We’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.
But 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 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…
And here’s Beach Ball Party, which involved counting, stacking, and chasing beach balls determined to make a break for it.
It 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.
Some 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 the mine you see below, but we built another one for a later event. You can find the step-by-step instructions here.
The 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.
The mines were staffed by high school volunteers from the Arts Council, who were suitably decked out in miner helmets.
Elsewhere 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, a gorgeous nautilus shell).
The 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).
We decorated the finished fractal trees with bird and leaf stamps, but you can also just use markers or color pencils.
And 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.
Some 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.
At 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.
It’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.
Here’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.
The 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.
For 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!
There 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.
Below is a list of what we offered at the event table. 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 instructions 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.
By 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.”
I 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.
One 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).
At 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.
Kids 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).
Like I said, their table was hopping – they estimate they went through at least 3,500 straws!
The thing I liked most about the project is that there was no limit to the shape, size, or intended use of the 3D models.
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! You can check out Part II here…prepare to meet Digitopolis’ famous celebrities, get a bit of hands-on history, listen to some musical fractions, and view some truly stunning representations of infinity…
First, 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.
The kids oohed and aahed over some of the precious stones…
But were equally impressed by the gigantic mineral specimens!
We visited a Allosaurus skeleton and a T. Rex skull on our way out of the building. Yes!
Back 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.
The 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.
The kids took their stash home in a cotton drawstring bag (left over from 
This 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.
It’s a diorama, a keepsake box, a mini exhibit, AND a lesson in ecology! Open the lid of this winter landscape and you’ll find the creatures that hibernate, burrow underground, and tunnel underneath the snow, complete with an information card!
We read Over and Under the Snow, written by Kate Messner, and illustrated by Christopher Silas Neal (Chronicle Books, 2011). A father and child ski over the deep snow in the woods. Even though it’s a world of white, signs of life are everywhere – squirrel, owl, deer, snowshoe hare, and fox. But under the snow is yet another world. Shrews and voles run in tunnels. Bullfrogs burrow in the mud, bears hibernate, and a queen bee sleeps, waiting for the first signs of spring. The book ends with the child in a cozy bed, dreaming of nature. An absolutely beautiful book, with gorgeous, bold illustrations set against snowy white.
Roll the paper into a tube and secure it with tape. Cut 4 tabs in the bottom of the tube (each tab should be about 1.5″ long). Fold the tabs outwards. Later, you’ll use these tabs to attach the tree to the box lid:
Cut 5-6 tabs in the opposite end of the tube (these tabs are much longer, about 5″). Fold them out gently, then twist them to create the branches of your tree.
Hot glue (or tape) the tree to the lid of the box. If you’d like to add a log to your landscape, use a brown marker to draw horizontal lines on a 3.75″ x 4.5″ rectangle of brown wrapping paper. Crinkle the paper, then roll the paper into a tube and secure it with tape. The final length of the log should be 3.75″. Set the finished log aside for a moment.
Your winter landscape is complete! Well, maybe not quite complete…
Bet you a