Problem Solving Strategies






What is problem solving?

It is a mental strategy/process that helps planning a method and undertaking it in such as way so that you can get the solution easily and it is more effective. It includes analyzing, discovering and solving, i.e. problem finding and problem shaping. The main reason for learning all about math is to become better problem solvers in all aspects of life.
It is easy to have a cross-out list, to see whether any operation goes with the word problem. If one doesn’t go with the problem, cross that out and then do it for the rest. Finally we would be left with one or two. If you remain with one operation, you would check if that goes and if it does, it is going to be easy to find the solution.
Example: If you have to problem-solve about this situation, what skill would you use?
Sam has fifteen carrots. His brother takes two of them. How many carrots does Sam have now?
Now from fifteen carrots, Sam’s brother takes two of them. How many are left with Sam?
1. You wouldn’t add because his brother took away two carrots.
2. You wouldn’t multiply because there is no product of any items involved.
3. You wouldn’t divide because there is no distribution between/among people.
Subtraction is left. Check if it fits,
So, from fifteen carrots, two are gone, how many are left? 15 – 2 = 13.
There are 13 carrots with Sam now.
Hence, subtraction is the correct skill to use in this situation.


Different methods of problem solving (graphs, equations, word problems)

Graphs (Using the Equation of a line-"mx+b"):

GraphProblemSolving1.jpg
GraphProblemSolving2.jpg

Equations:

As you might know, the word "equations" is derived from the word "equal."
Expressions and equations are mathematical symbols and variables.
Expressions don't have an equal sign, while equations do.

Addition Word Problem:
AdditionProblem.jpg
"I wrote "x" in the place of total marbles since that is what we don't know; that is the problem is asking for."
Answer: Jenny and Kenny together have 12 marbles

Subtraction Word Problem:
SubtractionProblem.jpg
Second Example:
Let the number of marbles of Greg= x
Greg has 17 more marbles than Jack, while Jack has 15.
So in this situation, more is a clue that this problem could be solved using addition,
17 more marbles+(than Jack)15=how many?
17+15=x
32=x
Therefore, x=32 marbles.
Check using subtraction-
32-17=15
OR
32-15=17
Answer: Greg has 32 marbles.


Word Problems:


Problem_Solving.jpg


REMEMBER:
Small number to big number is a clue to division (ex: 2 miles per hour, how many in 2 hours?)
Big number to small number is a clue to multiplication (ex: 5 miles in 2 hours, how many in 1 hour?)


Citations:

http://www.homeschoolmath.net/teaching/teach-solve-word-problems.php
http://en.wikipedia.org/wiki/Problem_solving
http://math.about.com/cs/testprep/a/ps.htm