Elementary Problem of the Week:
Tips for Writing Solutions

How do you write a good math solution?

• writing a complete solution
• keeping your work organized
• checking your math
• rereading your explanation

Writing a Complete Solution

Writing a good math solution is similar to writing a good story. Since no one can read your mind, you need to give enough information so that your audience will understand what you mean. If you do not write your thoughts down, your readers may never know the whole story.

One good way to make sure you include enough information in your solution is to pretend you are explaining the problem to a friend who does not know anything about it. Imagine yourself leading your friend on a tour of your thinking as you solved the problem. How did you start? Where did you find the information you used? What were your calculations? How did you check your solution?

Don't fall into these traps:

The Missing Numbers Trap
Sometimes students will write out their solutions without using the numbers that helped them get the solution. When they do this, it is difficult for the readers to understand where the student went right and where the student went wrong.

The Missing Words Trap
Sometimes students will write a list of numbers, formulas, or equations without explaining what they were thinking. When this happens, it is hard for a reader to learn how to solve the problem from the explanation.

It's Not E-Mail Trap
Sometimes students will write their solutions as though they are writing e-mail. When e-mailing, people don't always use capital letters and punctuation. Math solutions that you submit to the Problem of the Week are not e-mails and should be written in the best form possible. The Math Forum likes to post well-written submissions.

Often there is more than one way to solve a problem. You might use a Venn diagram, algebra, guess and check, graphing, or you might make a table. Whatever method you choose, the most important thing is to explain your steps very clearly. Even when something seems obvious to you, you should write it down very plainly so that someone reading what you wrote will know exactly what you meant.

Keeping it Organized

Sometimes it is hard to put thoughts into words. One way to improve your communication is to keep your work organized. Where you put spaces in your answer can change how well your reader understands your solution. How you use math symbols can change the meaning of your equations.

Tips

1. Break long explanations into several short paragraphs, each one with its own idea or step. Leave a blank line between paragraphs.
   
   
2. When using symbols in number sentences, leave spaces between the numbers and symbols. Which is easier to read?
   
   

   543 x 24 = 13,032                    543x24=13,032            
   

   
   See how a space on either side of the symbols makes reading easier?
   
   
3. Be careful how you use the equals sign. The numbers and expressions on each side of the symbol must be equivalent. You can't always perform a new operation on an answer that you just got. Sometimes it makes the equation untrue.
   
   

   Correct                                
                               
   5 + 4 = 3 + 6                       (This shows 9 = 9)
   
   3/5 = (3/5 * 2/2) = 6/10            (This shows 3/5 = 3/5 = 3/5)  
            
   
   Incorrect
            
   5 + 4 = 9 - 7 = 2 x 6 = 12          (This shows 9 = 2 = 12 = 12)
   
   
   Correction
   
   5 + 4 = 9, 9 - 7 = 2, 2 x 6 = 12    (This shows three equations
                                        with the answers 9, 2, and 12)
                                        
    
   

Checking your math

When you finish writing your solution, it is always a good idea to go back and check your math.

• Check the numbers that you typed. It is easy to type 862 instead of 826.
• Make sure you added, subtracted, multiplied, and divided accurately.
• Is your decimal point in the right place?
• Don't forget the unit labels. Did you measure in meters? pounds? degrees?

Rereading your explanation

When you think you are finished, read through your solution to make sure that it makes sense. Did you answer the right question? Did you answer all parts of the question? Does your explanation say what you were thinking? Does it explain the math in a way that will help someone understand how to solve the problem?

One strategy that really works is to read your answer out loud. When you read your work out loud, you are more likely to notice things that you would like to change.