Get the Powers to Act from Fresh Ideas



May 20, 2013

Study Skills | Problem Solving | Start With the Doable


Mathematical Methods


We have reviewed so many books, principles, methods and techniques for doing school examination Math. We have tried them out with our classes and have found some of them useful and practicable. Here we are sharing those battle-tested. proven methods with you.

This week, we're discussing the method of starting with the doable.

When reading a math problem, sometimes you can see all the way through to the solution. On such occasions, you don't need any help. But at other times, you feel stumped or overwhelmed. You may even become panic-stricken. How do you control such unhelpful feelings? You need to remain calm and even a bit hopeful. In How to Solve It, George Polya calls the development of such emotional muscles an essential part of a student's mathematical education, insisting that a maths teacher should not fail in this responsibility.

Easier said than done? Yes. Exhortations, preaching, theoretical explanations alone will never do. We must make the kids see and feel for themselves. With advanced or mature students, the teacher may even model such emotional stability behavior.

Exercise 1.
1. Imagine you are in a very important exam. You get 3 minutes to answer the question below.
2. "For how many three-digit integers will reversing the order of the digits yield a two-digit multiples of thirteen?"
3. You don't need to solve this actually. Just record your own emotional reaction and that of your child.


Answer: The question comes from "Zen in the Art of the SAT" by Matt Bardin and Susan Fine, 2005, page 7-9. It was meant to freak out the typical SAT taker and to invoke their Maths anxiety.
If you decide that the question is too much, too high for a P6 student, how can you make it more approachable?


Exercise 2.
1. Which of the following are the multiples of 2?
2, 3, 4, 10, 11, 22

Answer: 2,4, 10, 22



2. Which of the following are the multiples of 13?
12, 13, 24, 26, 35, 39

Answer: 13, 26, 39


3. What are the first 8 multiples of 13?
(13 x 1), (13 x 2),(13 x 3), ...

Answer: 13, 26, 39, 52, 65, 78, 91, 104


Exercise 3.
1. The following is a list of the multiples of 13 from smallest to biggest.
Pick out the "two-digit multiples of thirteen"
13, 26, 39, 52, 65, 78, 91, 104

Answer: 13, 26, 39, 52, 65, 78, 91


Exercise 4.
1. You need a three-digit integer and you reverse the order of its digits(e.g. 912 becomes 219) to get 13.
What is that three-digit integer?

Answer: 310


2. From which three-digit integers do they come from?
26, 39, 52, 65, 78, 91

Answer:
26 comes from a reverse of a 3-digit ... such as ... 620
39 comes from a reverse of a 3-digit ... such as ... 930
52 comes from a reverse of a 3-digit ... such as ... 250
65 comes from a reverse of a 3-digit ... such as ... 560
78 comes from a reverse of a 3-digit ... such as ... 870
91 comes from a reverse of a 3-digit ... such as ... 190


Their moral from this is to walk through the open doors and look for such doors patiently and with optimism. "You may think there's something great behind one of those locked doors, but if you can't get to it, it's useless. The open door is the only one that provides a point of entry." page 7-9, Zen in the Art of the SAT by Matt Bardin and Susan Fine, 2005.



My moral from this is : most of the times a complex problem is nothing more than a bunch of simpler, smaller problems.

Can you help your kid look for and find the smaller ones,the open doors?

Can you teach your kid the right time, the right place, the right way to give up and search for the open doors?


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