Word problems are the expressions of logical and mathematical sequence with the use of basic contemporary written languages.
For us to solve word problems mathematically there is a need to convert them to mathematical expressions using numbers, figures and alphabets.
The basic rules employed by mathematicians consciously or unconsciously can be split into three steps; these steps are listed below:
Step 1: list your given data (if possible draw)
Step 2: state the necessary formula.
Step 3: apply the formula by inputting the given and discovered data.
A question is set based on inductive reasoning (that is from the answer the steps are reversed back to create a problem or question). It is now left for the problem solver to use deductive reasoning to get back to the answer. To do this the gestalt needs to be rearranged, and the first step in doing this is to list the given data. It is advisable to produce a diagrammatical representation of the question; even when it is not required this will help to unleash the hidden details of the question.
Let us take an example.
A rectangle is 8cm long and its perimeter is 30cm. find the breath of the rectangle.
List your given ( if possible draw)
Length of the rectangle = 8cm
Perimeter of the rectangle = 30cm
Breadth of the rectangle = bcm
The first step in solving the mathematical problem is complete, i.e., we have succeeded in listing the given data.
State the necessary formula.
The next step is for us to state the necessary formula; to do this deep thinking is required. This will help us to rearrange our gestalt based on the observation of the listed given data and the associated diagram. The clues needed to determine the necessary formula are imbedded in the listed data and the diagram. The perimeter of the rectangle is given, so we can establish a link between the unknown breadth and the given perimeter.
Perimeter = length +breadth +length + breadth
Where length l=8 breadth = b Perimeter= 30
We have been able to rearrange our gestalt and identify the link between the known perimeter of a rectangle, and the unknown breadth of the rectangle.
Apply the formula by inputting the given and discovered data.
Perimeter =l +b+l+b
Where length l=8cm Perimeter = 30cm
Perimeter = 8+b+8+b
30 = 8+8 +b+b
30 = 16 + 2b
2b = 30-16
2b = 14
Divide both sides 2
b = 7
These three steps are the basic principles employed in solving word problems.
Mathematicians apply these rules consciously and unconsciously.