Teacher Guide to Problem Solving

Solving a math problem is all about having a good strategy. With the right strategy, you cannot only solve any problem, but you can do so quickly.

Regardless of your specific strategy, it is useful to begin by outlining the math problem.

Outlining a math problem has three steps:

1. Write the problem down.
Rather than try to figure out the solution in your head, write the problem down. Spell out specifically what it is you want to know and what information you have to that end.

2. Translate words into numbers.
Next, translate words into numbers and functions into symbols. For example, write two as "2" and plus as "+" - science has proven that the vast majority of people find working with numbers and symbols easier to work with than words when performing mathematical calculations.

3. Perform the calculation.
Lastly, perform the actual calculation. While this step can be relatively straight forward, it can also be one one of the most time consuming parts of solving a math problem.

Methods for Solving Math Problems

To this end, there is a variety of methods you can use, some of which will be better in some scenarios than others. Through trial and error, you can find the method that works best for you.


Combining like terms is a necessity. For example, if you were adding up a purchase at a candy store, it would be impossible to total your purchase if you were trying to add dollars and cents without noting their differences. Likewise, grouping together dollars and cents individually before adding them together is easier and faster than try to add everything together at once.


Similarly, you may find that combining numbers into manageable pieces helps as well. For example, if you were to add together the following: 7+3+2+8+5+5+6+4+9+1 you would get the answer "50". However, you could have come to that conclusion far more quickly had you began by adding the numbers together in groups of two - 7+3, 2+8, 5+5, 6+4, 9+1. Doing so would have yielded you 5 groups of 10, which, through multiplication, you know to equal 50.


Alternatively, you may want to divide and conquer the problem. You would do this by dividing the problem into small pieces. For example, if you were trying to add together 91 and 84, you may find it easiest to "divide" 91 into two parts - 90 and 1. When you do likewise with "84" (80 and 4) you can create an addition problem of 90+80 and 1+4.


Lastly, consider using the "take away" method. This works by subtracting numbers incrementally. For example, if you were trying to determine the difference between 1,000 and 541, you would begin by subtracting 541 from 550 - the result is 9. Hold that number to the side and subtract 550 from 600 - the result is 50. Finally, subtract 600 from 1,000 - the result is 400. To get your total (the difference between 1,000 and 541) simply add together the totals you had held back - in this case, that would be 9 + 50 + 400, or 459.

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