C.A.M.P. 2017 Day 4


Our morning started off with AMC 8 prep questions, card games such as SET and tongues, a Rubik’s cube mosaic, and NIM.  The Rubik’s cube mosaic was pac man and four ghosts.  Students played these activities until 9:30, when it was time to go to class.

In math class, we started by analyzing the trick that Frances performed on the previous day using Fibonacci sequences. The students used algebraic notation to analyze the trick. We also learned a quick method to multiply any number by 11. The next trick we learned was the 3 Button Trick. In this trick, the spectator switches the positions of 3 buttons, telling the magician about each switch. Then the  spectator chooses a special button, and silently switches the  other 2. The spectator continues switching as before, until they decide to stop. Then the magician guesses which button was the chosen one. The students  analyzed this trick using diagrams in order to see how the trick works. Finally, Frances performed a trick called The Baffling Prediction to close out class.
The Computer Science class again started with a quick revision of all commands and terms learned so far. This is a necessary practice, as what students learn everyday builds upon the knowledge acquired in the previous days. After making sure everyone was ready to learn new things, Matt introduced students to fun commands such as mousePressed, mouseX, and mouseY. These commands allowed students to make their code more interactive and their animations more responsive. All students made sure to take advantage of this powerful tool.

In Art today, some students opted to use their color explorations from day 3 to construct interesting patterns, sequences, collages, and shapes. The idea was to exploit different gradients of color in order to establish an interesting visual effect. One of the nice things with this project is that since each student focused on only a few color tones, the project gave students the chance to share vastly different colors with each other, which was nice to see. On the other hand, many students painted and perfected their own clay models, crafting small boxes to carry them in. One of the most satisfying things for us to see was that even the creators of these geometric puzzles struggled to put them back together! We can’t wait to see how their friends and family react.

Afternoon activities were Rubik’s  cube, juggling, and Origami.

C.A.M.P. 2017 Day 3


Today was our third day of Bard Math CAMP 2017!  Our day started off with distributing t-shirts at check-in because today was picture day!  We all gathered for a picture at 9:30 right outside the RKC.

In math class, we found a number pattern that allowed us to divide any whole number by 9 without using a calculator. After Frances performed a trick using only numbers at the end of yesterday’s class, everyone had a chance to think about how it works that evening at home. Then today, we used the number pattern and algebraic notation (a new concept!) to explain why the trick works for any multi-digit number. Later, we learned about  the Fibonacci sequence, and Frances performed a trick for the  class where the students made their own Fibonacci sequence and Frances guessed the sum knowing only one number of the sequence.

In Computer Science class students learned two powerful framework methods – setup and draw. These methods allow one to specify which commands should be executed once and which should be run repeatedly. In result students were able to play around with their code and create small animations. This was undeniabley the most exciting part of the class for the majority of the students!

During Art class, we gave the students a first introduction to color theory, describing different complementary colors and how artists use this idea to achieve colors they see in real life. After having them choose two tones with which to experiment, the kids created an assortment of squares that were all colored with their own various experiments. Outside of class, students have been building Rubik’s cube mosaics, but now they also have an assortment of small squares built out of colors they created for themselves. Hmm…

Afternoon activities were Rubik’s cube, juggling, and recess games.  Recess games included games such as freeze tag, dude, zip-zap-zop, 21, and what time is it mama bear.

Blog by Maya Schwartz, Kate Blaine, Marysia Tran, and Andres Mejia

C.A.M.P. 2017 Day 2


Our day started off with activities such as SET, NIM, and a Rubik’s cube mosaic.  The design for the Rubik’s cube mosaic was the superman logo.  We then split into our  two groups and went to computer science class and math class.

We started our class by figuring out the magic tricks that we had learned on day one.  the class then proceeded to learn the penny trick.  The penny trick is where the magician puts at least 15 pennies on a table in the shape of a “9.”  the audience member has a tiny piece of paper and picks a number between 7 and however number of pennies there are.  They then start at the bottom of the 9 and count up first, up to the number they have chosen, and then around, again, counting up to the number they have chosen.  after they reach their destination penny, they place the piece of paper under the penny.  The magician, who has looked away the entire time, guesses the correct penny the piece of paper is under.

In the computer science class the students first reviewed all the Processing commands learned the day before. Then they learned more commands and got a little bit more familiar with the software. They were also introduced to the concept of variables in Computer Science. Finally, they modified the code that they were working on yesterday using variables to see how useful they are. Some of them got really creative with their drawings!

For art, the students continued to work on their clay pieces, which were in what Susie called the “leather-hard” stage of development. One difficulty in this stage was that when the clay dries, it shrinks slightly. Students rose to the challenge both mathematically and artistically, either using tools to smooth out the edges of their shapes so that they fit, or creating new shapes to place in the gaps created by the shrinkage.

After this, some students began using cardboard or wood to create small frames for their shapes to fit into, while others opted to try creating new puzzles. In either case, it was exciting to see that they were more familiar with how to work with the materials they were given and also thinking more carefully about how they wanted to craft their puzzles.

Afternoon activities today were a hike to Blithewood Gardens, Rubik’s Cube, and paper folding.

Blog by Maya Schwartz, Kate Blaine, Marysia Tran, and Andres Mejia

C.A.M.P 2017 Day 1


We started our day ambitiously, playing a revised version of “set” where students all got the change to meet each other, after being assigned a “set” card and being sent out to meet two others who would complete a “set” trio. It’s the CAMP’s official opinion that the students were far better at achieving this goal than any of the staff.

Since the theme for this year is mathematics, magic, and mystery the  math class today focused on card tricks and the mathematics behind it.  The first thing they did was a card trick called the “27 card trick.”  The magician lays out 27 cards in three columns of nine cards each.  They ask the audience member to pick a card and only tell the magician which column it is in.  They shuffle up the cards in a very specific way and figure out which card it was.  Students then got into groups and tried to figure out how the trick works.  Frances then got the  class together and then explained it.

Frances then demonstrated the “missing card” trick where the  magician guesses which card is missing from the deck.  The  magician asks the audience member  to pick a card and keep it, and not show it.  The magician then starts setting individual cards on the table and eventually guesses the card in the audience members hand.

One Student Learns The Art Of Deception 
In the mathematical art section, students were asked to take the beginning steps in creating their own geometrical puzzles. At first, they were given some basic parameters about how to break a square into different pieces and after outlining the process, they began creating their own clay models, materializing these different their drawings. These pieces will be used to  draft various mental challenges they can pose to friends or family: the puzzle is to reconstruct an image from an assortment of small shapes.

The computer science class started with a small exercise demonstrating the differences between the natural language we use everyday and a programming language. The students were asked to write a list of commands that would make Matt (the instructor) draw a diamond shape on the board. To the frustration of all students, none of the attempts were successful. This showed how rigorous and specific a programming language is. Then the students were introduced to Processing, the software they’re going to learn and use in the next few days.

After lunch, students divided up into three groups for afternoon activities.  The three activities offered today were hiking to the Parliament of Reality, working on solving the Rubik’s Cube, and drawing portraits of each other.

Blog by Maya Schwartz, Kate Blaine, Marysia Tran, and Andres Mejia

2017 CAMP Staff

Here is our 2017 CAMP staff!

 Senior Staff 


Frances Stern

Frances teaches math to teachers and students in New York City, working with struggling students and those eager for more and deeper math.  She has a master’s degree in mathematics and has written two books for parents and teachers, both titled Adding Math, Subtracting Tension, for grades pre-k to 2 and grades 3-5.  Drawing, painting, hiking, learning to juggle and folk dancing are favorite non-math activities.

Matthew Hughes

Matt works as a software developer at Wayfair. He graduated from Bard College in 2013 as a Math major, and went on to continue his studies at Georgia Institute of Technology for a degree in Computer Science. He’s taught various subjects including sight-singing, algebra, and a brief stint on basic technological literacy. He’s excited to expand his teaching experience in computer science at CAMP.



Susan Tarnowicz

Susie is a visual artist and teacher living and working in the Hudson Valley.  She studied painting and visual perception at the Rhode Island School of Design and has taught art at both the middle and high school levels.  Susie loves drawing, growing food, the woods, and all ways that math and art co-create!

Junior Staff

Andres Mejia 

Andres is a rising Senior at Bard College and is a native New Yorker from Queens. In his free time, he enjoys listening to music, playing guitar, and of course doing math. He was junior staff at CAMP for the Summer of 2015, and is excited to get back!

Kate Blaine

Kate is a junior at Bard College, majoring in math and music. She is from Rochester, NY, and enjoys playing piano, reading mystery novels, and experimenting with Rubik’s Cubes. She is a co-head of the Bard Math Circle, and is very excited to be working at CAMP for the first time!

Marysia Tran


Marysia is a senior at Bard College majoring in Computer Science and Math. She is from Warsaw, Poland. She tutors for Bard Prison Initiative and is the head of the Asian Student Organization. She enjoys traveling, learning about other cultures and dancing. It is going to be her first time working at the Bard Math CAMP.



Maya Schwartz

Maya is a junior at Bard College majoring in math.  She is from Cincinnati, Ohio.  This is her first year working for Bard Math CAMP.  Aside from attending Bard, she enjoys figure skating, horseback riding, and traveling. 


High School Volunteers


Alex Warren

My name is Alex and this is my second year as a CAMP high school volunteer. I live in New York City and am going into my junior year at the Bronx High School of Science. I like all things math and I am really excited for this years CAMP. As a former camper in the program, I think that this year will really be a great one. Some of my hobbies are computer science and robotics. I enjoy learning about math and also doing magic tricks, which is why I think that this next week will be a great one.

Daniel Knop

 Hi, my name is Daniel Knop. I am so excited to be a part of the CAMP staff team! I am a rising senior at Arlington High School in Poughkeepsie, New York. I’ve been involved with the Bard Math Circle through their AMC exams since 8th grade. Aside from math, I like to spend my free time playing soccer, playing tennis, reading, and playing trombone. I can’t wait to start my first year of CAMP!


 Daniel Rose-Levine

Hi, I’m Daniel Rose-Levine. I attended CAMP for 3 years, and this is my first year as a high school volunteer. I have been doing the AMC 8 and AMC 10 exams for a few years. This year I will be starting my sophomore year at Red Hook High School. Some things I like to do include running in cross country and track, as well as playing violin in an orchestra and fiddle group. I also enjoy speedcubing, which is solving Rubik’s Cubes as fast as you can.


Sasha Fraser
Hi, my name is Sasha Fraser. I attended C.A.M.P. for three years, and I am returning this year as a high school volunteer. I’m homeschooled, and I am going into tenth grade. Some of the other things I enjoy are: reading, photography, and dancing ballet. I loved C.A.M.P. and am so excited to be returning as a high school volunteer!




Program Director: Japheth Wood, PhD 

Japheth is a math professor at Bard College who co-directs the Bard Math Circle, which he co-founded in 2007. Japheth envisions math circles as an effective way for mathematicians around the world to make a greater impact on math education at all levels, as well as opportunity to refresh and innovate their own teaching. He teaches undergraduate math courses both in the undergraduate college at Annandale-on-Hudson, and with the Bard Prison Initiative at Eastern Correctional. During the summer, he teaches at the Hampshire College Summer Studies in Mathematics program. He has also worked extensively with pre-service math teachers through Bard’s Master of Arts in Teaching program, and was the executive director of the New York Math Circle for several years.

Volunteer Coordinator: Lauren Rose, PhD

I enjoy sharing my enthusiasm for mathematics with others and believe that mathematics can and should be made accessible to all. With this in mind, I co-founded the Bard Math Circle, an enrichment program for K-12 students, the Mid-Hudson Math Teachers Circle, an enrichment program middle school math teachers, the Mid-Hudson Mathematics Conference for Undergraduates, and the mathematics major in the Bard Prison Initiative. I particularly enjoy integrating Bard students into these programs, which expands their mathematical experience and creates a vibrant and inclusive mathematics community at Bard.




Rubik’s Cube JAM

The Bard Math Circle is hosting a Rubik’s Cube JAM this Wednesday, June 28th, 2-4pm at the new Red Hook Community Center, 59 Fisk Street, Red Hook. http://www.redhookcommunitycenter.org/ Beginners are welcome, and experienced cubers are invited to come meet other cubers. There will be 2×2 and 3×3 cubes for sale for $5 each. Kids under 10 years old must be supervised by a parent or guardian. Pass this on to you friends and neighbors!

2017 AMC 10/12B Results

We offered the AMC 10/12B Contests at Bard College on Wednesday, February 15, 2017. Nineteen students participated.

You may find the questions, answers and solutions here: AoPS AMC 10B Wiki | AoPS AMC 12B Wiki

The AMC 10/12B program featured the math contest, pizza, and a math talk by Bard math professor Lauren Rose on Weird Dice.

Bard 2017 Results on the AMC 12B:

Total number of students taking the exam: 3
School Team Score (sum of top 3 scores): 220.5 = 100.5 + 70.5 + 49.5

Average score for entire school is: 73.5
Average score for grade 12 is: 49.5 (1 Student)
Average score for grade 11 is: 85.5 (2 Students)

Bard 2017 Results on the AMC 10B:

Total number of students taking the exam: 16
School Team Score (sum of top 3 scores): 370.50 = 130.5 + 129.0 + 111.0

Average score for entire school is: 76.9
Average score for grade 10 is: 78.0 (2 Students)
Average score for grade 9 is: 78.3 (6 Students)
Average score for grade 8 is: 82.2 (5 Students)
Average score for grade 7 is: 64.5 (3 Students)

Top scores at Bard:

    Daniel Knop, 100.5 points (11th grade, age 16, Arlington High School), Certificate of Distinction
Anonymous, 70.5 points
Anonymous, 49.5 points

    Owen Dugan, 130.5 points (8th grade, age 13, Homeschool), Certificate of Distinction, Certificate of Achievement
Aryadeepta De, 129.0 points (7th grade, age 12, Acadia Middle School), Certificate of Distinction, Certificate of Achievement
Walden Yan, 111.0 points (9th grade, age 14, Avon High School)

The Certificate of Achievement is awarded to Students in grade 8 and below who scored over a 90 on the AMC 10, and students in grade 10 or below who scored over a 90 on the AMC 12.

The Certificate of Distinction is for students who qualified for the AIME. The 2017 AMC 10/12B cutoff scores for the AIME are 120 and above on the AMC 10B, and 100.5 and above on the AMC 12B.

Anonymous means that the high scoring student above prefers to remain anonymous!

Schools represented:

  1. Acadia Middle School, Clifton Park, NY 12065
  2. Arlington High School, Lagrangeville, NY 12540
  3. Avon High School, Avon, CT 06001
  4. J. Watson Bailey Middle School, Kingston, NY 12401
  5. The Harvey School, Katonah, NY 10536
  6. Homeschool
  7. Lagrange Middle School, Lagrangeville, NY 12540
  8. Linden Ave. Middle School, Red Hook, NY 12571
  9. New Paltz High School, New Paltz, NY 12561
  10. Orville A. Todd Middle School, Poughkeepsie, NY 12603
  11. Red Hook High School, Red Hook, NY 12571
  12. Rhinebeck High School, Rhinebeck, NY 12572
  13. Spackenkill High School, Poughkeepsie, NY 12603
  14. Van Wyck Junior High School, Wappingers Falls, NY 12590


Math Circle programs for March 2017

Join us this month for our March Math Circle Programs:

Tivoli Math Circle 
Location: 86 Broadway, Tivoli, NY 12583
Date: Friday, March 3rd
Time: 4:00 until 5:30 pm

Kingston Math Circle 
Location: 55 Franklin Street, Kingston, NY 12401
Date: Saturday, March 11th
Time: 1:00 until 3:00 pm

Rubik’s Cube Club 
Location: Bard College in RKC room 111
Date: Friday, March 10th
Time: 4:00 until 5:30 pm

Spring 2017 Math Circle Programs

A belated Happy New Year from the Bard Math Circle to you! We are ready to hit the ground running with several events coming up soon. See below for information on our Library ProgramsCompetitionsRubik’s Cube Club and CAMP

Library Programs

We have two library programs this month.

Tivoli Free Library

Our February Math Circle at the Tivoli Free Library will be this Friday, February 3rd. The Tivoli Free Library is located at 86 Broadway, Tivoli, NY 12583. We will play games, solve puzzles, and tackle interesting problems from 4:00 until 5:30 pm.

Do you love coming to Tivoli and want to mark your calendars ahead of time? The remaining dates for this academic year will be March 3rd, April 7th, and May 5th, same time same place!

Kingston Library

New for 2017! Our Kingston Math Circles will feature several math explorations this spring that are favorites at math circles around the country. Our January Kingston Math Circle is on Saturday,  February 11th. We welcome one and all to the Kingston Library at 55 Franklin Street, Kingston, NY 12401. Join us upstairs in the Community Room from 1:00 until 3:00 pm for some enriching problem solving and fun, math-themed crafts!

We would love to see you at all of our upcoming Kingston Math Circles! The remaining dates for this academic year are March 11th, April 15th, and May 13th.

All library programs are run on a drop-in basis, and registration is not required. We do ask students to sign in each time, and to provide their name, grade, and school. This is done electronically for Kingston, so please sign in using this link at least once this year.


AMC 10/12

The AMC 10 is a 25-question, 75-minute, multiple choice examination in secondary school mathematics containing problems which can be understood and solved with algebra and geometry concepts. The AMC 12 is a 25-question, 75-minute, multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts.

The Bard Math Circle is proud to offer the AMC 10/12 B exams on Wednesday, February 15, 2017 at Bard College. This activity is offered at no cost, but due to limited space, registration is required in advance.

There are still spots remaining, so act fast! To register please click here.

We will host two prep sessions in the weekends leading up to the exam and email registrants with details. For more information, please consult the registration page or emails us at bardmathcircle@gmail.com.

Rubik’s Cube Club

Back by popular demand! Our first Rubik’s Cube Club meeting of the semester will be on February 17th with location and time TBD. Stay tuned for more information!

Mark your calendars! The remaining dates for this academic year will be March 10thApril 14th, and May 12th.


Our Creative and Analytical Math Program for middle school students will return the week of August 28 — September 1, 2017. Please save the date! We’ll let you know more information when the application is open later this spring. (Use the  update subscription preferences link below to let us know you’re interested in CAMP.)

For a list of other summer math enrichment opportunities for middle school and high school students, please visit:

The Art of Problem Solving’s list of Mathematics summer programs (http://artofproblemsolving.com/wiki/index.php/Mathematics_summer_program)

The American Mathematical Society’s list of Summer Math Camps and Programs for Students

Start your year off right – with math, of course!

Bard Math Circle