by Paul

While students attempt to solve math word problems, any difficulties that arise are often because a process, or a series of steps, is not being followed. Although math word problems exist in an infinite variety, you are more likely to get the correct answer, through fewer difficulties, by following a problem-solving strategy.

A core strategy which applies to solving virtually all math word problems can be divided into four sequential steps – Read, Plan, Solve, Check. Let’s elaborate on each of these.

Read: The goal in this first step is to understand the given math word problem. This step is the most important since it paves the way and direction for the next three steps. You may need to read the problem more than once, perhaps even two or three times, until you understand well the given details and have a clear sense of what you are asked to find. Underlining and/or highlighting relevant and important words and details often help to comprehend the word problem. As well, don’t hesitate to illustrate the problem’s details with a quick and rough sketch or diagram. An illustration will often help a great deal in focusing on the relevant details.

Plan: Once the word problem is understood, the next step is to plan your mathematical approach to solve this problem. The main task here is often to choose the correct mathematical operation – addition, subtraction, multiplication, division, or other. You may need to reread the word problem in order to choose the correct operation(s). If in doubt on selecting the right operation, then search in the details for key-words or expressions which will often, but not always, suggest the appropriate operation.

For example, addition is suggested by the terms - sum, total, add, plus, combine quantities, increased by. Subtraction is implied by the terms - difference, minus, decreased by, reduced by, subtract, how many more, how much greater. Multiplication may be inferred from the words - product, multiplied by, times, of, add repeatedly. Division is suggested by - divided by, quotient, remainder, divide, split into equal parts. Keep in mind that it is always better to understand the entire word problem than to rely just on key words for directions.

Solve: Now that the word problem is well understood and you have a plan in mind on how to solve it, the plan can be applied. At this step, you’ll often write your planned equation and then solve for the unknown quantity.

Check: Although this is the final step, it is not any less important than the previous steps. The goal here is to ponder over the final answer – does it make sense? Is it reasonable? Does it specifically answer the question posed by the problem? As an extra confirmation that your answer is valid, test this final answer with respect to your applied equation. If the final answer is questionable or proves incorrect, then it’s necessary to return back to the “Read” step and work through the four steps again.

Now let’s demonstrate the above four step problem-solving strategy:

Example 1

Michelle drove 975 km on Monday and 1 468 km on Tuesday. How much farther did she drive on Tuesday than on Monday?

Read: Michelle drove farther on Tuesday than on Monday, and we’re asked to find out by how many kilometers farther.

Plan: We need to subtract Monday’s distance (975 km) from Tuesday’s (1 468 km), because the comparison is with respect to Monday.

Solve: 1 468

- 975

-------

493

====

Check: Is the answer reasonable? Within the given range of given values (1 468 to 975), a difference of 493 seems reasonable. To confirm, let’s check the applied subtraction equation with the opposite operation, addition.

493

+ 975

-------

1 468 - Since this equals the value (1 468) with which we started the “original equation” above, the answer of 493 km is thus confirmed.

Therefore, Michelle drove 493 km farther on Tuesday than on Monday.

Example 2

Six friends commute to work together, Monday through Friday. These friends have known each other for the last thirty years. The total weekly gasoline, parking, and car maintenance expense is $168.00. How much should each friend pay per week?

Read: The six friends share the weekly cost of transportation, and we’re asked to determine the equal amount to be paid by each. Note that the fact that they’ve known each other for over thirty years is not relevant in solving this word problem.

Plan: The total cost of $168.00 needs to be split into six equal amounts. This calls for division.

Solve: 168.00 ÷ 6 = 28.00

Check: Does the final answer make sense? For a total of nearly $170.00 per week, $28.00 paid by each of six persons seems reasonable. To confirm, let’s check the applied division equation with the opposite operation, multiplication.

28.00 x 6 = $168.00 - Since this equals the value (168.00) with which we started the “original equation” above, the answer of $28.00 is thus confirmed.

Therefore, each of the six friends should pay $28.00 for a total of $168.00.

In summary, the four sequential step problem-solving strategy (Read, Plan, Solve, Check) is a very useful and necessary tool to solve word problems in math. The amount of time and work involved at each step depend on the length, complexity, and math level of the word problem. These four steps are dependent on one another because a change at any one step will typically affect the results at the other steps. Furthermore, with greater practice, your math skills and word problem solving skills will improve. You’ll soon be working simultaneously through more than one of the four steps at a time. Be sure to check with our teachers about any math questions, or about any of the many courses we offer. See you at our Learning Centre!

Test your reading comprehension of this reading!

Try some math word problems to improve your word problem skills:

Skillswise - choose the “Problem Solving” links, then the corresponding “Quiz.”

Syvum - choose a link from Arithmetic Word Problems 5.1 to 5.9, then click on “Quiz” followed by “Fill in the blanks . . .”

For reference and further reading, see these sites:

(March 1, 2009)

(Includes all 2002 to date Weekly Features with descriptions)

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