In Summer 2022, the Greater Princeton Branch of AYLUS (GPA) continued a training program for students who are interested in the American Mathematics Competitions (AMC). GPA members (5/29, 6/5, 6/12, 6/19, 6/26, 7/10, 7/17, 7/24, 1 hr for all on each day) including Development Minister Ryan Tian, members Kevin Zhao and David Ji, are organizing this training program.
The AMC program leads the nation in strengthening the mathematical capabilities of the next generation of problem-solvers. Through classroom resources and friendly competition, the AMC program helps America’s educators identify talent and foster a love of mathematics. The AMC program positively impacts the analytical skills needed for future careers in an innovative society.
The American Mathematics Competitions are a series of examinations and curriculum materials that build problem-solving skills and mathematical knowledge in middle and high school students. In 1950, the first Mathematical Contest, sponsored by the New York Metropolitan Section of the Mathematics Association of America, took place. It was given in approximately 200 schools to around 6,000 students in the New York area only. Today, the competition has grown to over 300,000 students participating annually, in over 4,000 schools.
American Mathematics Competition 8 (AMC 8): AMC’s middle school level competition.
American Mathematics Competition 10/12 (AMC 10/12): AMC’s high school level competition.
American Invitational Mathematics Examination (AIME): AMC’s invitational competition for high scoring AMC 10/12 participants.
United States of America Mathematical Olympiad (USAMO) and United States of America Junior Mathematical Olympiad (USAJMO): AMC’s top invitational competition for high scoring AIME participants.
The Putnam Competition: An annual mathematics competition for undergraduate college students in the United States and Canada.
Ryan Tian, David Ji, and Kevin Zhao collaborated to host the first AYLUS Math Competition Class on 5/29 from 8:00 to 9:00 pm. To begin the meeting, Ryan, David, and Kevin welcomed all the students and gave a brief introduction regarding how the class will function. Four students, Elin Su, Kathy Zhao, Katie Zhao, and Tiffany Tian, attended the Zoom meeting. After ensuring all students were in the Google Classroom, they discussed where everything can be found within the Google Classroom, the class syllabus(accessible at
https://docs.google.com/document/d/1DC8eixwl6M4Hw-9sZAkG0LOXlEDJm8KmCmW33Yhe
YYg/edit?usp=sharing), and how time will be split up for each meeting. They discussed how the
class will focus on four main categories of mathematical problems, namely Algebra, Counting
and Probability, Number Theory, and Geometry. Each topic will then be split into subtopics for
each week. Additionally, they informed the students that classes are generally going to have 10
minutes of homework review, followed by 25-35 minutes of topic introduction and examples,
and 15-25 minutes of exercises. Next, they introduced the main objective of the class, which was a pre-assessment designed to gauge the skill level of the students(accessible at
https://drive.google.com/file/d/1V9o0wiej7yYgrnxlRisDON5RK1UFj-JH/view?usp=sharing).
The problems were compiled before class by the instructors and cover a variety of skills often
tested in MathCounts and American Mathematics Contest 8. The number of problems and
problem difficulty were also comparable to that of MathCounts and AMC 8 with a few challenge
questions. Through these problems, the instructors could know which skills they needed to spend a little more time on and which skills the students were already comfortable with. The
pre-assessment was to be completed by students within an hour and started at around 8:10pm.
During this time, Ryan, David, and Kevin stayed in the Zoom meeting to answer any questions
from the students. They also discussed what each person will be doing before and during the next meeting, and they started working on preparations for the next class. The pre-assessment
concluded at 9:10pm with everyone having submitted their pre-assessments by 9:20pm.
After pre-assessment submissions, students were given the chance in the Zoom call if
they had any questions and were encouraged to keep working on any problems they didn’t finish.
Furthermore, Ryan, David, and Kevin scored the pre-assessments and returned students’
submissions on Google Classroom. The instructors noted that most students had a pretty good
foundation of skills as a majority of students were able to answer many of the easier questions.
They also noted that most students understood basic geometry, algebra, and arithmetics, but a
the majority of students struggled on one of the easier counting problems. Following these results, Ryan, David, and Kevin concluded that they should spend more time on Counting and
Probability, replacing a Number Theory meeting with one for Counting and Probability.
Ryan Tian, David Ji, and Kevin Zhao hosted the second AYLUS Math Competition Class on 6/5 from 8:00 to 9:00 pm. For this meeting’s preparation, David was in charge of making the homework while Ryan and Kevin worked on the in-class presentation which included examples and exercises. To begin the meeting, Ryan, David, and Kevin asked the students for any questions regarding last weeks’ pre-assessment. Six students, Elin Su, Grant Li, Harri Lu, Kathy Zhao, Katie Zhao, and Tiffany Tian, attended the Zoom meeting. For the meeting, David was in charge of explaining any questions regarding problems on the pre-assessment. Subsequently, Ryan, David, and Kevin moved onto the main subject of the meeting, Arithmetic and Linear Equations. They discussed some strategies to simplify arithmetic problems as well as some tricks to watch out for. Next, they explained how to solve problems related to speeds and rates and tips on assigning variables in algebraic equations. Finally, they explained the basics of linear equations in the 2-D plane.
Ryan Tian, David Ji, and Kevin Zhao hosted the third AYLUS Math Competition Class on 6/12 from 8:00 to 9:00 pm. For this meeting’s preparation, David was in charge of making the homework while Ryan and Kevin worked on the in-class presentation which included examples and exercises. To begin the meeting, David asked the students for any questions regarding last weeks’ homework and answered those questions. Four students, Harri Lu, Kathy Zhao, Katie Zhao, and Tiffany Tian, attended the meeting. After homework questions, Ryan, and Kevin moved onto the main subject of the meeting, More Linear Equations and Quadratic Equations. For linear equations, they discussed more complicated problems than those in the previous week, such as problems using a system of equations. Additionally, they discussed quadratic equations, including special products and the quadratic formula.
Ryan Tian, David Ji, and Kevin Zhao hosted the fourth AYLUS Math Competition Class
on 6/19 from 8:00 to 9:00 pm. For this meeting’s preparation, David was in charge of making the homework while Ryan and Kevin worked on the in-class presentation which included examples and exercises. To begin the meeting, David asked the students for any questions regarding last weeks’ homework and answered those questions. Six students, Elin Su, Harri Lu, Kathy Zhao, Katie Zhao, Leo Fan, and Tiffany Tian, attended the meeting. After homework questions, Ryan, and Kevin moved onto explaining the main subject of the meeting, More Linear Equations and Quadratic Equations. For linear equations, they discussed more complicated problems than those in the previous week, such as problems using a system of equations. Additionally, they discussed quadratic equations, including special products and the quadratic formula.
Ryan Tian, David Ji, and Kevin Zhao hosted the fifth AYLUS Math Competition Class on
6/26 from 8:00 to 9:00 pm. For this meeting’s preparation, David was in charge of making the homework while Ryan and Kevin worked on the in-class presentation which included examples and exercises. Six students, Grant Li, Harri Lu, Kathy Zhao, Katie Zhao, Leo Fan, and Tiffany Tian, attended the meeting. To begin the meeting, David asked the students for any questions regarding last weeks’ homework and answered those questions. After homework questions, Ryan, and Kevin moved onto explaining the main subject of the meeting, Basic Counting Techniques and utilizing Venn Diagrams. They gave students advice on how to avoid overcounting and using venn diagrams with two or three sections.
Ryan Tian, David Ji, and Kevin Zhao hosted the sixth AYLUS Math Competition Class
on 7/10 from 8:00 to 9:00 pm. For this meeting’s preparation, David was in charge of making the homework while Ryan and Kevin worked on the in-class presentation which included examples and exercises. Five students, Elin Su, Harri Lu, Kathy Zhao, Katie Zhao, and Tiffany Tian, attended the meeting. To begin the meeting, Ryan and Kevin asked the students for any questions regarding last weeks’ homework and answered those questions. After homework questions, they moved onto explaining the main subject of the meeting, Casework, Constructive Counting, and Complementary Counting. They gave students advice on how to break down a complicated counting problem into smaller, simpler cases that were easier to solve. Furthermore, they explained constructive and complementary counting, a problem solving strategy of counting what is not wanted and subtracting that from the total possible outcomes.
Ryan Tian, David Ji, and Kevin Zhao hosted the seventh AYLUS Math Competition
Class on 7/17 from 8:00 to 9:00 pm. For this meeting’s preparation, David was in charge of making the homework while Ryan and Kevin worked on the in-class presentation which included examples and exercises. Five students, Elin Su, Harri Lu, Kathy Zhao, Katie Zhao, and Tiffany Tian, attended the meeting. To begin the meeting, David asked the students for any questions regarding last weeks’ homework and answered those questions. After homework questions, Ryan and Kevin moved onto explaining the main subject of the meeting, Factorials, Permutations, & Combinations. They defined what were factorials and how to calculate them, and explained the difference between permutations and combinations as well as their respective formulas. They gave students advice on how to easily tell which problems required the use of permutations and which required the use of combinations. Furthermore, they exemplified how many counting problems, such as pathing problems, can be solved easily through permutations or combinations.
Ryan Tian, David Ji, and Kevin Zhao hosted the eighth AYLUS Math Competition
Class on 7/24 from 8:00 to 9:00 pm. For this meeting’s preparation, David was in charge of making the homework while Ryan and Kevin worked on the in-class presentation which included examples and exercises. Five students, Grant Li, Harri Lu, Kathy Zhao, and Katie Zhao, attended the meeting. To begin the meeting, David asked the students for any questions regarding last weeks’ homework and answered those questions. After homework questions, Ryan, David, and Kevin moved onto explaining the main subject of the meeting, Probability. They explained how to solve probability questions using counting techniques introduced in previous weeks such as constructive counting, casework, and complementary counting.
