Zigzagging from hastily drawn dots, the colorful lines jutted up, down and everywhere across the wrap-around white boards in Room 302. With Nicole Westbrook’s catchy song streaming in the background, pairs of Upper School students took turns making as many lines as they could without overlapping. Then they erased their work, found new partners and started all over again.
Sophisticated skill-building was occurring during this fast-moving warm-up game*, setting the stage for another upbeat session of “Problem-Solving for Competitive Math,” a new FOCUS course for Classes 10-12, led by Upper School Math Teacher Patrick Aquino.
Encompassing disciplines like algebra, geometry, number theory, counting and probability, the elective has been designed to further challenge dedicated mathematicians by exposing them to material not typically found in their regular classes. What’s more, students are further supported as they extend their interest in and aptitude for a subject they already know and love.
The overarching goal of “Competitive Math” is to build and strengthen the skills and tactics needed to successfully compete in team and individual student math competitions. These contests include the American Mathematical Contest 12, known as AMC 12, a 25-question, 75- minute multiple-choice examination, and the American Invitational Mathematics Examination, or AIME, a 15-question, three-hour exam. All students who take the AMC 12 and achieve a score of 100 or more (out of a possible 150) or are in the top 5% are invited to take the AIME.
“Let’s roll our desks together and sit in circles,” said Mr. Aquino, helping his students rearrange the furniture. “Pick team leaders. We’re going to work on this together.”
Moments later, three small groups began to tackle a set of questions. With pencils and erasers at in hand, they read the problems out loud and shared their ideas for solving each tricky challenge. Although the leaders helped focus their thinking, everyone contributed to the discussion.
As they worked their way through the problems, Mr. Aquino checked in with each group. “I want you to think about your strategy,” he reminded one. “How can you account for that?” he asked the second team. “What did you come up with?” he inquired of the third. When this team leader exclaimed, “Oh!” after she solved a challenge, Mr. Aquino exclaimed, “Wow, nice work!”
When the first page was done, the class had the chance to demonstrate their knowledge. “Let’s present now!” announced Mr. Aquino. He chose the order of the teams but allowed each to pick which question they wanted to unpack. The teams took turns coming up to the white board at the front, where their problems were illuminated, to diagram their work.
For example, one team shared their strategies behind unraveling question #6: After Sally takes 20 shots, she has made 55% of her shots. After she takes five more shots, she raises her percentage to 56%. How many of the last five shots did she make?
Another team talked about their plan for problem #8: Find the number of two-digit positive integers whose digits total 7.
These presentations soon became full-class conversations with Mr. Aquino and the rest of the students deepening the inquiry with their insightful comments. Although the atmosphere was light and fun, a serious appreciation for math’s beautiful complexities and the students’ impressive problem-solving skills were on vivid display.
After a quick break, more problems awaited. “We’re going to start on #11 when we get back. The questions get even harder,” said Mr. Aquino, eliciting smiles of anticipation. Without a doubt, these Upper School students will continue to excel as this industrious class continues.
*From the book “Math Games with Bad Drawings: 75 ¼ Simple, Challenging, Go-Anywhere Games – and Why They Matter” by Ben Orlin