TeacherVision - Lesson Plans, Printables and more Free Trial  Member Benefits  Sign In    
Click Here
Mar 6, 2015
We have merged TeacherVision's international content onto one website. Educators around the world can use TeacherVision.com to browse an extensive library of teaching materials. You can still find relevant content for Australia, Canada, the United Kingdom, and the United States in our Educators' Calendars.  [x] CLOSE

Problem Solving: Choose the Operation

Page 1 of 2

What Is It?

The process of "choosing the operation" involves deciding which mathematical operation (addition, subtraction, multiplication, or division) or combination of operations will be useful in solving a word problem. For example, one way to solve the following problem is to think of it as a problem of subtraction, e.g.:

If there are eighteen students, and six students are not here today, how many are present?

18 - 6 = ?

In comparison, the following problem can be thought of as a problem solved by addition.

If there are twelve students in class today and six students are absent, how many are there in all?

12 + 6 = ?

Why Is It Important?

Choosing mathematical operations is an important part of the larger process of translating English sentences into mathematical expressions. Success depends upon two things:

(a) the ability to understand the literal meaning of the sentence

(b) the ability to express this meaning mathematically

Students who cannot understand the literal meaning of the sentence will not be able to express it mathematically, even if they have the necessary mathematical skills. (Imagine trying to solve a word problem in a language you don't know, such as Arabic.)

Even if students can understand the literal meaning of the sentence, they will not be able to solve the problem unless they can also express this meaning mathematically. In other words, successful solutions to word problems involve both reading skills and mathematical skills. In particular, choosing an operation involves, in part, identifying language clues that suggest mathematical interpretations. Consider the following examples.

If there are eighteen students, and six students are not here today, how many are present?
If there are twelve students in class today and six students are absent, how many are there in all?

The phrase "not here" conveys the concept of taking away—or subtraction. Alternatively, the phrase "in all" may signal a problem solved by addition.

Instead of teaching how to solve word problems as a separate concept, teachers should embed problems in the mathematics-content curriculum. When teachers integrate problem solving into the context of mathematical situations, students recognize the usefulness of strategies (NCTM, 2000).

Teachers must make certain that problem solving is not reserved for older students or those who have "got the basics." Young students can engage in substantive problem solving and in doing so develop basic skills, higher-order-thinking skills, and problem-solving strategies (Trafton and Hartman 1997).

How Can You Make It Happen?

Choosing the operation is a difficult skill for some students, especially those struggling with reading. There is no single solution. A combination of strategies will work best.

  1. Identify Key Words

    It may help to work with students to identify certain words that are commonly associated with mathematical operations. For example, the following phrases or words often suggest which operations to use. Consider displaying a table such as this in your classroom and add words and phrases as you find them in word problems.

    in all
    how many
    how much change
    how many more
    how much more
    in all groups
    how many each
    how many groups divided equally

    It may also help to have students take turns thinking out loud as they work through word problems. For example, consider the following problem.

    Juanita took twenty dollars to the mall. She bought a headband for three dollars and a bracelet for seven dollars. How much did she have left?

    A student might think aloud (or write) something like this:

    First I added three plus seven dollars because it said "three dollars and seven dollars" so I knew that meant to add. So, that was ten dollars. Then I subtracted ten dollars from twenty dollars because it said "How much did she have LEFT" so I knew that meant to subtract.
  2. Get to the Bottom of the Problem

    While the "key word" approach may provide hints, many problems do not provide overt clues. For example, to understand the following problem, one must understand the meaning of the words absent and present. There is no substitute for understanding the vocabulary of a word problem and what it means. This involves finding the important pieces of information, and may require students reading the problem several times, and/or students putting the problem into their own words.

  3. Draw a Picture

    Drawing a picture or diagram is often a good intermediate step in translating a word problem into a mathematical expression. For example, consider the following word problem.

    If there are eighteen students, and six students are not here today, how many are present?

    This problem may be represented graphically using a picture. You could draw eighteen children in a row, then cross out six of them.

    Or a table such as this:


    Once presented in this way, the problem may be more easily seen as a problem of subtraction, because we are clearly "taking away" some parts from the whole. Consider having student create their own standard visual representations for problems involving addition, subtraction, multiplication, and division—then have them practice choosing from among their representations given particular word problems.

  4. Unnecessary Information

    It is important to encourage students to read an entire problem before starting to solve it-deciding which information is important and which information is not needed. One method is to have them practice with problems that have too much information, such as:

    Emma rode her bike the same distance as Michael. It is 12 miles from Emma's house to school, 4 miles to the library, and 1 mile to the playground. If Michael and Emma rode a total of 26 miles, how many miles did Emma ride?

    Can students find 13 miles as an answer? Discuss the incorrect answer they might have found if they didn't focus on the important information. Have students create their own word problems that contain too much information, and challenge each other to solve them.

 Previous   1   2   Next 

Free 7-Day Trial for TeacherVision®

Sign up for a free trial and get access
to our huge library of teaching materials!
Start Trial


Galactic Hot Dogs Reading Marathon
Join the Galactic Hot Dogs Reading Marathon! Read each episode as it's re-released with newly revealed facts, behind-the-scenes illustrations, and the inside scoop. Make it official by pledging on the blog to read each chapter with Cosmoe. Your students will love following the exploits of these space travelers, and you'll love the educational elements that can easily be paired to the stories.

Handwashing Awareness
Kids are especially susceptible to contracting and spreading viruses during the winter months. Prevention starts with proper handwashing. Show students how to keep germs away.

March Calendar of Events
March is full events that you can incorporate into your standard curriculum. Our Educators' Calendar outlines activities for each event, including: National School Breakfast Week (3/2-6), World Orphan Week (3/4-11), Boston Massacre (3/5/1770), Daylight Saving Time Begins (3/8), International Women's Day (3/8), Teen Tech Week (3/8-14), Pi Day (3/14), St. Patrick's Day (3/17), Spring Begins (3/20), Make Your Own Holiday Day (3/26), and World Theatre Day (3/27). Plus, celebrate Deaf History Month (3/15-4/15), Music In Our Schools Month, Women's History Month, and Youth Art Month!

Poptropica Teaching Guides
Poptropica is one of the Internet's most popular sites for kids—and now it's available as an app for the iPad! It's not just a place to play games; each of the islands featured on the site provides a learning opportunity. Check out our teaching guides to four of Poptropica's islands: 24 Carrot Island, Time Tangled Island, Mystery Train Island, and Mythology Island.

Take Our Survey!
Help us improve TeacherVision by taking our brief survey. Thank you for your input!

Women's History Month
March is Women's History Month. Talk to your students about the accomplishments women have made—as well as the adversity they have faced.