How to Solve Math Problems
For the 2009 school year, I revised these handouts into a one-page reference that I could slip into the back of each student’s homemade white board. For details, see:
That’s a Tough One!
What can you do when you are stumped? Too many students sit and stare at the page, waiting for inspiration to strike — and when the solution doesn’t crack their heads open and step out, fully formed, they complain: “Math is too hard!”
So this year I have given my Math Club students a couple of mini-posters to put up on the wall above their desk, or wherever they do their math homework. The first gives four questions to ask yourself as you think through a math problem, and the second is a list of problem-solving strategies.
How to Solve a Tough 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.
- 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.
- Does your answer make sense?
- Do you have the correct units (inches, cm2, kg, etc.)?
- 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.)
Sharing the Fun
If you would like to download these handouts for your students, here are the files:
For this and many other excellent books about teaching math, check out the Let’s play math! bookstore.