Good luck to students from Albany Area Math Circle who will be joining middle school students from all over the country--indeed all over the world!--in taking the AMC8 this Tuesday. Back when I was an 8th grader, I never could have imagined that math could be this much fun!
Here's one of my favorite problems from an old AMC8 (#19 2000). (Click on the image to make it larger and clearer.)
There are some tedious and time-consuming ways to solve this problem, but if you think about it for a while, there's a very beautiful and cool "outside the box" way to solve this problem very quickly and elegantly. (Or maybe we should call it a "redefine the box" way to solve the problem!) What is great about the cool "redefine the box" solution is that once you see it, it's very easy to check your work and be sure your answer is correct. (If you do it the tedious, hard way, there are more places to make silly mistakes and go astray.)
For hints and solutions to this and other old AMC8 problems, check out this link.
No matter whether you are taking the AMC8 with Albany Area Math Circle along with students at Hebrew Academy or at your own school (shout-outs and kudos to Iroquois Middle Schools and Van Antwerp Middle Schools, who will be administering the AMC8 for the first time this year!), you will be taking part in a great event along with almost 200,000 strong and enthusiastic problem-solvers around the world!
A few things to remember:
What to bring: a couple of #2 pencils with erasers. (Good mathematicians make mistakes, so good erasers are important!)
What NOT to bring: Please do NOT bring any calculators. Their use is NOT permitted under current rules.
What to expect: Challenging outside-the-box math problems designed to encourage middle school students to stretch themselves mathematically. They are harder than regular classroom math tests because they require insight and creativity, but they are also more fun and rewarding to solve. There will be awards and recognition for high-scoring students, but the real prize is the encouragement to children to learn and grow mathematically. Especially if this is your child's first experience with contest math, it's important to encourage realistic goal-setting.
Shooting for 100% is not realistic--in some years, nobody in the whole state gets all 25 questions correct, even though the contest is taken by thousands of strong math students across the state. About 170,000 strong math students take the contest nationwide, and there are even some international contestants from places such as China, Greece, Romania, and Turkey. Getting more than 50% correct is a strong above-average performance, even for an experienced 8th grader.
My advice to pass on to your students: I'll tell you what I told my own daughters when they took such exams. My motto is "Have a good time!" "Do the best you can and enjoy the problem-solving experience. As long as you enjoy learning from working on mathematical challenges, the experience is a successful one worth celebrating. I am proud of you just for embracing this challenge and struggling with these problems."
After the contest: One of the most valuable parts of the contest is the camaraderie and fun of talking over answers afterwards. There is time specifically set aside in the schedule to do this. For some problems, there are several different creative ways to approach and solve the problem, and it's great for students to compare and discuss those approaches afterwards.
One important note: It's fine for students to talk the problems over among your local testing group after the contest BUT you must NOT discuss the contest via email, Internet, or any other method with students outside that group until after November 24. Some schools receive special permission to take the contest late for a variety of reasons, and it is important not to spoil the integrity or fun of their contest experience by disclosing anything about the problems until that date.
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