Tessellations.” Decorating surfaces with tiles spans many cultures, and many centuries. But did you know that the geometry in Early Islamic art was so intricate, it was unrivaled for over 500 years?

tiles 1Kids put their tiling and tessellating skills to work by gluing 3/4″ paper tiles to a 6″ x 6″ square of tagboard. This project was really bright and beautiful.

tiles 2That’s it for history – how about some games? JaZams, our local family-owned toy store hosted a event area called “The Game is Afoot.” JaZams chose 8 math games for various age ranges (you can see their official selections here), and set each of them up on a series of tables. Kids could drop by to play the waaaaay popular Rubik’s Race…

game is afoot 1Or entire families could take a break and play Number Ninjas.

game is afoot 2Heck, maybe you could even beat Einstein at Qbitz! After the event, the games were donated to a local non-profit family shelter.

games is afoot 3For the musically adventurous, there was “Musical Fractions,” an activity composed by senior Matt Smith and freshman Demi Zhang. Kids used percussion instruments (assorted floor drums, wood blocks, maracas, a wooden fish, claves, and sand blocks) to learn how to play, and recognize, wholes, halves, quarters, and eighths. They also learned about musical structure and patterns.

musical fractionsEach instructional session ranged between 10 to 15 minutes. I wasn’t able to catch an entire one, but I did manage to grab a few seconds of this one. Just listen to those fractions!

I have one last thing to share with you. Team Digitopolis in their awesome event t-shirts.

front of shirtsAt big events like this, my staff and I wear costumes so that people can find us quickly in the crowds (helloooo Victorian Steampunk spelunker). For Digitopolis, however, I decided to go with t-shirts, and asked student artist Aliisa Lee to design them. Here’s a closer look at her beautiful cityscape!

digitopolis by aliisa leeOn the backs were our favorite numbers. Let’s hear it for 9, 2, and 11! Woot woot!

back of shirtsI’d like to send a million, trillion, zillion, googolplex thanks to everyone who made this event possible, and who generously gave their time to make math fun, approachable, unusual and fun. An extra shout out to the Princeton University students, and the student athletes who volunteered so energetically and enthusiastically! Thank you so much, everyone!