A Day in Digitopolis, Part I

day in digitopolis part 1We’ve all wanted to jump into books. Who doesn’t, for example, want to go to Diagon Alley and hit the shops? Join Hazel for stories in the Honeycomb? Explore Babilonium with Candy Quackenbush? Or sail the skies with Matt Cruise on the Aurora? Part of my job at the Cotsen Children’s Library is to bring these places to life for kids, and this month, we headed to The Lands Beyond to visit Digitopolis, the mathematical kingdom in The Phantom Tollbooth.

The math event was intended for children ages 4-10, and my goal was to make it full of exploration, demonstrations, games, challenges, and unexpected connections. And by the four million eight hundred and twenty-seven thousand six hundred fifty-nine hairs on my head, I think we did it!

A Day in Digitopolis took place in the atrium of Princeton University’s Frick Chemistry Laboratory, a soaring, three-story structure of glass and metalwork. Here’s our welcome desk with two student volunteers and Pi balloons.

digitopolis welcome deskBut before I get started on all the details, I’d like to introduce our event collaborator, Bedtime Math. Founded by Laura Overdeck, Bedtime Math is a NJ-based nonprofit organization that provides playful, zany math problems for parents to do with their kids everyday. In addition to sharing their content through their books, e-mail, and free app, they created Crazy 8s, an after-school math club that has been launched in over 6,000 locations nationwide. These guys know, and love, math.

bedtime math booksBedtime Math brought 3 fantastic activities to the event: Spy Training, Beach Ball Party, and Glow-in-the-Dark Geometry. Here’s Spy Training, which was all about codes and ciphers…

spy trainingAnd here’s Beach Ball Party, which involved counting, stacking, and chasing beach balls determined to make a break for it.

beach ball partyIt also involved Ellen Williams (who you last spotted being pelted with marshmallows in this post) inflating dozens and dozens of beach balls for kids at the event. That’s her in the lower right corner of the photo, hard at work. Very impressive lungs has our Ellen (did I mention she sings in multiple choirs?).

But the total show stopper was Bedtime Math’s Glow-in-the-Dark Geometry. This took place in a darkened classroom off the main event floor. Here, kids could build illuminated structures with glow stick bracelets and styrofoam balls. The results were totally amazing.

glowing geometrySome kids decided to use the original plastic connectors that came with the bracelets to make unique geometric creations. Here’s one of my favorites. A series of loops that, when spun, becomes a sphere!

 

Bedtime Math was recently invited to the White House to take part in an early STEM learning summit. Seriously. When it comes to amazing math connections for kids, Bedtime Math has it down!

Moving to a different section of the event floor, we find the fabled number mines of Digitopolis. In the book, Milo, Tock, and the Humbug learn that numbers are, in fact, excavated out of the earth, much like jewels and precious stones. The talented Maria Evans from the Arts Council of Princeton built a 6′ tabletop mine out of cardboard boxes, papier-mâché, Valspar faux stone spray paint, and a couple of giant plastic gemstones I found in our art cabinet. YES!

number mines 1The mines were stocked with an assortment of wooden numbers. I used 4″ numbers I found online at Woodcrafter. If you’d like a cheaper option, I recommend printing paper numbers on card stock.

At the event table, kids reached into the mine, extracted a number, and then decorated it with a combination of metallic markers and glitter markers. We also had plastic gems and glue on hand for some additional bling.

number mines 4number mines 5

number mines 2The mines were staffed by high school volunteers from the Arts Council, who were suitably decked out in miner helmets.

number mines 3Elsewhere in Digitopolis was the “Fibonacci Forest,” hosted by the Stony Brook-Millstone Watershed Association. This table focused on math in nature. Specifically, symmetry, shapes (like spheres, hexagons, spirals), fractals, and Fibonacci numbers. The Watershed brought a ton of items for kids to touch, connect with, and explore (including my personal favorite, this nautilus shell).

nature math 1nature math 2The Watershed also did a cool fractal tree project. It involved a half-sheet of green paper, brown markers, and rulers (here are the instructions if you’d like to see them).

nature math 3We decorated the finished fractal trees with bird and leaf stamps, but you can also just use markers or color pencils.

nature math 4And speaking of wildlife, how about some zebra math? We were delighted to be joined by Princeton University Professor Dan Rubenstein from the Department of Ecology and Evolutionary Biology. Among other things, Dan does field work with African zebras.

zebra math 1Some researchers believe that zebra stripes exist to confuse predators. So Dan and his constituents developed “Dazzle Confusion,” an iPad game in which kids “become the lion” and tried to tap black, white, or striped moving targets to determine which one is most difficult to hit.

zebra math 2At the end of the game, the program tabulated the kids’ results and displayed them on a large screen. As the event progressed, the results continued to accrue. This lead to conversations about data collection, measurement, central tendencies, and averages.

zebra math 3It’s worth noting that although there was much variation on kids’ “strikes” on the targets, there was a strong trend (p < .08) showing that the striped targets were hardest to hit! How’s that for some real world math?

Continuing with the technology theme, the Princeton Women in Computer Science designed an original math game for kids using Scratch, a visual programming language developed by MIT.

scratchHere’s a screen shot of the game, which was created by sophmore Lucy Lin. If you’d like to test drive the game yourself, here’s the link.

scratch screen shotThe game was cool, but even cooler was the fact that there was another laptop running tandem to the gaming laptops that showed all the algorithms behind the Scratch program. And volunteers were on hand to answer any and all questions about computing. They also had a couple of encryption puzzles for kids to crack.

Meanwhile, the Princeton Chemistry Outreach Program (we’ve exploded things with these guys before) was busy making awesome math / science connections with kids. Dr. Wagner and her students ran hands-on experiments with parts per million, vitamin c clocks, and timed invisible ink.

chemistry outreach 1chemistry outreach 2chemistry outreach 3For those who prefer their math undiluted, the Princeton University Mathematics Club came out en force to host a “Playful Problems” table. Here, kids found a plethora of logic puzzles, word problems, visual puzzles, calculator tricks, the works!

math club 1math club 2There were 12 different activities for children ages 4-10. The activities ranged from easy to moderately difficult. Here’s an example of our simplest puzzle, which was created by Casandra Monroe (whom you first met here). Here’s the template if you’d like it.

milo number grid puzzleBelow is a list of what we offered at the event table (if you’d like more details on any of them, just e-mail me!). In addition to using Google to find some of these puzzles, Math Wizardry for Kids (Barron’s, 1995) and How to be a Math Genius (DK Children, 2012) were terrific resources.

  • Suduko
  • Lattice multiplication
  • Logic grid puzzle
  • Matchstick puzzles (we used Q-tips instead of matchsticks)
  • Milo number grid maze (see above)
  • 24 Game
  • Multiplying by 9 finger trick
  • Make a paper star with only 1 cut
  • Superimposed shapes puzzle
  • Visual sequencing puzzle
  • Word problems
  • Birthday calculator trick

Important! If you put together your own Playful Problems table, make sure you provide an answer sheet for each problem. That way, parents and kids can check their answers or get a little hint. Also important! No matter how easy the puzzle, provide an answer sheet (you don’t want younger kids to think that their puzzle was too “easy” for a solution sheet).

For those wanting a bit a exercise with their mathematics, we had a giant 16′ x 16′ floor maze (building instruction for it are in this post). Kids had to get from start to finish in the maze – without making a single right-hand turn. If you got stuck, the solution was posted on some glass doors opposite the entry to the maze.

no right turn maze at eventBy the way, did you notice the cute play cart parked in the upper right corner of the above image? That’s one of our “Trio of Treats.”

trio of treatsI always try to include something for the littlest patrons, so I bought 3 adorable food carts and stocked them with math play sets. The food carts are by KidKraft (Sweet & Sunny Lemonade Stand) and the play sets are by Learning Resources. We used  Piece-A-Pizza Fractions, Number Pops, and Count ‘Em Up Popcorn.

And, because little kids love to take things in and out of containers, I bought a fabric basket for the pizza cart, a plastic box with a hinged lid for the ice pop cart, and a clear container for the popcorn cart. After the event, we donated the carts and math sets to a local non-profit preschool.

trio of treats customerOne of the most popular event tables, however, was “Visit the 4th Dimension.” It was hosted by scienceSeeds (whom you first met here, and then again here).

scienceseeds 1At the event table, kids learned about the different dimensions (1st is a line, 2nd is a square, 3rd is a cube, 4th is a tesseract). ScienceSeeds brought their 3D printers to the event and made models. You can see a tesseract in progress below. Awesome.

scienceseeds 2Kids could also make 3D models of their own using drinking straws and plastic connectors. You can buy the plastic connectors online (from Strawbees). However, scienceSeeds has a die cut machine and was able to purchase the die cuts (from Accucut) and make their own connectors from plastic sheets (from Grafix).

scienceseeds 4Like I said, their table was hopping – they estimate they went through at least 3,500 straws!

scienceseeds 3The thing I liked most about the project is that there was no limit to the shape, size, or intended use of the 3D models.

3D model 13D model 23D model 53D model 33D model 4

If plastic connectors are not in your budget, I’ve seen similar activities that used straws and pipe cleaner pieces (like this one), or sculptures that that involved cutting and sliding the ends of bendy straws into one another (like this one). I’ve also seen toothpick and marshmallow, (or toothpick and gum drop) geometric structures. But I tend to avoid those because of food allergies.

Whew! Believe it or not, I’m only halfway through all the event activities! I’ll be back on Friday with Part II, including some of Digitopolis’ famous celebrities, a bit of hands-on history, musical fractions, and some truly stunning representations of infinity…

See you Friday!

Gold Fever

gold fever

It sparkles and shimmers. Could it be gold? Well, you might strike gold and get rich…or you might be fooled by some glittery pyrite! We made some awesome geology connections at To Be Continued, our story time for 6-8 year-olds, including rocks that sing!

We read Missing on Superstition Mountain by Elise Broach (Henry Holt, 2011). Brothers Simon, Henry, and Jack have moved from Chicago to Superstition, Arizona. The sleepy little town is shadowed by the looming and unforgiving Superstition Mountain, which has a history that none of the adults seem to want to share. The boys have been forbidden to go into the mountains, but when Josie the cat runs away, they follow her and soon uncover a mystery that involves three human skulls, a lost gold mine, and the strange, seemingly supernatural, power of the mountain. Can the boys and their friend Delilah survive Superstition?

In addition to a secret gold mine (which is totally awesome), Missing on Superstition Mountain has quite a bit about rocks, landscapes, and geology. When we finished the book, I thought it would be cool to do some rock-based activities. And Princeton University have some fantastic resources when it comes to geology.

department of geosciencesFirst, we took a walk across campus to Guyot Hall, home of the Department of Geosciences. Their central office space is lined with display cases full of rocks, gems, fossils, and minerals.

case 1The kids oohed and aahed over some of the precious stones…

case 2But were equally impressed by the gigantic mineral specimens!

case 3We visited a Allosaurus skeleton and a T. Rex skull on our way out of the building. Yes!

dinosaur skeletonBack at the library, I had samples of pyrite for the kids to look at (courtesy of Laurel Goodell, manager of the undergraduate labs in geosciences). Pyrite is called “Fool’s Gold” because of its sparkly gold appearance, but it’s actually a mineral.

pyriteThe kids couldn’t take home the big samples of pyrite, but I did find some smaller pieces on Amazon. I bought three, 0.2 ounce boxes of pyrite nuggets for $5.79 a box. They arrived powdered with black grit, so be prepared to do some major rinsing, and maybe a little scrubbing, before you given them to kids. But as you can see below, they cleaned up nicely and there were some pretty good sized pieces in there.

pyrite nuggetsThe kids took their stash home in a cotton drawstring bag (left over from this event). I also tucked a little information sheet inside the bag too (here’s the template if you’re interested). But I saved the best geology connection for last. Did you know that some rocks can produce musical notes?

lithophoneThis is a lithophone. It’s a xylophone with tone bars that are made out of stone (as opposed to wood or metal). When you strike the stones with a mallet, they produce a musical tone. But not all rocks sing! It takes a lot of trial and error, as well as a lot of chipping and grinding to make rock tone bars. The stones you see above are limestone, sandstone, and granite.

The lithophone was made by Tom Kaufman, owner of Tinkertunes Music Studio in Michigan. I commissioned him to build it for a Journey to the Centre of the Earth event in 2013. After the event, the lithophone went to its new home in the geosciences lab.

Ready for a little rock concert?


If you think that’s cool, you should check out Tom’s lithophone fence. It plays “Row Row Row Your Boat” as you run around it with a mallet! The fence was installed at the Gerald R. Ford Presidential Museum in Grand Rapids, Michigan for ArtPrize, an annual art contest.


Many thanks to Laurel Goodell and the Department of Geosciences for the pyrite and lithophone loan! 

Sneak Peek: Giant Floor Maze

giant floor mazeYou’ve been getting little hints on our Instagram, but here’s an exclusive first look at something big on our horizon. This month, my library is hosting a major math event. It’s called A Day at Digitopolis (named, of course, after the famed city in The Phantom Tollbooth). Today, you’re going to get a sneak peek at one of the activities – a giant 16′ x 16′ floor maze. But this is no ordinary maze! You have to get from start to finish without taking a single right-hand turn. Want to build one of your own? Read on!

I first encountered this puzzle at the Manhattan Museum of Math (home of the famous square-wheeled trike!). Their version, however, is a no left-hand turn maze that’s digitally projected on a big section of their exhibit floor. A floor projection wasn’t an option for us, nor was a vinyl mat, nor cardboard. The answer? $30 worth of green contact paper and a maze design by Robert Abott.

robot abott's maze

©2009 by Robert Abbott

I did have to make a couple tweaks to Robert’s original maze. In his version, there are a couple of sections where the path goes right to the edge of the maze (specifically, on the left, right, and top sides). I added a border of green boxes to keep the pathway entirely enclosed.

added boundriesOnce I finalized the maze design and decided that it was going to be 16′ x 16′, I had to calculate how much contact paper we needed. The rolls I found on Amazon were a standard width of 18″, so I just had to determine the length. I work best with models, so I crafted a little maze, in which 1″ = 1 foot.

dr. dana's modelOnce I added up the lengths of all the pink pieces, I had a rough estimate of how much contact paper we would need (112.25′). I ordered two, 75′ rolls, which left plenty of extra paper for mistakes. The task of actually building the maze fell on Marissa and Casandra Monroe. Casandra is a Princeton University student and super math whiz!

casandraCasandra sketched the maze on graph paper, in which 1 square = 1 square foot. Then she drew a 16 x 16 square and sketched the various pieces inside it. To make the calculations nice and simple, she made path through the maze 1′ wide.

casandra's diagramThen, Marissa and Casandra headed to the library’s cavernous main lobby and started building. They laid down the outer walls of the maze first:

arranging the exteriorAnd then cut and placed the internal pieces of the maze.

arranging the interiorWhile they were filling in the pieces, they used a measuring tape to keep the path as close to 1′ as possible (even though there were some areas where the path was wider).

measuring the pathwayMarissa and Casandra kept the backing on the contact paper. But to keep the pieces from curling up, they used masking tape loops to temporarily adhere it to the floor.

tape loop expertThey also used permanent marker to label the backs of all the pieces and match them to a diagram of the maze.

writing the lettersThe morning of the event, we’ll be able to glance at the diagram, check the backs of the pieces, and peel and stick the maze quickly (we’ll have a measuring tape on hand to remeasure the pathways too).

set-up diagramAll in all, the maze took about 3 hours to put together. Cue “Eye of the Tiger!”

eye of the tigerThree important things: 1) Don’t forget to mark the start and finish of your maze (we’re using extra pieces of contact paper with “start” and “finish” written on them in permanent marker); 2) At the event, make sure to have the solution posted somewhere nearby (or available as a handheld map); and 3) Test the maze!

Ian, our faithful maze tester, went through the maze and soon discovered that one of the green blocks was, if fact, making a necessary turn impossible. So Marissa and Casandra adjusted it, and sent Ian through again. No problems after that!

ian tests it outThe real test, of course, will be at the event. There might be some last minute tweaks or unforeseen problems when crowds of kids are introduced into the equation. I’ll dutifully update this post if there are!

This isn’t the first time I’ve used contact paper to make large-scale event activities. Check out our most popular toddler activity ever, right here.