Running an enrichment mathematics program for 11 years now, and holding various Olympiads every year, has given us some insights we’d like to share with you.
We suggest to begin each problem by asking a child to explain clearly, verbally, exactly what it is he or she is being asked to find. Then encourage kids to to follow their instincts, try different approaches, and see what works or doesn’t. Kids shouldn’t feel badly if they try an approach that doesn’t work. Trying things out is the way to learn, and overcoming inhibitions is especially important for kids new to Olympiads.
The goal of this class is to help children learn to solve mathematics problems that are really ingenuous. And not only to solve them, but to become enthusiastic, excited and determined to find the answer to these clever problems. Mathematics requires precision; the answer is either right or wrong. But there are many routes to the precise mathematical answer, and many mathematical insights and strategies that can help kids exercise all their natural curiosity, intuition and knowledge to get the right solution.
During this course, we’ll introduce kids to a variety of topics that will involve using different strategies and approaches.
Let’s see the problems offered at the recent Olympiad by MOEMS.
Each of the 6 circles contains a different counting number. The sum of the 6 numbers is 21. The sum of the 3 numbers along each side of the triangle is shown in the diagram. What is the sum of the numbers in the shaded regions? 
The first step in solving a problem is to know clearly exactly what you are being asked for. Take a closer look at the problem. It asks for the sum of the 3 numbers in the corner of the triangle. It does not ask for the specific numbers themselves. Practically every kid, even those who got the right answer, tried to find the specific numbers, which makes the problem much harder than it needs to be. Realizing that the sum has to be the difference in the total of side lengths (30), and the sum of the 6 numbers (21), makes it obvious that this difference is 9.
But the other strategy may be used…
Here’s another example where understanding exactly what you’re being asked for makes all the difference in solving a problem. “If 5 pears and 3 apples cost $2.80, and 4 pears and 2 apple cost $2.20, what is the cost of 1 apple and 1 pear?” The problem doesn’t ask how much an individual apple and pear cost. It asks for the cost of the two together, something much easier to solve.
Look again at the latest MOEMS's contest, choose this time the following problem
What is the sum?
81 + 18 + 72 + 27 + 63 + 36 + 54 + 45 + 4
You can be sure that an Olympiad problem isn’t just seeing if a kid can add a column of numbers. If kids realize that the numbers can be combined into sums of 99, for example, instead of adding up the numbers one by one, the problem becomes more interesting and easier to solve. We’d ask kids to develop as many strategies as possible to solve this “simple” problem. Dear parents and students! Welcome to School Plus online Math Olympiads training course!
