Ho Math Chess Research and Articles > How to raise math competition ability quickly


19 Mar 2013

 

How to raise math competition ability quickly

 

Frank Ho, Amanda Ho

 

Math teachers at Vancouver Ho Math Chess Learning Centre

 

www.mathandchess.com

 

If you have trouble to read some math fonts then please go to the following site to read the entire article.

http://www.scribd.com/doc/131376556/How-to-Raise-Math-Competition-Ability-Quickly

 

A student's math competition ability takes time to develop and the math competition ability is raised gradually through continually working on math problems, but is there any way that a student's ability (say the students are already at grade 6 or grade 7) could be raised more quickly than normally could have done when student had not had the time to work on some math competition problems at younger age? In other words, how do we train a late bloomer to prepare for math contests?

If students could learn the following math concepts as earlier as possible after building the 4 basic operations including whole numbers, decimals then they will possibly do much better in math contests. This idea can easily be transferred to prepare students who are interested in preparing any math entrance exams such as SSAT or any enrichment math programs.

  1. Know how to work backwards especially in fractions.
  2. know how to use the concept of 1 or 100%
  3. Can comfortably convert the three types of data among decimals, fractions, and percents without any problems.
  4. Know the concept of quantity divided by its corresponding fractional number and also the concept of fractional numbers.
  5. Learn fractions right after learning the 4 basic operations, the reason is the concept of converting improper fraction to mixed fraction involves the concepts of division, multiplication, and addition all in one operation. Also it teaches the concepts on why dividend is found by using the divisor  quotient and then adds the remainder. An equation concept is learned at this stage also.

There are a few computation techniques which can be sued to make computations much easier, they are listed as follows:


 

 

 

  1. If the answer for fraction is  then it should be written as 7. However when doing the following computation, it will be a different story.

         

          Why use "Invert and Multiply" in fraction division?

           =   

          Use Unitary method, we know there are 7 of , so when it is divided by  7 then the           result is just  From this example we know that a fraction can be a "division" such as        operation and also a "multiplication" operation such as 7  .

  1. When encountering fraction division, a multiplication is performed. When encountering a multiplication, a division is actually performed, for example the following 24 12 is performed first before multiplication.

          24 2  5 = 10

  1. A fraction involves left to right order of operation, top to down operation, and also diagonal operation. The following example demonstrates three operations.

          ?

          The reducing operation involves top/down and diagonal and the final result is obtained      by multiplying numbers across from left to right.

  1. Because the fraction operation is so powerful, often the word problems of % or ratio is transferred to fraction and the fraction operations are performed to solve the problem.

 

  1. We must learn how to translate English sentences into math sentences.

          Example 1 For every 3 girls there are 2 boys.

          It could be thought as a repeating pattern problem such as the following:

          BBBGGBBBGGBBBGG......

          It could also mean the ratio of boys to girls is 3 to 2.

          It could also mean there are 3 boys for every 5 children and there are 2 girls for every 5 children.

          Example 2 Find a number less than 100 and is divisible by 5, 6, 7, and 8.

          This problem just means to find LCM of 5, 6, 7, and 8.

6. Take one third means divide by 3.

     For example, One-third of a number adds 30 are 66. What is the number?

    

66  60 = 6

6  3 = 18

7. Often a math operation can be "seen" clearly when converting to fraction operation.

     9

=

= 9

8. Take care of negative sign and reduce as early as possible to avoid troubles.

    Example

    Compute

 

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