Friday after school is often a time to wind down from the stress of a busy week. It’s not typically the best time slot to offer an after-school club, but for Yilin G. ’21, Sophia H. ’20, Everett P. ’22, and Youyou W. ’19, it’s the perfect time to relax by working on fiendishly difficult math problems like this one:
A rectangular floor that is 10 feet wide and 17 feet long is tiled with 170 one-foot square tiles. A bug walks from one corner to the opposite corner in a straight line. Including the first and the last tile, how many tiles does the bug visit?
But, why do they do it? Is it actually fun?
“I find solving hard math problems fun and enjoy the process of digging into it. Archimedean solids, one of my favorite geometric models, have only 13 possibilities among all the various combinations of different shapes. Math is amazing!” —Yilin G. ’21
“After classes end on Friday, I find it relaxing to sit down and work on math problems with some friends. The low-stress environment allows us to engage in concepts that we can’t encounter in the standard curriculum, making us better math students and problem-solvers overall. Although we may not always reach a problem’s solution easily, we learn to persist in our efforts and learn from mistakes. Of course, the satisfaction we get from being able to figure it out on the first try makes the sometimes tedious puzzling all worth it in the end.” — Sophia H. ’20
Aside from the enjoyment, strengthening one’s problem-solving skills is beneficial in many ways. It encourages students to believe in their ability to think mathematically and to see that they can apply and extend the mathematics they’ve learned in the classroom in new and interesting ways. It puts the focus on making sense of mathematics by using a problem context rather than learning math as an abstract concept.
So far this year, our Harrisburg Academy Mathletes have participated in several events. In September, they competed in the American Math Society’s “Who Wants to be a Mathematician” contest, along with 5000 students nationwide, where students attempted to solve 10 challenging problems in 15 minutes. In October, the team attended the Capital Area Interscholastic Mathematics Competition, hosted by the Dickinson College mathematics department. Twenty-five teams from the capital area competed in this all-day event consisting of team and individual rounds. Harrisburg Academy earned 5th place team with Yilin G. ’21 placing 4th and Alex S. ’22 placing 11th in the individual round comprised of 101 students. Most recently, we had 10 Harrisburg Academy students take the Mathematical Association of America AMC contests held in February. There is one test for students in grades 9/10 and one test for students in grades 11/12. Each contest consists of 25 questions with a maximum score of 150 points. Only 2.5% of those taking the AMC 9/10 test score above 110 points and this year, Yilin G. ’21 scored 106.5. Congratulations to our students on these accomplishments!
Looking ahead, Harrisburg Academy will send a team of three students (Yilin G. ‘21, Sophia H. ‘20, and Youyou W. ‘19) to the HACC Mathematics Competition, which will be held on April 26. The contest will consist of four events. The first event will be an individual speed test. The second is a two-part individual test. The third event will be a team relay. The fourth part will require the team to work together to solve several problems. We wish our students all the best as they work hard to prepare for this competition.
So, what about that bug we met at the beginning of the blog who was trying to get from one corner of a rectangular floor to the opposite corner? How many tiles does the bug visit? In case you won’t sleep tonight until you know the solution, here’s a hint:
From one corner the bug travels 10/17 (or approximately 0.588) feet vertically for each 1 foot traveled horizontally. Note that the bug will cross either 1 or 2 tiles for each 1 foot it travels horizontally. The total number of tiles crossed is greater than 20 but less than 30.
You’ll have to stop by room 107 on a Friday afternoon at 3:10 p.m. if you want to know the solution!
Learn more about Harrisburg Academy on our school website.