Friday, December 16, 2016

2016 AMC 8 Results are in!

We offered the AMC 8 Exam at Bard College on November 15, 2016, followed by an engaging math talk on Topology and the Euler Characteristic, presented by Bard math professor Steven Simon.

(For detailed solutions to the contest problems, click HERE.)

Our next contest event is the AMC 10/12B on February 15, 2017. 

Visit our Contest Page for more information.

2016 AMC 8 Summary

Total number of students who took the exam at Bard: 35
School Team Score (sum of top 3 scores): 66.0
Average score for entire school is: 12.6
Average score for grade 8 is: 14.8
Average score for grade 7 is: 12.3
Average score for grade 6 is: 12.4
Average score for grade 5 is: 12.5
Average score for grade 4 is: 7.0

Top scores at Bard:

Please visit
our Contest Page for this information.
Schools represented:

Acadia Middle School, Clifton Park (2)
The Albany Academy, Albany (1)
J Watson Bailey Middle School, Kingston (6)
Brinkerhoff Elementary School, Wappingers (2)
Buckley Middle School, Rhinebeck (1)
Great Barrington Steiner School, Great Barrington (1)
Haldane Middle School, Cold Spring (1)
High Meadow School, Stone Ridge (1)
Highland Middle School, Highland (2)
Home School (4)
Lagrange Middle School, Lagrange (1)
Lenape Elementary, New Paltz (1)
Linden Avenue Middle School, Red Hook (2)
Loudonville School, Albany (1)
Meadow Hill School, Newburgh (1)
Mill Road Middle School, Red Hook (1)
Miller Middle School, Kingston (2)
Monroe Woodbury Middle School, Woodbury (1)
St. Martin de Porres School, Poughkeepsie (3)
Van Antwerp Middle School, Niskayuna (1)

Sunday, December 11, 2016

2017 AMC 10/12 B at Bard

Registration is now open for the 2017 AMC 10/12 B contests at Bard College.


The event is for high school students with a passion for problem-solving. Advanced middle school students are also welcome. There is no charge, but registration is required in advance to reserve your seat at Bard.

After the exam, students will be treated to a snack, followed by an engaging math talk by a Bard College mathematician.

Bard undergraduate math majors are offering preparation sessions during the weekends leading up to the contest.

Date: Wednesday, February 15, 2017
Time: 4:00pm - 7:00pm
Location: Bard College Reem-Kayden Center for Science and Computation (RKC)
Address: 31 Campus Road, Annandale-on-Hudson, NY 12504

Saturday, October 1, 2016

2016 AMC 8 Registration is open!

The Bard Math Circle is hosting the national AMC 8 contest on Tuesday, November 15, 2016 from 4:30 - 6:30 pm.


The event is for students with a passion for problem-solving who are in grade 8 or below and under 14.5 years of age on the day of the contest. There is no charge, but registration is required in advance to reserve your seat at Bard.

After the 25-question, 40-minute, multiple choice exam, students will be treated to a snack, followed by an engaging math talk by a Bard College mathematician.

Bard undergraduate math majors are offering preparation sessions during the weekends leading up to the contest, starting on October 1, 2016.

Date: Tuesday, November 15, 2016
Time: 4:30 PM to 6:30 PM
Location: Bard College Reem-Kayden Center for Science and Computation (RKC)
Address: 31 Campus Road, Annandale-on-Hudson, NY 12504

Register on Eventbrite.

Friday, September 9, 2016

Join our new Rubik's Cube Club!

Curious about Cubing? Interesting in Solving?

Join our new Rubik's Cube Club!

There will be instruction for beginners, and advanced cubers can hone their technique. 

Bring a cube if you have one, but not required. 

Location: RKC at Bard College
Time: 4:30-6:30 pm
Dates: 9/16, 10/14, 11/18

Sunday, August 28, 2016

CAMP Day 5

Friday marked our final day of CAMP. Despite the sadness of the end of the Bard Math Circle CAMP quickly approaching, we were able to have an awesome and fun last day that began with our mathematicians working to solve a number of math problems and puzzles. Some of the problems were taken from the AMC, a competition that Bard Math Circle hosts at Bard every year, while others were found by our high school volunteers to let our mathematicians warm up their brains! These bright young students were able to whiz through many of these problems on their own and the more difficult ones they discussed with their peers to try to find a solution.

Our schedule was a little different for our last day. We had gotten far enough in our math class to combine the class with computer science! Side by side, we compared a list of how to create fractals geometrically, mirrored by the code that would be entered into the program in NetLogo to achieve the same transformation of a figure. Together, we learned the specific code that creates a scaling transformation and the code that translates our x-coordinates. Then, we split up in pairs to input this code and try to discover the specific commands that would program the proper translation of the y-coordinates. We all came up with the code that will generate the Sierpinski triangle in NetLogo and then some of us even went on to develop the code that would create other fractals from the Yale Fractal Lab worksheet that we had received in math class the day before. We were able to learn how to turn the rules we discovered the day before into code that would create these fractals!

After lunch we returned to the RKC to finish up what we needed to in art and to take a short break before returning to class. Some students who had been learning the algorithms of the Rubik's cubes over the last few days, picked up a few of the cubes to practice and show their new skills to their friends. Some students even helped others who had not been to any of the Rubik's cube activities to see how to start solving the Rubik's cube.

In art class we finished designing and altering our fractal lamps in order to have them ready to present to our parents and friends at the open house that was happening at the end of the day. After finishing the creation of the lamps we discussed the installation of our art pieces and ventured out into the lobby of the RKC building (as well as some other rooms in the building) to install our art in beautiful and interesting ways. Some of the lamps were placed in a dark room with lights strategically placed within them. While others were attached to strings and then hung over the railings above the lobby. The lamps hung perfectly in front of the windows letting the light shine through them in just the right way to display the beautiful ways in which we had cut and sculpted the paper to make the lamps: finally now illuminated in the way they were meant to be.

After some final preparations of our computer programs and art pieces we were ready for our open house! Parents began to arrive and the students were able to showcase their accomplishments of the week. In one room the computer screens were filled with the wonderful and fascinating results of the code that the students had been writing to create fractals that we had learned about in math class. In the lobby one could see marbled paper and fractal lamps hanging from the second floor in front of the big windows and installed in tactical places to highlight the beauty and individuality of each piece of art. And in one room the lights were turned off to let the lamps really shine! The dark room showcased the amazing shadows that could be created by a light shining through the intricate lamps. After sharing with the parents, the staff was introduced and brief announcements were made before the Bard Math Circle CAMP of 2016 came to a close. Every student in the program this summer was absolutely brilliant and a joy to work with. Thank you to every student mathematician and staff member that made this amazing week the success that it was!


-Meagan (with the help of some amazing math CAMP friends!)

Friday, August 26, 2016

CAMP Day 4

Thursday was our fourth day of CAMP and for our morning activity we played an observational game entitled "Find the Chief." We sat in the auditorium in an ellipse, per the students’ request, and learned how to play this exciting game! A detective was picked and then asked to leave the room. While the detective was away we picked a chief who would serve as our leader. When the detective returned, the chief would begin performing a motion of their choice (a common favorite is to clap) and then the rest of the group would follow the chief. The chief’s job is to repeatedly change their motions while trying to make sure the whole group can follow them; the detective’s, to pick out the chief from the rest of the group. One of our student’s observantly pointed out that a great strategy would be to pick fake chiefs, who could watch the real chief, while the rest of the group could watch the fake chiefs to throw the detective off! After this fun game we started our classes of the day.

Our fractal lamp shades continued to be individualized as we accumulated our art projects from the week into our final art piece as we pleased. Alexis (one of our superb TAs) even taught us how to cut paper in simple ways resulting in intricate and gorgeous radial fractals! Some of us even added these radial fractals to our lamps!! Other students found more ways to incorporate the marbled paper they had created in the beginning of the week. In addition to working on our lamps we watched a video of a dancer who choreographed dances on sand that would result in geometric patterns drawn in the sand!

In math class we were able to apply our recently obtained knowledge of how we can use geometry to create and draw fractals! We experimented with applying planar transformations—specifically scaling and translating—onto the unit square to begin to make the Sierpinski triangle. We developed a set of rules that would transform the figure between stage 0 and stage 1, and then observed how the figure would change after multiple iterations of the rules we found together. Through this exercise, we were able to better understand how fractals are created using planar transformations. Frances, our lovely math instructor, then gave us a worksheet from the Yale Fractal Lab to work through in order to attempt to look at fractals, that had already gone through multiple iterations of a set of rules, and be able to discover these sets of rules on our own.

Our math class showed us the geometry behind making fractals, which connected fluidly to our computer science class where these brilliant mathematicians learned how to program our computers to make the fractals for us. We programmed commands that essentially perform the equivalent of scaling and translating, but instead of performing these planar transformations on points on a graph written on paper, the transformations were applied to our turtles in the world that we created in NetLogo. The students were able to see the program they created forming these fractals, and be grateful for the computers because they had personal experience with how complex and difficult it can become to compute and create fractals by hand!

Following lunch we held the much anticipated game of capture the flag: Team Team versus Team Mystic!!  Both teams defended their flags admirably, but Team Team was able to capture Team Mystic's flag and return safely to their side without being caught!  The teams then united again to hear about options for their afternoon activities: finishing tessellation art, continuing work on their stunning lamp shades, or learning about the Physics of Chaos Theory from one of our excellent TAs Victoria!

And to end the day we hosted another game of Bard Math Circle CAMP Jeopardy! Today we achieved a new wonderful accomplishment: we were able to have a Jeopardy game that was not only filled with excitement, but also was filled with listening to other teams answer each question. We learned that, instead of planning an answer in case another group misses the questions, it actually is beneficial to listen as other teams guess because then it helps us understand the questions better and also makes it less likely to restate a wrong answer if the questions gets to your team! Another exciting part of this day's Jeopardy was that during the game we all got our CAMP shirts to wear on the last day! So at the end of the fourth day of camp everyone left with more than they had when they came in that morning: a little extra knowledge and a fun shirt!

Thursday, August 25, 2016

CAMP Day 3

On Wednesday we began the journey of our third day of the Bard Math Circle CAMP of 2016 by experimenting with tooth picks to try to solve the many matchstick puzzles that one of our fantastic TA's, Alexis, brought in for us to think over.  Some of us in pairs, and some individually, impressively worked through the sheet of puzzles solving many if not all of the matchstick problems!

We started our math class by learning more about planar transformations! We split up into groups of two or three to experiment and see if any pairs of planar transformations are commutative (meaning the resulting figure after both planar transformations were applied was not affected by the order in which the transformations occurred). Each group drew their findings on the board and presented their conclusions. After that, some students started drawing the Sierpinski triangle by beginning with an equilateral triangle as Stage 0, and then repeatedly "cutting" out a fourth of the previous stage’s triangles after each iteration. We then recorded the area and perimeter of our shape at each stage to observe what was happening to the triangle!

In art class our Sierpinski triangles, that we had made the day before, became three dimensional one of a kind sculptures! We noticed that the paper caught the light in really beautiful ways and so we began to design unique lamp shades using our marbled paper and the texture of the Sierpinski triangle.  So in order to add our own individual personalities to these fractal lamp shades everyone took their own steps to alter their designs: making constellational cut outs, layering, cutting out more shapes, attaching geometric solids, and more. And some of us simply spent time as designers, imagining and working through different ideas on our own as well as with our classmates.  

We learned about and started practicing our pair-programming techniques in computer science, where one of the students served as the driver and the other a navigator. This way we get to share ideas and come up with creative solutions together; when more of these brilliant computer scientist/artist/mathematicians are working together, the more amazing the solutions can become. Then we did a fun exercise where each person in the class said a line of code as we tried to write a program together. Additionally, we learned about creating functions in the code tab to make each button have only one function controlling it. This makes it easier to edit our program!

After a rousing game of blob tag, following lunch, these mathematicians split into three groups: some of us went to play a game entitled Staying Rational in the Infinite Hotel, some went to continue to explore the mysteries of the Rubik’s cube, and others went to learn about tessellations and create some beautiful and fascinating tessellation artwork.

We finished our day as we normally do with a rousing game of Bard Math Circle CAMP Jeopardy. Today the game was very similar to the day before, but we added the excitement of prizes! Origami paper was handed out as a prize that the students could use to create the intricate origami designs that we have learned during camp. Everyone went home happy: with a smile, some origami paper, and some new knowledge about math!

-Meagan (as normal with help from other lovely Math CAMP friends)

(Photo of Sierpinski's triangle courtesy of