Today was a very special day in Bard Math CAMP history – the very first CAMP reunion! CAMP alumni/ae, staff members, parents, and friends gathered in the lobby of the Reem-Kayden Center once again for a selection of math games and puzzles – old favorites like Ghost Blitz and the Towers of Hanoi, along with some fun new challenges like Tantrix (How can you use all the hexagonal tiles to make a blue loop? A red loop? What about a yellow loop?).
A table full of math puzzles was the perfect place for former CAMPers to reunite with old friends and to hear about what everyone’s been up – from aerospace research and a hackathon for data science to full-time jobs in tech.
Next, everyone trekked over to the dilapidated dodecahedron – a mysterious, nearly invisible sculpture in front of the math building – to try and make it pop out while discussing what its mathematical structure might be – a stellated dodecahedron? The dual of a truncated icosahedron?
Finally, the former CAMPers & co. retired from the heat into the musty shade of Preston Theater for a math movie night of sorts – we all piled into the velvet folding seats to watch Secrets of the Surface: The Mathematical Vision of Maryam Mirzakhani on the big screen.
The day was full of sunshine, laughs, and healthy dose of CAMP nostalgia. Just like math puzzles and do-decorating, the reunion is sure to become a new CAMP tradition – where past, present, and future CAMPers can come together and celebrate their shared love of all things mathematical.
The second day of this year’s CAMP started off with a variety of fun math games – Ghost Blitz, Spot It! , a big game of Set, the towers of Hanoi, and a miniature version of chess. The CAMPers were also presented with a “problem of the day”: How many possible Ghost Blitz cards are there?
“… If the object is on the card, then you grab [that object], and if not, you grab the [object] that has nothing in common with the others.”
In Frances’ math class, small groups within SINE had come up with different conclusions about how many cards you could possibly get with a certain number symbols on each card. They were each asked to draw and explain their diagram solutions at the board – some using the “line method”, some using the “grouping method” to show every combination of symbols.
Meanwhile, the COS group launched into an in-depth analysis of Spot It!(both the full and junior versions), making observations to ask questions about how the game works and trying it out together as a class by constructing simple versions – 0 symbols, 1 symbol, 2 symbols – from scratch. Next, the broke into small groups to tackle the 3-symbol case.
To get started, one group decided to use digits instead of letters to stand in for symbols, recognizing that Rule #3 of Spot It!caused Symbol 1 to appear on every card. They then used process of elimination to figure out what the other digits (symbols) on each card should be – once two cards have one symbol in common, they can’t have any other symbols in common. By the end of class, the CAMPers had come up with apretty solid argumentthat with 3 symbols per card, there must be 7 cards.
After math class, the SEC group brought their flash drives to Computer Science, where they continued their exploration of shapes and coordinates, then brainstormed how they would go about making shapes that change. Next, they talked about how to fill in color values and how RGB colors channels work – each 24-bit pixel is split between the R channel, the G channel, and the B channel, so they each get 8 pixels. After that, they split into groups, planning out the code to make a shape and change its color – on paper, before they tackled the computers.
After class, CAMPers met in the RKC lobby to sort themselves into their pre-lunch elective groups: learning mathematical magic tricks with Frances, practicing the ability to think fast with improv games, and solving more pencil-and-paper puzzles.
After a great lunch at the Kline Dining Commons (plus unlimited scoops of delicious local ice cream), the CAMPers split up again into CSC and SEC for Computer Science and Art, respectively.
Computer Science at CAMP focuses on the underlying properties of computers and the instructions that humans feed into them. Understanding binary (strings of 0’s and 1’s that encode base-10 numbers), as well as logical operators (NOT, AND, OR, etc.), sets the foundation for the CAMPers to learn any programming language they choose in the future. With those two concepts in mind, the CSC group started working with truth tables to put it all together.
Meanwhile, the SEC group made progress on their Spot It! decks, adding the symbols they designed to index cards.
At the end of the day, the CAMPers all filed into the Bito Auditorium for more math games, like Ghost Blitz, Chocolate Fix, Rush Hour, and Set.
Day 2 got all the CAMPers thinking deeper and going further, asking questions and working together to find the answers. The rain outside didn’t stop them from using their trademark creativity to find ways to have fun indoors. We can’t wait for more discoveries on Day 3!
This year marks an exciting point in the history of CAMP: the program’s 10th anniversary! Starting today, the CAMPers (some returning, some new) are going to learn about combinatorics – the mathematics of counting and combining things.
First thing this morning, the CAMPers gathered under the staircase in the Reem-Kayden Center to try out a variety of Spot It! games – with themes like Pixar, Minions, Marvel, and Harry Potter. Each box has a deck of circular cards, and each card has a certain number of symbols on it. Any two cards will have exactly one symbol in common, no matter which cards you pick out. There are lots of ways to play, but most groups started with the simple yet highly competitive version: Whoever finds the common symbol first “slaps” the card and gets to take it.
After a quick orientation (and a “Happy Birthday” song for one of our CAMPers), the SINE group started talking about fractions – how to think about fractions as things (like apples or elephants) when considering operations like division of fractions. CAMPers learned that what we’re really doing when we divide 3/4 by 2/3 is put the fractions into a common denominator – 9/12 and 8/12 – then divide 9 pieces into groups of 8 pieces each. You would get one group with a remainder: 8/8 + 1/8 = 9/8.
“If I had 10 apples and I asked you to put 2 oranges into a group, could you do it? No, because apples aren’t oranges.”
“What we really need to do is let go of our predisposed notions and realize that apples ARE oranges.”
Next, they broke into groups to analyze the Spot It!decks: How many cards are there in each deck? How many symbols are there on each card?
Then Frances introduced them to a useful tool: Graphs. In the case of Spot It!, dots represent individual symbols and lines represent the connections between them – the cards they have in common. The CAMPers made graphs with pipe cleaner edges tied together at each node, while others chose to draw them on paper.
In Computer Science class, the SEC group started processing in Java – in other words, getting the computer to draw stuff. They learned about functions like size() (which controls the size of the canvas) and different shapes – for example, ellipse() . Given the function ellipse(100, 100, 50, 30); , the CAMPers were asked to “vote” on the following question: Where on the screen will the ellipse appear, and why? Next, they were given a coding challenge: Create a canvas of 800 by 800, then draw 4 ellipses, one at the center of each quadrant. Finally, they learned to use the rect() function to create – you guessed it – a rectangle and figured out the function to change the color of a shape.
After class, the CAMPers split up into groups, each with a fun elective to try: learning to juggle with Japheth, trying out pencil-and-paper puzzles like “Star Battle”, and learning how to solve a Rubik’s Cube with CS instructor Shiven. The CAMPers had a lot of fun with indoor activities, even though a thunderstorm was brewing outside.
After lunch, the CSC group had Computer Science class, where they learned about converting numbers to binary – the language of computers.
Meanwhile, the SEC group went to Art class to start brainstorming symbols for their own personalized Spot It! decks.
Finally, the CAMPers reconvened in the auditorium for a “math fair” of games, activities, and puzzles to choose from: paper puzzles, Rubik’s Cubes, Set, and of course, Spot It!
The first day of CAMP’s 10th year was full of fun puzzles, new challenges, and lots of laughs! Using their creativity to answer questions as they come up will set a great foundation for their explorations on Day 2.
