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:

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.”

— Kaylin

“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.’”

— Ky’Yah

... And Now for Some Math

This was a Challenge Problem last summer at our Bard College site. Challenge Problems encourage students to work collaboratively; once it's solved, the whole program gets a prize. (For this one, a sleepover on the last night!) So now it's your turn... can you solve it?

Malachi takes 42 pieces of candy, each of which is either a Skittles or an M&M, and arranges them in a circle letter side down (so they look identical!). He tells Hodaya that 23 of the candies are next to at least one Skittles, and 35 are next to at least one M&M. If Hodaya can figure out how many Skittles and how many M&Ms there are, she gets all of them!

How can Hodaya figure this out? (The answer appears below the image.)

Solution:

The important thing is to go step-by-step to figure out what you can.

If there are 23 candies next to at least one Skittles, that means 42-23=19 candies are not next to any Skittles — so they must be next to two M&Ms.

If 19 candies are next to two M&Ms and 35 are next to at least one M&M, that means 35-19=16 are next to exactly one M&M.

Now here's the key insight. Suppose there are x M&M's. Each M&M has a neighbor on the left and on the right, so if you add up for all the pieces how many M&M neighbors they have, you should get 2x. Well, we know that 19 candies are next to two M&Ms, so they have a total of 38 M&M neighbors. And 16 are next to one M&M, so they have 16 M&M neighbors. That gives 54 total M&M neighbors.

Divide by two to get 54/2=27 M&Ms in total.

With 42 candies in total, subtract out the M&Ms to get 42-17=15 Skittles.

Sometimes, it's amazing how much you can figure out with what seems like too little information!