How to Solve Math Problems

[Photo by Aaron Escobar. This post is a revision and update of How to Solve Math Problems from October, 2007.]

What can you do when you are stumped by a math problem? Not just any old homework exercise, but one of those tricky word problems that can so easily confuse anyone?

The difference between an “exercise” and a “problem” will vary from one person to another, even within a single class. Even so, this easy to remember, 4-step approach can help students at any grade level. In my math classes, I give each child a copy to keep handy:

• How To Solve a Tough Math Problem

[Note: Page 1 is the best for quick reference, especially with elementary to middle school children. Page 2 lists the steps in more detail, for the teacher or for older students.]

Homemade White Boards

I made each student an individual “white board” — a clear page protector filled with white card stock (or several sheets of typing paper). Dry erase markers wipe off easily, and we can insert graph paper or other templates for the lesson of the day. Then I printed the first page of my problem-solving handout and slipped it into the back of each page protector.

At the beginning of each year, and then occasionally throughout the first semester, we go over the system more thoroughly, explaining each step in depth…

How To Solve a Tough Math Problem

Ask yourself these 4 questions:

1) What do I know?

• List the facts or information given in the problem.
• Underline or circle any key words, such as factor, multiple, area, or perimeter.
• Watch out for mixed units!
• Express the facts in math symbols, if you can.

2) What do I want?

• Describe the goal, what the problem is asking you to find.
• Underline or circle any key words, such as sum, product, next, or not. (Small words are easy to miss!)
• Express the goal in math symbols, if you can.

3) What can I do?

• Combine the given facts. Can you get closer to the goal?
• Try a tool from your Problem Solving Tool Box [see below].
• Do one little step at a time.

4) Does it make sense?

• When you get an answer, always look back at the original problem one more time.
• Check 3 things:

1. Does your answer make sense?
2. Do you have the correct units (inches, cm², kg, etc.)?
3. Can you think of a way to confirm that your answer is right?

Problem Solving Tool Box

• Draw a diagram or picture.
• Act the problem out, step by step.
• Make a systematic list, chart, or table.
• Look for a pattern.
• Simplify the problem. (Try it with smaller numbers.)
• Restate the problem in another way, or look for a related problem.
• Think about “Before” and “After” situations.
• Work backwards.
• Guess and check. (Try something and see if it works.)

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Edited to add: This post is an excerpt from my book Let’s Play Math: How Homeschooling Families Can Learn Math Together, and Enjoy It!