With BEAM 6 Los Angeles' first two weeks in the book, we thought we'd take a minute to talk about one of the students' favorite parts of the day: Open Math Time! Every day at BEAM 6 includes four hours of academics: two hours of class and two hours of Open Math Time (OMT). During OMT, students choose from a menu of options, or propose their own work. They can do basically anything mathematical! Students can work individually or in groups; as long as the time is productive, any arrangement is fair game! OMT exists for a number of reasons:

- BEAM classes don't assign homework, because it just doesn't seem right for a summer program! But, it's important to practice new ideas to really learn them. So, students use some of their OMT for short, required Problem Sets (PSets) from each class.
- BEAM believes in flexibility and choice. We want students to build the best possible summer for themselves!
- Middle schoolers are learning a lot about themselves. Students may never have been given the flexibility to choose their groupings or tasks. This is a huge opportunity for growth.
- Strong mathematicians become stronger by spending more time on math. By sharing with students the joy of self-paced, self-directed learning, we give students the tools they need to challenge themselves to learn independently.

Ever since our first summer of BEAM 6, students have **raved **about OMT. It becomes many students' favorite part of the day. And our BEAM 6 LA 2018 students are no different! Here are some reviews from our early program survey:

As you can see from the check boxes. students have a suggested menu of options for how to spend their OMT. Most students chose the following options:

# PSets From Class

Every member of the faculty gives students about 15 minutes worth of extra work at the end of each class in the form of problem sets. Problem sets (PSets) are designed to help students practice and solidify new skills, extend understanding, and explore curiosity. For example, a student in a KenKen class might solve a more challenging puzzle, while a student learning to program in Python might add a new command to the program they're writing. Students working on PSets can head to their teacher's classroom to chat about the work and ask for support.

Want a flavor of a PSet? Here are some sample problems from two of our classes:

### Exponents: The Super-Powers of Numbers

Find a number with five or more digits, all 0s and 1s, that is 7 in Z11 (in other words, it has a remainder of 7 when divided by 11).

### Voting: How to Run a Country

A group of 4 friends want to do the same activity during activity time. Their options are to do any of the following: soccer (S), drama (D), frisbee (F), board games (B), or painting (P) and they decide to use Borda Count to decide the activity they should do. Consider the table of preferences below:

a) 5 points are assigned to a 1st place vote, 4 points to a 2nd place vote etc. What activity is the Borda count winner in this instance? (Make sure to give the Borda scores to justify your answer).

b) Is it possible for only one person to changing their ranking (in any way) so that painting is the only Borda count winner? If so, give the person and their new ranking and the new Borda counts of each alternative. If it is not possible, thoroughly explain why it is not possible.

# 100 Problem Challenge

This is exactly what it sounds like: a hundred problems selected by Dan Zaharopol (BEAM Founder and the Executive Diretor of the Art of Problem Solving Initiative, Inc.) to challenge the students mathematically and bring them just to the edge of mathematical proof. There’s a big board with 100 spaces for the 100 problems, and we write in the names of students who’ve completed problems. If all 100 are solved before the end of week 5, the entire program wins a prize!

Try out a sample problem for yourself:

### Problem 1

A friend tells me that she has three children, and that if you multiply their three ages you get 72. “I don’t have enough information to figure out how old they are!” I reply.

“All right,” she says, “if you add their ages, you get the street number from my address.”

I know where she lives, so I do some calculations. “I still don’t know how old they are!” I reply.

“Well,” she replies, “the oldest is really good at chess.”

Now I know how old they are. How old are her children, and what is her street address?

# Art of Problem Solving/Alcumus

Another major goal of BEAM is that our students (new to enrichment math) have access to the same resources and opportunities that other middle schoolers all over the country already have! So, we connect them all with accounts for the Art of Problem Solving (AoPS), and encourage students to start with Alcumus. Alcumus is a free, self-paced tool that works students through math skills, starting at pre-algebra. It's fun and it's something students can use for years to come!

Becoming familiar with AoPS and Alcumus know will have major benefits to BEAM 6 alums during 7th grade, as AoPS offers a free, online pre-algebra course to any BEAM 6 alum who completes the Alcumus pre-work to demonstrate to BEAM that they plan to take the course seriously. And as our students age, we sign individual students up for AoPS classes whenever they need an enrichment boost, and are looking to challenge themselves (the combinatorics and number theory classes are a particular hit!).

We're so glad students are enjoying OMT and the rest of BEAM 6. It's clear that BEAM 6 Los Angeles is off to an incredible start! Want to read more? Check out what our own Executive Director, Dan Zaharopol, had to say on his blog: