Sunday, March 6, 2016

2016 Mathcounts State Prep : How to Avoid Making Careless Mistakes

Why Can Some Kids Handle Pressure While Others Fall Apart? from the New York Times

Relax! You'll Be More Productive from the New York Times

First, please read Mathcounts "Forms of Answers" carefully for a few times and remind yourself not to write down the unallowable answers.

Stop Making Stupid Mistakes by Richard Rusczyk from Art of Problem Solving

How to Avoid Careless Mathematical Errors from Reddit

Common errors from all my students: 

Number 1 issue with most of the boys/and a few girls who have strong intuition in math is their horrible handwriting since their minds work much faster than their hands can handle. (See!! I'm making excuses for them.)

I call some of my students "second try ___ [Put your name here.] or third try ____ because I don't need to teach them how to solve a problem but the normal pattern is that it has to take them twice or three times to get it finally right. Thus, they need to slow down and organize their thoughts.

Practice your numbers:  4 (it's not 21), 7, 9 (don't dislocate the circle on top), 2 (don't make it looks like a 7), etc...  

35 cents is very different from 0.35 cents.

Unless stated, you write improper fraction as your answer. Make sure to simplify the answer.

Many mistakes happen when it involves fractions, negative numbers, parenthesis, and questions that
have radicals on the denominator and you need to simplify it, so make sure to double check your math.

Some problems takes many steps to reach the final solutions. Some involve lots of data, extreme long strings of information so if those are your weakness, skip them first and go back to them later.

Every point is the same so don't stay with a tedious question too long and panic later not able to finish the last few harder questions which might be much easier to solve arithmetic wise if you know how.

Circle questions trouble many students. Make sure you are aware of what's being tested.
Is it circumference or area, is it diameter or radius, is it linear to area (squared) or vice versa ?
Are the units the same (most frequently appeared errors)?

Don't forget to divide by 2 for the triangle, times 6 if you use area of an equilateral triangle to get the hexagon. For geometry questions or unit conversions, don't do busy work, write down the equivalent equations and cancel like crazy.

Same goes to probability questions, cancel, cancel and cancel those numbers. You don't need to practice mental math multiplication for most of the Mathcounts problems. Think Smart!!

The answer for probability questions can only be 0 to 1, inclusive.

For lots of algebra questions, manipulations are the way to go or number sense. Use the digit clue to help you narrow down the "trial and error" method. 

Make sure you have the terms and space type questions right. Calendar questions, how many numbers (inclusive, exclusive, between, ...), Stage doesn't necessarily start with 1 or 0.
Make sure you don't over-count or under-count.

Mos students got counting questions wrong when it involves limit.

Case in point : How many non-congruent triangles are there if the perimeter is 15? 
Answer: There are 7 of them.  Try it !!

To be continue...

1 comment:

  1. Oh My God! Where were you when I decided to become a liberal arts major because I "wasn't good enough" at math? Twenty years later, while tutoring my very talented son in math, I finally realized that my real problem wasn't lack of some mysterious inborn math talent. It was really just disorganization, failure to read directions, and apocalyptically horrible handwriting! Before I started tutoring him I thought it would be all mind-stretching set theory and kick@$$ nonlinear dynamics applications. But no. It's mostly "put your equal signs in a column so know what side of the equation you're working on, don't skip steps even when you're "sure" you know the answer, and try to write numbers that other sentient beings can actually read." Sigh. Now I look back at my checkered career in college math and just ... well ... facepalm!