Bard Math Camp Day 5

Our last day of Camp began in a flurry of activity as Campers received their T-shirts and made the final touches on the Rubik’s Cube Mosaic.

In Math class, we learned magic tricks designed to help us understand math better using addition. We finished off our lessons and challenges from the week and prepared to present our knowledge to our parents,

After, in Art, we finished the last of our clay projects and collected all the art we had created throughout the week, including our origami creations and our playing cards. We discussed and observed how these creations connected with what we had been learning about fractals.

In Computer Science, we spent the last day finishing our project of creating a Sierpinski Gasket Triangle on the Computer and also collected all of our previous codes including our bifurcation maps to show our parents during open house.

We ended camp with an Open House for parents, where the children all presented their art pieces and projects. Camp ended with lots of amazing reviews and lots of nostalgia, ready for the school year to begin.

Bard Math Camp Day 4

Day 4 of C.A.M.P. began with a flurry of activity as more campers joined the effort to complete the Mosaic and taught each other new games such as Backgammon and chess.

In Computer Science, we continued on our journey to learning and mastering NetLogo. We also continued to deepen our knowledge of computers and their systems while utilizing concepts from Math to supplement our computer science lessons.

After, in Art, we finally got to work with clay. We used it to creating amazing fractal designs and also showed how precise we could be in our measuring.

Lastly, in Math, we did advanced math using fractals and learned how to calculate the dimensions of any shape. We also learned how there are more than just 1D, 2D, and 3D figures, and sometimes the dimension can be between numbers and less than one. Math challenged us to think outside of the normal constructions of what we hear in everyday life but it also pushed us to connect what we see with what we are learning.

Our electives today included capture the flag, drawing, and the Rubik’s cubes. With our Mosaic almost finished, it’s a race against time.

Bard Math Camp Day 3

Day 3 of camp began with  race to complete the Rubik’s cube mosaic! This has been a lengthy task that will require manipulating 400 Rubik’s cubes.

In Computer science, we began forming fractal images through NetLogo and utilizing the concept bifurcation from Mathematics. We managed to return the output of the function we used through code thereby demonstrating the significance of computers to calculate our functions. All of this at the press of a button!

Art gave us a creative outlet as we finished creating our very own decks of cards and moved on to creating 3D figures with fractal designs.

Finally,  in our last class, Math, we learned another way to create the Sierpinski Gasket using a large sheet of paper with an equilateral triangle on it. We marked the midpoints of this triangle, and then connected all three points to create 4 triangles inside the large triangle. We then repeated  this process, finding the midpoints in each of the enclosed triangles and connecting them to create smaller triangles within a larger triangle.

For our electives, we had the option to work to complete the mosaic, to play an intense game of Mafia, or to go on a relaxing Nature Hike through the Meditation Garden. Needless to say, today was a very busy day for all our campers.

Bard Math Camp Day 2

Everyone arrived bright and early full of energy for the second day of CAMP! We began with a variety of warm-up activities to get our brains on track for more math and logic. We had teams learning to solve Rubik’s cubes, campers pairing up to play Rush Hour and other campers solving a variety of puzzles.

Soon after in computer science, we continued our challenge from the previous day with some groups going more in-depth to understand computers and other using NetLogo to make create variables such as turtles and cows that can draw squares in the language. They were challenged to be able to kill their turtles and perform various other actions on these variables. Their next challenge: Functions.

In Math class, campers reviewed information from yesterday and then dove deeper into fractals. They analyzed the rules for creating the Sierpinski Gasket fractal.  They began forming connections between the mathematical connection of fractals to their application in Computer Science.

Lastly, in Art, we began making our very own deck of cards! Each camper made their own set, with 4 houses. They had the option to make up their own houses or use the traditional hearts/spades/diamonds/clovers. We used stamps and various other art materials to create them.

At the end of the day we hiked to the Parliament of Reality and learned how to grass whistle. Others took their creativity to the studio and went painting and the last group had an intense Rubik’s cube championship.


Bard Math CAMP Day 1

It’s the first day and there’s lots of excitement and nervousness as old friends connect and meet new friends over an assortment of games including rush hour, human feline puzzles and huge 10 person rounds of Set.

In Computer Science, our teacher Yulia pretended to be a Robot and challenged the campers to right specific instructions that would lead her to draw a square onto the  board. We divided up into groups of three and our biggest challenge was to write instructions as specific as possible otherwise our robot had a lot of room for misinterpretation. The goal was to demonstrate how coding requires precision in wording, efficiency and thoroughness so that Yulia would follow their exact directions and draw a vertical line up instead of drawing a vertical line down. We then shifted to the computers and focused on the basics  of computer science and how it compares to mathematics.  After a brief review, we began exploring NetLogo, where we hope to be able to make our variables, turtles, draw a square  like we did our Robot Yulia.

In Mathematics, we started with listening to Michael Frame’s Yale TedX talk.  We learned about fractals, which are patterns made from infinite repeats, but do not exist in real life since there are a finite number of repeats. After the video, we moved on to creating the fractals. To create the fractals:

  1. Draw a large Square on Graph Paper, labeling the x and y coordinates up to 1
  2. Mark the coordinates(0,0),(0,1),(1,0),(1,1),20 other points within the square and three points on the edges
    • To each point: Halve the x, and y and lightly plot in a new color and connect the two points
    • Add 1/2 in the x direction to the shrunken value from step 1 and plot in this same new color
    • Add 1/2 in the y  direction to the shrunken value from step 1 and plot in this same new color
    • Take a new color and apply the same rules to these new points . Repeat. Observe the movement of the point as it forms a fractal.

In Art, we explored centuries old puzzles including Tangrams, T puzzles, Mysto Squares and so much more. We collaborated with friends new and old to defeat the mystery behind each game.

The students ended their first day at CAMP with an intense games of 4 corners, sharks and minnows while also having the option to hike to Blithewood to view the lawn razing goats, or practice the lost art of paper folding: Origami.


2019 CAMP Staff

Bard Math CAMP Day 5


Today was the last day of CAMP!

In computer science, we wrapped up the week by learning more about the actual hardware of computers. In small groups, we each got a tower that we opened up and explored the computer guts inside. We had a small scavenger hunt for specific parts we had discussed during the week such as the CPU (Central Processing Unit), PSU (Power Supply Unit), and motherboard. Following our exploration of the towers, we came back together for a class discussion about more important computer vocabulary and misconceptions about things such as Wifi and servers.

In Math class, with Japheth, we finally got to uncover together the math behind liar’s bingo. After solving the mystery using all that we have learned about binary this week, we split up into pairs to work with different problems that we later found were extremely related. Some people worked with counting subsets, some with counting divisors, some with letter combinations, and more! Through these problems and a small tour around the classroom to discuss everyone’s sorted solutions, we realized that each of these problems were related to Pascal’s Triangle!

In art, students had a chance to continue working on their clay fractals from the day before. Students then utilized the idea from clay fractals and created cookies using this design. The cookie dough was kneaded and then combined to create a fractal pattern for the cookies. When students finished this, they had a chance to combine all of the things they worked on over the course of the week into one piece of art.

From 2:30-3:30, we had our CAMP open house for parents!

Blog by: Meagan Kenney, Elliott Goldstein, and Maya Schwartz.

Bard Math CAMP Day 4


Today was the fourth day of CAMP!

In art, students continued to expand on the fractal idea that they began to work on Wednesday. At the beginning of class, students were able to finish or improve upon their fractal paintings. After, students received clay (of either black, white or gray coloring) and kneaded them until they were thin enough to be put together, Students kneaded them to fit a triangular shape, then combined two of the kinds of clay and stretched them out. When the students cut the clay, a triangular fractal was visible. Students then used these triangular fractal cross-sections to spell out their names or create designs.


In computer science, students learned the properties of boolean logic relating to truth tables. Students learned about true/false statements that contained the boolean operators or/and. After working through more complex logical statements (i.e. true and (not true or not false)), students utilized these ideas to work with circuits. Students considered the properties of circuitry and the flow of electricity with boolean logic.

In math class, with Japheth, we learned about Hasse diagrams: a handy way to organize a number and all of its divisors to learn more about the divisors themselves. After learning two examples of these diagrams we all tackled creating the Hasse diagrams of the numbers one through thirty. We then sorted these interesting pictures and discussed our findings as a group. This helped us to solve one of our mysteries from Day 3 of how to characterize numbers with exactly four divisors. Through this exploration we showed that all numbers with exactly four divisors are either the product of two distinct primes or the cube of a prime!

After-lunch electives included Zome Tool, Open Studio, and Rubik’s Cube.

Blog by: Elliott Goldstein, Meagan Kenney, and Maya Schwartz.

Bard Math CAMP Day 3


Today was the third day of CAMP!

Today in Computer Science we got to practice our skills as drivers and navigators of our programs: one student would type the code out while the other kept watch for typos and helped guide the driver in writing the program. We mainly used Python to learn how to compare multiple compound logic operations by testing all possible inputs and comparing outcomes. Additionally we learned more about variables and functions and to utilize them to make our coding more efficient!


In math class we started with a fun trick. We had a huge collection of strips of papers with numbers colored black or red. When a student read out the colors of a random strip to Japheth, slipping in one lie about a color, Japheth was able to tell the exact number for which the color was lied about. Was he using magic? Binary logic? Who knows! Then we started an extensive exploration of the positive integers up to 30 and their divisors. We sorted the numbers by how many divisors they had and then began to analyze each group. Through this analysis we found that we could prove that a number has exactly two divisors if and only if it is prime. And also, we found that a number has exactly three divisors if and only if it is a square of a prime number! There’s so much more to learn from this exploration that we will continue to see in the remaining days of CAMP!

In Art, the students worked on creating fractals. Fractals are figures in which each part of the figure has the same structure as the whole. Fractals contain similar patterns that happen continuously on a progressively smaller scale. To make the fractals, students cut a piece of paper into 4 sections and then re-arranged the patterns after cutting. Students then were able to customize their fractal by coloring it.

After-lunch electives included juggling, creative writing and reading, and Rubik’s cube.


Bard Math CAMP Day 1


Today was the first day of CAMP!

The students started their day by collecting their t-shirts, making their name tags, and going into the auditorium for some morning activities.  Morning activities included working on a Rubik’s cube mosaic, playing cards, and juggling.

 Starting with the warm-up activity, scavenger hunt, the kids hit off the art session with flaming conversation. The scavenger hunt was designed for them to get to know each other with prompt like: “find someone who has a dog with a fun fact” or “find someone whose favorite season is winter”.
The students then worked with beads to make necklaces that would “spell out” various binary spellings of words. The ASCII alphabet (American Standard Code for Information Interchange) is a binary system in which each letter is formed by a certain pattern of 1’s and 0’s. With two different colors of beads, students assigned each a value of 1 or 0, and then made words/initials out of these beads. Students also learned how to make “magic wooden blocks”, a structure of blocks that could be manipulated and moved in various ways.
In Computer Science, we learned how to develop the logical operation called XOR or “exclusive or.” We used our knowledge of other logical operations to extract the compound logic operators that would give us XOR, which is only true when the inputs differ (that is one is true and one is false). After forming the XOR using our Boolean operators we acted out how XOR would play out in a circuit. Some of us acted as different currents while others were gatekeepers who determined the output that would occur at each logic gate depending on how the two currents entered the gate as on or off. And then some of us used this new logical operation to further explore how one can use Boolean operators in Python, while other students built the XOR circuit using little bits!
In Math, we delved into symbolic logic through truth tables. The students learned about the binary operators “and” and “or”, as well as the unary operator negation.  After learning about truth tables, they worked on riddles about an island that has two types of people: liars and truth-tellers.  This relates to binary by considering the falses to be 0’s and the truths to be 1’s, thus linking the mathematics and computer science workshops.
The after-lunch electives today included recess games, Rubik’s cube, and hiking.
Blog by: Meagan Kenney, Leah Leiner, Elliott Goldstein, Shuang Cai, and Maya Schwartz.