Let’s Do The Numbers

lets-do-the-numbersWelcome to the number mines of Digitopolis, the famous kingdom from The Phantom Tollbooth! This fall, we hosted a table at Princeton University’s annual Community & Staff Day event. Big crowds meant that we needed something simple, but we wanted to be creative too. Since we had successfully offered the number mines at a massive math event last spring (you can read about it here and here), we decided to bring them back for more numerical fun.

Alas, the original number mine (which was artfully constructed by the Arts Council of Princeton) wasn’t salvaged after the math event. This meant that Katie and I had to build our number mine from scratch. The first part of this post describes how we ran the event table. The second part describes how we build the mine.

At the event, kids would reach into the number mine and pull out a plain wooden number. I bought the numbers online from Woodcrafter, where they range in size, thickness, price, and font. I got the 4″ numbers that were 1/8th of an inch thick. Each number cost 56¢.

wooden-numbersWe found that 4″ was a great size for decorating, but if 56¢ per piece is outside your budget, you can go smaller. A 1″ number of the same thickness, for example, costs 23¢. Or, if you want to go even cheaper, skip the wood and print your numbers on white card stock. We loaded the numbers into the mine, and the kids “dug” them out with their hands.

reaching-in-1Once kids found a number they liked (7 and 8 were very popular), they went over to the number decorating area, which was stocked with metallic makers, glitter markers, small gemstones, and glue. We had a relevant quote from the book on display too. Kids really got into decorating. One little girl spent 25 minutes working on her number!

decorating-the-numbersNote! If you use squeeze glue (as opposed to hot glue) make sure to have paper towels or small paper plates handy so families can safely transport their numbers home. Hand wipes are also a good idea for sticky fingers and tabletops. Katie and I dressed for the occasion in miner’s helmets and safety vests.

dr-dana-and-katie-number-minesSo, that’s our event table…now for constructing the mine! You certainly don’t have to get as elaborate as we did. You can create a mine by covering a box with grey paper. Cut a hole in the box’s lid, throw some numbers in there, and have kids reach into the box! Or you could skip the mine altogether and just do the number decorating part of the project. But if you do want to build a mine, here’s how we did it.


Find a big, flat box that isn’t too deep. You don’t want kids to have to reach too far down for the numbers – especially the little ones. We used a 34″ x 54″ inch box lid, and then attached 6 photo storage boxes to the bottom using hot glue and packing tape. This resulted in a mine that was 5″ deep. Here’s a shot of the underside.

number-mine-step-1Since the box lid didn’t reach all the way to the bottom of the photo storage boxes, we closed the gap by attaching big strips of corrugated cardboard to 3 sides of the mine. We left it the mine open in the back so we could restock numbers during the event.


Cut holes in the top of the box. We found it helpful to draw the holes before we started cutting. That way, we could be sure we weren’t cutting into any of the support boxes and we knew that the numbers would fit through the holes.



Create the rocky, craggy landscape of your mine. We bunched up big pieces of black bulletin board paper and attached them to the box with masking tape (you might recognize that texture from this Instagram pic).



Now for the really, really messy part. Papier-mâché. We don’t have a sink in our work space, and the nearest bathroom is far, far away. So we wanted to create the smallest mess possible. In other words, we didn’t want to cook, mix, or blend any sort of papier-mâché paste (or dilute any glue). After a little research, we settled on liquid starch.

Below are our tools – 2 enormous jugs of liquid starch, 2 plastic roller trays, and 4 paint brushes (the bristle brushes worked better than the foam ones). Oh, and we also put a plastic tarp under the mine so we wouldn’t ruin the table.

number-mine-toolsSince we had a lot of area to cover, we used big, 6″ x 16.5″ pieces of newspaper. Occasionally, we use a smaller strip for edges or crevices, but mostly we stuck with the big ones.

number-mine-step-4_1The liquid starch held up well! It did coat our hands with sticky residue that required multiple rounds of soap and scrubbing to remove, but it wasn’t too bad. Honestly, the worst thing about the liquid starch was the fact that it was scented. “Mountain Fresh” scent to be exact. Hoo boy. You could smell the mountains the minute you took the cap off. After a couple minutes, the fragrance was looming in the room like a big, ominous fog. Katie put together a little graphic to convey the overpowering Mountain Freshness.

mountain-fresh-freakoutWe left the first layer to dry overnight. For the second layer, we got a little experimental. While researching liquid starch, we learned that some people absolutely rave about using white paper towels and computer printer paper for papier-mâché projects, especially if the projects are going to be painted later. So we decided to give it a try. We papier-mâchéd the bottom of the mine with paper towels, and the top portion with computer printer paper.

number-mine-step-4_2Wow, did the paper towels suck up the liquid starch! The printer paper needed much less. But the printer paper was so stiff, it created unwanted gaps like this one:

stiff-gap-problemThe solution was to drape a liquid starch-soaked paper towel over it. Below is that same gap with the paper towel over it. As you can see, the soft paper towel completely obscures the gap. I didn’t officially test this, but I believe newspaper would obscure gaps as well, perhaps even better than the paper towels.

stiff-gap-problem-solvedI was a little worried the paper towels were too transparent. But overnight, they magically dried to solid white.

number-mine-step-4_3In the above photo, you can see there were still wet patches in crevices where the liquid starch had pooled. Katie hit those with a hair dryer, no problem. And we should add that, even now, things were still smelling quite Mountain Fresh.


Time to paint! We used this awesome textured-stone effects spray paint by Valspar. It’s fun, but pricey ($10 a can at Lowe’s). Our mine required 3 cans.

stone-spray-paintA cheaper option would be to use gray paint to cover the mine, then dab on darker gray  with a piece of sponge. This will get you a textured surface, without the hefty spray paint price. Once the spray paint had dried (which, we might add, finally dissipated the Mountain Fresh fragrance), we decorated some numbers and attached them to the mines with hot glue. We hot glued some large plastic gems on as well – purchased from the wedding favor aisle at Michaels Craft Store.

number-mine-step-5And this, dear readers, is when we discovered the fatal flaws in regards to paper towels:

  1. When dry and spray painted, paper towels become incredibly brittle. I poked a hole right thorough one section while merely tapping on it (we eventually covered the hole with the number 8).
  2. The texture of the paper towel absolutely comes through in the end. So if your paper towels have little hearts embossed on them, you’re going to see little hearts under the paint.
  3. The edges of the paper towels are clearly defined. Unlike the newspaper and the printer paper, you can definitely see the edges of the paper towel under the paint. So our rocky surface looked like, well, draped paper towels. You could even see the dotted perforations that separate the paper towels.

paper-towels-not-goodThe printer paper, on the other hand, was much sturdier and the edges were hidden under the paint. The lesson? DON’T use paper towels for papier-mâché projects. Use newspaper and printer paper instead. In fact, I highly recommend printer paper for the second layer of painted papier-mâché projects. Very sturdy, holds paint very well.

However, paper towels are what we used and their brittle weakness made me and Katie very, very nervous. We were positive that kids were going to put their hands right through the mine as they leaned in to select numbers.

reaching-in-2Anticipating trouble, we brought duct tape and a couple of step stools to the event. The stools elevated the kids right up to table level, allowing them to keep their weight mostly on the stools and not on their hands. So the paper towels held, but there were a couple time you could see them bending. Katie and I would brace ourselves for a tearing, crunching, breaking sound. Thankfully, it never happened. Whew!

The BiblioFiles Presents: Norton Juster

Norton Juster photo courtesy of Random House

Author photo courtesy of Random House

Just posted! It’s our first BiblioFiles webcast in front of a live audience, and our guest is Norton Juster, author of the legendary book, The Phantom Tollbooth.

Milo is a boy who doesn’t know what to do with himself, isn’t interested in much, and doesn’t see the point in anything. But when a mysterious package containing a toy tollbooth arrives in his room, everything changes.

Past the tollbooth are the Lands Beyond, which house places like Dictionopolis, the Valley of Sound, the Doldrums, Digitopolis, and the Mountains of Ignorance. Milo is soon joined by a pair of unusual travel companions, Tock and Humbug, as he attempts to bring Princesses Rhyme and Reason back to settle the warring kingdoms of Words and Numbers.

First published in 1961, The Phantom Tollbooth is wacky, smart, odd, fun, strange, and completely captivating. It is often compared to Alice’s Adventures in Wonderland in terms of its intelligence, word play, and impact on children’s literature. Now, in over 50 years of publication, The Phantom Tollbooth, with its iconic illustrations by Jules Feiffer, has been analyzed in scholarly papers, quoted in dissertations, included in graduate classes, documented on film, read aloud in elementary school classrooms, passed along through generations of families, and newly discovered by young readers. It is, and will always be, a seminal book in the history of children’s literature.

In addition to The Phantom Tollbooth, Norton Juster has written The Dot and the Line: A Romance in Lower Mathematics, Alberic The Wise and Other Journeys, As: A Surfeit of Similies, The Hello, Goodbye Window, Sourpuss and Sweetie Pie, The Odious Ogre, and Neville. In 2011, The Annotated Phantom Tollbooth, with introduction and notes by scholar Leonard Marcus, was released.

Follow this link to the BiblioFiles interview

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! 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…