Tackling Math Word Problems, Step by Step
Many students, even those who excel at math, can get spooked by word problems. Try using these steps when faced with intimidating word problems.
Step One: Read each problem twice, slowly and carefully.
First, read to understand the problem. The next time through, look for numbers and keywords that tell you which operation(s) to perform. Circle these details, and underline the question you are being asked to answer.
Here are some examples of keywords that point to each operation:
- Addition: sum, total, altogether, increased by, in all, and, plus, combined, more than, added to, perimeter
- Subtraction: difference, less than, minus, take away, fewer, left over, are not, remain, how many more, reduced by, decreased by, greater than, farther, left
- Multiplication: times, each, of, twice, product, area, factor, multiple, multiplied by, array, rows of, columns of, groups of, equal groups, distributed, as much as
- Division: half, split, quotient, divisor, dividend, equal groups, each, separate, divided by, shared equally, distributed, cut up, average
Step Two: Make the problem visual: translate word problems into word equations before plugging in any numbers, or draw a picture to represent the problem.
This tip is especially useful if you tend to have trouble solving word problems. Read the word problem, once sentence at a time. Think about what is happening in the problem, and put those words into an equation. You can also draw a picture to represent the information in the problem.
Step Three: Swap in the numbers.
Most of the time, math is simple: it’s just a bunch of numbers that represent values in the real world. This is why most math problems require a specific label—the numbers in your answer relate to a quantity or measure of a real thing. In this step, you are substituting in numerical values for the words you used in Step Two. Look back at the numbers and keywords you circled in Step One, and match them to the words they represent in your word equation from Step Two.
Step Four: Determine the Order of Operations, if necessary.
Depending on what grade you’re in, your math problems may be just one step, or they may have multiple steps. More complicated problems may have more than one math operation in the same equation. If this is the case, solve each step, one at a time, using the Order of Operations:
- Grouping Symbols: parentheses, then brackets
- Multiplication ↔ Division (can be solved in either order)
- Addition ↔ Subtraction (can be solved in either order)
It is important to remember to solve these steps one at a time, in the correct order, always working left to right, when solving an equation with multiple operations.
Step Five: Solve one step at a time, and show all your work.
Just because you may be allowed to use a calculator doesn’t mean you should rely on it to do all the work for you. Calculators can be finicky—so don’t type the entire equation into your calculator and expect to get the correct answer. Instead, solve one step at a time and “bring down” the rest of the equation that you have yet to solve. Don’t forget to show all your work, even if you used a calculator. Not only will your teacher want to see how you arrived at your answer (which is helpful if you end up making a mistake), this will also help you to understand the problem better. Continue to solve one step at a time until you arrive at the final answer.
Step Six: Check to make sure your answer is reasonable.
Even the smartest mathematicians in the world can make a silly mistake. Make sure you don’t lose points on a problem because of a simple calculation error. Determining whether or not your answer is reasonable is easy!
- You can simply ask yourself if your answer makes sense, given the information in the problem.
- You can also use rounding to estimate whether your true answer is close to an estimation of the answer.
If you determine that your answer is unreasonable, go back to Step Five and see where you could have miscalculated. If everything looks correct, perhaps you set the problem up incorrectly, or used the wrong operation. Reread the problem, then make sure Steps Two and Three are done correctly.
Step Seven: Check your work using inverse (opposite) operations.
Once you have a reasonable answer, the surest way to check your work is to solve the problem backwards, with the answer you found in Step Five. The goal is to arrive back at the same information you were given in the problem. To work a problem in reverse, you will use inverse (opposite) operations. For example, if you solved the problem using division, check your work using multiplication.
Here are some other inverse operations:
- Addition ↔ Subtraction
- Multiplication ↔ Division
- Exponents ↔ Roots
- Distribution ↔ Factorization
Step Eight: Print your answer clearly, using proper units and labels
Review the question you underlined in Step One. This should tell you which units or label to use, but if you don’t see any, look back at the problem to find the right label. Now, turn the question into a statement, inserting your answer from Step Five. Make sure you print legibly! All the work you just did will mean nothing if your teacher can’t read your answer. 😉