Welcome to the BEAM Blog!
Summer 2021 in Review
Building on what we learned last summer, we made key changes to our online tools and other program elements to build a strong community and encourage students to dive deep into problem solving this summer. After the program, Ayaan told us, “This summer made me realize that the math I enjoy is the creative, puzzling kind.” Here are some highlights…
Building on what we learned last summer, we made key changes to our online tools and other program elements to build a strong community and encourage students to dive deep into problem solving this summer. After the program, Ayaan told us, “This summer made me realize that the math I enjoy is the creative, puzzling kind.” Here are some highlights:
Challenge Accepted
Every summer, Discovery students participate in the 100 Problem Challenge, 100 fun and difficult problems that lead students towards the idea of mathematical proof. This year, students solved three times more problems than last summer, and one student solved 20 problems on his own — a new BEAM record! Another student told us he especially enjoyed these problems because they engaged his “big brain energy.”
Everybody loves pasta!
At the beginning and end of each day, students and counselors met with the same small group so they could really get to know each other (which happens naturally when we’re in person, but is harder to recreate online). While doing a morning icebreaker, one group quickly realized that everyone’s favorite food was pasta. From then on, everything they did was pasta themed!
Can we chat?
BEAM students couldn’t get enough of Zulip, our online chat platform, which served as a sort of virtual lunch table, with lots of students sharing inside jokes and memes. Counselors posted daily polls that pulled even shy kids out of their shells. Students could also earn “badges,” in the form of emojis that appeared next to their names on Zulip. Some got a 👻 for solving the Problem of the Week, 🏆 for working on a team, and special emojis for counselor challenges, like ✊ for telling Ngoc your favorite joke! Badges were so popular, we're planning to use them at our in-person programs.
Persevering through tough problems
At OMT, students work on math of their choosing on their own or with others. This year, we expanded OMT to give students more time to work independently on the math they love. Mia chose to work on the Problem of the Week during her first session. After the session was over, she said, “My goal was to give it my all. I didn’t give up and I kept strategizing how to solve it.”
BEAM Students Think Big
A couple of our favorite comments from the summer:
“BEAM has changed my perspective of learning forever. This program has helped boost my confidence, makes me love math and learning, and shows me skills that will help me in the future. I am excited about my classes showing things like new math vocabulary, patterns, and skills that make my brain feel satisfied, and how to prove my theory/conjecture is correct.”
“I like that there are a lot of ways to solve a problem and I like that there’s math in anything and everything. It’s like a universal language that not a lot of people can speak but when you finally get it, it’s just such an incredible feeling of ‘I did that.’”
BEAM's Winter Newsletter is here!
Read about BEAM weekend classes, early decision college acceptances, and more in our winter newsletter, and if you aren’t already a subscriber, you can sign up here:
Last Friday, BEAM's quarterly newsletter arrived in the inboxes of all our subscribers. The newsletter features:
An inside look at one of BEAM’s Saturday classes from BEAM instructor, Ken Baron.
Catching up with some of the awesome things our students are doing.
Staff Picks: recommendations from staff members about what to read, watch, listen to, and more
Announcement that we are running our summer programs online again.
A reminder: we’re hiring!
Missed it? You can read the newsletter now
Make sure you don’t miss the next one! Sign up to receive BEAM’s quarterly updates.
BEAM's Winter Newsletter has arrived!
Last Friday, BEAM's quarterly newsletter arrived in the inboxes of all our subscribers. The newsletter features:
An update on BEAM’s Multiply Your Impact Matching campaign
An overview of BEAM’s busy fall
Staff Picks: recommendations from staff members about what to read, watch, listen to, and more
Recent accomplishments of BEAM students
A reminder: we’re hiring!
Missed it? You can read the newsletter now
Make sure you don’t miss the next one! Sign up to receive BEAM’s quarterly updates.
BEAM's Fall Newsletter has arrived!
Today, BEAM's quarterly newsletter arrived in the inboxes of all our subscribers. The newsletter features:
An introduction to BEAM Summer Away at Harvey Mudd College, our sixth summer site
An invitation to BEAM’s Puzzles and Trivia Night
A recap of College Prep Week
Staff Picks: recommendations from staff members about what to read, watch, listen to, and more
Recent accomplishments of BEAM students
Slightly mathy trivia from last year’s Puzzles and Trivia Night for you to try out!
Missed it? You can read the newsletter now.
Make sure you don’t miss the next one! Sign up for our quarterly newsletter.
BEAM's Pre-Summer Newsletter has arrived!
Today, BEAM's quarterly newsletter arrived in the inboxes of all our subscribers. The newsletter featured:
Information on our largest summer of operations yet
A recap of College Decision Day
Highlights from BEAM’s recent Career Day
“What We’re Reading”: a look at the College Board’s new “adversity score”
Recent accomplishments from BEAM students
A math puzzle for you to try out!
Missed it? You can read the newsletter now.
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… And now for some math
At BEAM, we love sharing math! So, as a new feature of our quarterly newsletter, we’re introducing a math problem.
At BEAM, we love sharing math! So, as a new feature of our quarterly newsletter, we’re introducing a math problem.
Our first problem comes from one of BEAM’s Saturdays classes for 8th graders and high school students this past semester. In this class, on combinatorial game theory, students learned about different kinds of games, that it is possible to add games together and treat them (sort of) like numbers, and how all of a certain kind of games are equivalent to one particular game called Nim. If you want a taste of this, here’s a classic problem students considered at the beginning of class.
Suppose there are 25 tokens in a pile. On each turn, players alternate removing either 1 or 2 tokens, and they keep going until the pile runs out. The last person who takes a token wins. (It doesn't matter how many they took, just who gets to take the last one.) Which player has a strategy to guarantee that they win, and how do they do it?
The solution is below, so scroll down when you’re ready.
The solution …
The first player can win by moving to 24 tokens. Once they’re at a multiple of three tokens, they can always make sure that their next turn ends on the next lowest multiple of three. Here’s how: if their opponent takes 1 token, they take 2; if their opponent takes 2, they take 1. Then together, they take three tokens, so their next turn ends with 21 tokens.
They do this over and over to go down multiples of 3: 24, 21, 18, 15, 12, 9, 6, 3, and 0, and they win because they took the last token!
If you’re wondering how to figure this out, the trick is to think from the end. What happens with one token? Easy, the first player takes it and wins. Two tokens? The first player takes both and wins. Three tokens? Now the second player wins: the first player is forced to leave their opponent with 1 or 2 tokens, which their opponent can take and win.
That lets you build up. If you’re the first player with four tokens, take one piece and now it’s like you’re going second but with only three tokens. If you’re the first player with five tokens, take two, doing the same thing. But from six tokens, you’re stuck: you have to leave your opponent with four or five, which is a winning position for the next player to go.
If you want a challenge, try figuring out the same game, but instead of being able to take 1 or 2 tokens, you can take 1 or 4 tokens. Now what pattern emerges?
Want more math? If you are not yet receiving our quarterly newsletter, subscribe here.
BEAM's Spring Newsletter has arrived!
On Friday, BEAM's quarterly newsletter arrived in the inboxes of all our subscribers. The newsletter featured:
High school admissions results
A look at our new empowerment groups
Information on our job openings for summer staff
"What We're Reading"
Missed it? You can read the newsletter now.
Make sure you don’t miss the next one! Sign up for our quarterly newsletter.
BEAM's End-of-Year Newsletter is Here!
Yesterday, BEAM's quarterly newsletter arrived in the inboxes of all our subscribers! The newsletter featured:
A look at the very first semester of BEAM College Support.
The announcement of our Year End π Matching Campaign
A recap of recent events at BEAM, including our annual Yale Splash field trip and Trivia Events in NYC and LA
"What We're Reading (and Watching)"
Information on our job openings for summer staff
Missed it? You can read the newsletter now.
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BEAM's Post-Summer Newsletter is Here!
Today, BEAM's quarterly newsletter arrived in the inboxes of all our subscribers! The newsletter featured:
Information about the first summer of BEAM Los Angeles
An invite to join BEAM for an upcoming fast-paced night of slightly-mathy trivia, 10/29 in NYC and 11/13 in LA!
What our alumni did this summer
"What We're Reading"
Missed it? You can read the newsletter now.
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BEAM's Pre-Summer Newsletter is Here!
Last Friday, BEAM's quarterly newsletter arrived in the inboxes of all our subscribers! The newsletter featured:
- An update on BEAM's growth (380 students at BEAM programs this summer!)
- Congratulations to our 12th graders on their college plans
- "What We're Reading"
- Updates on BEAM Los Angeles
Missed the newsletter? You can always read it online. And make sure you don't miss the next one! Sign up for our mailing list.
