TeacherVision - Lesson Plans, Printables and more Free Trial  Member Benefits  Sign In    
Click Here
Feb 27, 2015
Search:   
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
Mathematics (5210 resources)
|
 

Problem Solving: Eliminating Possibilities


Page 1 of 2

What Is It?

Eliminating Possibilities is a strategy in which students remove possible answers until the correct answer remains. Here's an example of a problem that can be solved by Eliminating Possibilities:

The product of an unknown number multiplied by four is less than 35. The unknown number is divisible by four. What two numbers could the unknown number be?

The answer can be found by eliminating the numbers that do not meet the rules and choosing the numbers (four and eight) that remain.

Why Is It Important?

This is a problem-solving strategy that can be used in basic math problems or to help solve logic problems. Eliminating possibilities helps students organize information and evaluate which pieces of information they will use, eliminating the information that does not fit. It encourages students to consider all options and narrow the possibilities to reasonable choices.

How Can You Make It Happen?

Introduce a problem to students that will require them to eliminate possibilities in order to solve the problem. For example:

In the game of football, a team can score either a touchdown for six points or field goal for three points. If a team only scores touchdowns or field goals but does not get any extra points (no points for an extra kick) what scores cannot be achieved if the team scored under 30 points?
  1. Understand the Problem

    Demonstrate that the first step is understanding the problem. This involves identifying the key pieces of information needed to find the answer. This may require students to read the problem several times or put the problem into their own words.

    In this problem, students understand that there is a finite set of possible answers. Students will have to find all of the possible answers and then narrow down the list according to the criteria in the problem.

    The score can be 1 through 29.
    The score must be a multiple of 3 or 6.

  2. Choose a Strategy

    The strategy of eliminating possibilities can be used in situations where there is a set of possible answers and a set of criteria the answer must meet.

  3. Solve the Problem

    First, list the numbers 1 through 29, because the problem states that the score was less than 30.

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

    Next, eliminate answers that are not possible solutions. Work through each criteria to find the solution.

    Any multiple of six would be a possible score of the game. If the team only scored touchdowns, they could score 6, 12, 18, 24 and so on. Therefore, all multiples of six should be eliminated.

    1 2 3 4 5 * 7 8 9 10 11 * 13 14 15 16 17 * 19 20 21 22 23 * 25 26 27 28 29

    Any multiple of three would be a possible score of the game. If a team scored only field goals, they could score 3, 6, 9, and so on. Therefore, all multiples of three should be eliminated.

    1 2 * 4 5 * 7 8 * 10 11 * 13 14 * 16 17 * 19 20 * 22 23 * 25 26 * 28 29

    The answer to the problem is that the following scores could not be the score of the game:

    1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29

  4. Check

    Read the problem again to be sure the question was answered.

    The scores that would not be possible in this game are listed.

    Check the math to be sure it is correct.

    Look through the answers you have eliminated and those that are remaining to make sure you have applied all the criteria in the problem.

    Determine if the best strategy was chosen for this problem or if there was another way to solve the problem.

    Eliminating possibilities was a good strategy to use for this problem.
  5. Explain

    The last step is explaining how you found the answer. Because this strategy involves logic, it is important for students to talk or write about their thinking. Demonstrate how to write a paragraph describing the steps you took and how you made decisions throughout the process.

    First, I listed the possible scores. Then I started to eliminate scores that were not possible. I found the multiples of six and crossed them out. Then I found the multiples of three and crossed them out. I was left with all of the possible scores.
  6. Guided Practice

    Have students try solving the following problem using the strategy of eliminating possibilities.

    Find the numbers between 10 and 30 that are divisible by 4.

    Have students work in pairs, in groups, or individually to solve this problem. They should be able to tell or write about how they found the answer and justify their reasoning.



 Previous   1   2   Next 

Highlights

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.

Teaching with Comics
Reach reluctant readers and English-language learners with comics! Our original teaching guide to the Galactic Hot Dogs comic series, as found on Funbrain.com, will take students on a cosmic adventure while engaging their creative minds. Plus, find even more activities for teaching with comics, featuring many other classic stores.


Free 7-Day Trial for TeacherVision®

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