Math

How would you do at a BEAM trivia night?

What does it look like to combine puzzles, trivia, and a bit of math? BEAM's Slightly-Mathy Trivia Nights do just that, challenging guests to work together with students on fun, weird, challenging puzzles. If you want a taste of what that means, here are four rounds from our 2018 event. Scroll carefully as we’ve included the problems and then the answers on a next page. (Warning: Round 4 is hard!)

Thanks to all the BEAM students, supporters, and staff who joined us for trivia nights in Los Angeles and New York. Please join us next year! Sign up for our mailing list to get announcements about events in 2019.

4 for 15: An hour of class at BEAM 6 Uptown

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This month, we're welcoming three new full-time staff to BEAM! One of them, Alyssa Loving Jung, is BEAM's new Development and Communications Coordinator. She spent her first week at BEAM visiting BEAM 6 and wrote this blog post about her experience. Welcome to the team, Alyssa!

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My goal is to sit in on four of BEAM 6 Uptownʻs math classes in a single hour. While I may have an advanced degree in mathematics (a Master's to be precise), it is an ambitious plan. I am eager to see what mathematics the BEAM 6 students will be tackling today. 

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To start off, I get to join the very beginning of a class that appears to be about exponents… or maybe number theory? I am not quite sure. On the board there is a question that immediately catches my eye. 

What is the ones digit of 569,423^22?

I can't help it. I immediately start scribbling work in my notebook trying to solve the question. But as discussion swirls around me, I am pulled away from my attempts to solve the problem, curious as to what the students are coming up with. Students wonder out loud how to deal with a problem like this without doing a dizzying degree of multiplication. The instructor, Juan, offers a friendly warning that such an approach would take much more time than they have in class. Returning to my page of notes, I gather from my own work that the key to the problem lies in spotting a pattern and not getting lost in the cumbersome calculations. 

Emily works during class. 

Emily works during class. 

Around me, I can hear students closing in on the pattern, and it is such fun that I must force myself to remember that I only have 15 minutes at most with them before I have to head to the next class. 

Even before my time is up, one of the students is up at the board presenting an idea.  

Collaborative mathematics, the courage to expose a budding solution, a still green idea, to an entire class of peers, is a crucial element of pursuing advanced mathematics. I am delighted that BEAM students are engaging with each other and their faculty like this. But glancing at the clock, I must tear myself away and head to the next class. 

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Here there is a very different sort of picture on the board. 

There are intersecting circles drawn and numbers scattered about. A student is at the board placing a number with care. While the numbers seem haphazardly distributed at first, the thoughtfulness of the student is the first clue that something more is going on. Then I notice the labels: factors of 6, multiples of 6, primes. 

They are exploring logic. The strange picture on the board I recognize as a Venn Diagram, a way to visualize the overlap and interplay between different sets. 

They move on from the Venn Diagram on the board to start working on a sheet of problems. A student notices ambiguity in one of the problems. The problem asks them to explore the statement "not A or B". He wonders if the instructor, Sian, means "(not A) or B" or rather "not (A or B)". 

The whole class takes time to investigate this subtlety. The process reminds me of writing math proofs during graduate school. Oftentimes the tiniest turn of phrase, the most minute missing detail, can make or break a complex mathematical argument. I am excited to see that the students are taking such care with the reading and writing of mathematics. But it is time for me to move on to my third class. 

TA Amaya works with student Karen on a problem set during Open Math Time.

TA Amaya works with student Karen on a problem set during Open Math Time.

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Yorlan works on an advanced geoemetry problem. 

Yorlan works on an advanced geoemetry problem. 

This class says Geometry and Logic in the corner of the chalkboard at the front. Apparently, it is another class on logic, but now there is geometry thrown into the mix. I am intrigued. 

The instructor, Xavier, is energetic and he calls each student by name as he peppers the room with questions. 

He wonders how we can figure out what c is when we know c^2=8. A student calls out that c is the square root of 8.

Xavier follows up, smiling, to see if Eduardo was just guessing, but no: 

"No, I didn’t guess..." Eduardo responds, "It's 'cause taking the square root is the opposite of squaring something." 

I am impressed that in one sentence Eduardo has gotten at the heart of what mathematicians mean by inverse equations. It is a concept that can confound even college students. But I can’t stay for more insights today. 

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I am off to my final class. As I slip into my seat, I am startled to see scrawled across the board: "Are there Aliens in the Milky Way?" 

A massive equation containing many letters is sprawled somewhere beneath it. The students are clearly in the process of grappling with the equation and what it means. The instructor, Susan, asks them to replace L = (1/10)^8 in their previous calculation, with L = (1/10)^2. Immediately, diligent pencil-scratching begins, heads bent, eyebrows furrowed with concentration. 

This is what I call the "dirty work" of mathematics. Complex computations don’t encompass what mathematicians do. Mathematicians are much more than mere human calculators after all. But such calculations do form an important aspect of the job of many mathematicians and scientists. BEAM students in this class are building the patience and the stamina to handle even very complex formulas, and learning some mind-boggling astronomy at the same time. 

Taro, a TA, observes Jamal as he contemplates a large numbers. 

Taro, a TA, observes Jamal as he contemplates a large numbers. 

Meanwhile, I have set a new personal record for how many classes I have attended in one hour, and better yet I have had the chance to think about some really cool math. I cannot wait for what the next hour of BEAM 6 has in store!

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Curious about the classes that Alyssa visited? BEAM 6 students all take classes in our four topic areas: Math Fundamentals, Logic, Math Team Strategies, and Applied Math. Within each topic, students get to choose from a menu of classes, so they each take a class that inspires their curiosity. In the mornings, when Alyssa was visiting classes, students were in either their Math Fundamentals class, which explores the why of elementary math, or Logic class, which focuses on how to justify your reasoning. Juan and Susan were each teaching Math Fundamentals courses, while Sian and Xavier teach courses in the Logic track. 

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Here are the full course descriptions for the four classes she visited!

Exponents: The Super-Powers of Numbers! (Juan) 

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Using the power of multiplication, we will build some really, really big numbers and compare them to see which ones will turn out to be the biggest. We'll also explore a strange planet which only has 11 numbers in it!

Cryptarithms and Other Arithmetic Puzzles (Sian)

If A + B = AC, then what is A + B + C?  Cryptarithms are math puzzles where the arithmetic is simple but the "thinking part" of the puzzle is challenging.  We will start with simple problems and build up a tool chest of logic strategies for solving these problems and all math problems.

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Geometry and Logic (Xavier)

Ever look at a problem and not know where to start? This class will develop your ability to solve complex problems. We will learn how seemingly incomplete information can be combined to form complete solutions.

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Big numbers, Small numbers, and In between (Susan)

Imagine you have a very long number line, with every number you’ve discussed this year in school on the number line. A new number is introduced. Where does it go? Are you sure? In this class, we will use a variety of tools (brain power, rulers, logic, and more) to identify the big numbers, the small numbers, and the ones in between.

Spotlight on Classes: Analytic Number Theory

Each week, the students are able to list their preferences for which classes they would like to take. They take one course for four hours a day, and another for two hours a day. Each week, new classes are offered and the students have the opportunity to immerse themselves in different advanced mathematical topics.

While each of BEAM’s classes explores incredibly interesting and advanced ideas, we’ve put together a spotlight on just one of the six courses offered this week: Analytic Number Theory with Cory. 

The class has just seven students, with a teacher and a teaching assistant—the kids get to really get to know one another and the staff members! In just three days, the class has gone from not knowing what a function is to being able to find the limit as n approaches infinity of f(n) = (-1)n/n: zero. The students are basically doing calculus without using the word “calculus” itself! 

Sitting in on the class, what is most impressive to our staff, even more than the sheer speed and intensity of the class, is how engaged each student is. Cory will give short lectures, but for a majority of the class, the students work in small groups in order to work on difficult problem sets. Mostly, they are teaching themselves the topics! Today in class, we were beyond impressed to see how each of the students was able to find patterns and draw conclusions from sequences of numbers.

When Anaís and Cynthia talked about the class, they said that they couldn’t believe how much they were learning in such a short period of time!

Jack agreed, saying: “I’ve learned more math in the past three days than I did in the last two months.” 

Cynthia, Jack, Anaís, and Alvin work together on the board

Cynthia, Jack, Anaís, and Alvin work together on the board

Week two classes are now officially over at BEAM 7 Union College. We can't wait to see how much learning takes place in week three!

Welcome to BEAM 6 2017

Week 1: Start of Something New

The summer is in full swing, but BEAM is just getting started. So far students have been assorted into one of two sets, either Calderón or Granville, and begun taking classes in Logical Reasoning, Math Fundamentals, Applied Math, and Math Team Strategies.

Faculty member David assists Justin, Jose, and Conaré during Open Math Time. 

Faculty member David assists Justin, Jose, and Conaré during Open Math Time. 

Some students are excited about taking their first class on computer programing, while others are asking hard hitting questions about force and relativity in their Space class.

"Give me more challenging problems" -Lilly ( Calderón)  proudly displaying her decorated binder

"Give me more challenging problems" -Lilly (Calderón) proudly displaying her decorated binder

Jason, Brianna, Messiah, and Mohammad are enjoying an exciting game of Kickball. 

Jason, Brianna, Messiah, and Mohammad are enjoying an exciting game of Kickball. 

Open Math Time (OMT) gave everyone a chance to work on problem sets in groups or ask for assistance from the Teaching Assistants.

Nicole, Maryam, and Aamirah working during OMT

Nicole, Maryam, and Aamirah working during OMT

Last week many students have attempted this week's challenge problem during their OMT. Ten students have already completed the Challenge Problem. Students are discovering they have a lot in common with kids from both sets during their daily and weekly activity times.

What's happened in the first week at Bard?

First things first. Where exactly is Bard? Located about about a 2 hour drive north of New York City, our site for BEAM 7 rests right along the Hudson River nestled among the trees. While at Bard, BEAM7 operates most heavily in three buildings: Keene, our home base and dormitory for students and staff; Kline, the cafeteria where we eat all three meals each day; and Hegeman, where most activities and classes take place!

 

Activities!

Pictured above: Counselor Kaylynn (middle) and instructor Javier (left of Kaylynn) play Set, a matching game which requires players to recognize patterns in a set of cards, with students Jack, Storm, and Seb. 

Pictured above: Counselor Kaylynn (middle) and instructor Javier (left of Kaylynn) play Set, a matching game which requires players to recognize patterns in a set of cards, with students Jack, Storm, and Seb. 

At BEAM, students get to choose between a variety of activities offered by counselors and faculty, ranging from high-energy sports and games to more relaxing crafts. So far this week, counselors have run:

  • Soccer, Ultimate Frisbee, Capture the Flag, Basketball
  • Mandala Coloring, Hexaflexagon Making, Paper Airplanes
  • THE Egg Drop Contest
  • Cloud Watching, Exploring Bard's Campus, Settles of Catan

And this is just throughout the first week! Over the next two weeks, the counselors and staff will have many more activities to come...


But what about the math?

A number of students work diligently on problem sets in their Math Team Strategies class, which reviews techniques for quick in easy problem solving in the face of seemingly difficult questions. Mathematicians can be a lazy bunch, so learning the techniques to making challenging problems easier is an important skill set!

A number of students work diligently on problem sets in their Math Team Strategies class, which reviews techniques for quick in easy problem solving in the face of seemingly difficult questions. Mathematicians can be a lazy bunch, so learning the techniques to making challenging problems easier is an important skill set!

So what math are the kids actually doing? This week, we have the following options:

  • Number Theory
  • Combinatorics
  • Turing Machines
  • Graph Theory
  • Math Team Strategies
  • Solving Big Problems

The best thing about our courses--besides the amazing instructors who design and teach them--students choose what interests them! Each student is in one of the first four options (called the core topics courses) and one of the last two options (called the problem solving courses). Stay tuned for more updates on what's happening at Bard for BEAM 7 2017!

"End of the Year" BEAM Spring Party 2017

Each year, BEAM invites all of their alumni to come together and celebrate the end of a successful school year. It's always great to see our alumni, play board games with them, and celebrate their accomplishments!

This year we added some cool stuff to our Spring partying! We had the return of the photo booth, some fun math puzzles (with prizes for those who completed them), a modular origami station, food including amazing Jollof rice made by Chuka's mother, and some piano playing. 

Modular Origami

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Board Games

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Photo Booth

Math puzzles

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We even had time to show off some of our talents. Pictured here is Mariam (8th grader) singing and Laura (BEAM staff member) playing the piano. Needless to say, we had an amazing time!

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Waking Up At BEAM

On Sunday, the BEAMers had woken up to the hustle and bustle of the city, but this Monday morning, they woke up to the country side’s silence.

After a pleasant walk to the dining hall through the ivy-covered and tree-filled campus, the students had breakfast, boosting their brains for the following Opening Challenge Set, a test designed to measure where the students are at in math. After completing the test, the BEAMers were taken outside, where icebreakers took place, even though the ice had broken a long time ago. Lunch followed, and then the students split up into their respective halls (Hopper, Noether, Ramanujan, and Euler) and received a step-by-step orientation on everything from their daily schedule to how to do laundry. Additionally, each student opened an Art of Problem Solving account as well. The BEAMers were then split up into the activities they had signed up for the night before, these being charades, soccer, a tour of the campus, and Fluxx (a card game). Afterwards, the BEAM instructors gave presentations on the courses they would be teaching this upcoming week, and the students filled out sheets with their preferences regarding the courses.

Later in the evening, while the instructors hid out, huddled together for hours, making sure every student was placed in the appropriate course, the BEAMers enjoyed free time back at the dorms and the basketball court. Hall meetings were held before bed, and the students would wake up tomorrow to their first day of class and to find out what course they’d been assigned to for the upcoming week. What a day for the BEAMers to look forward to.