## Problem Solving by Working Backwards

As I’ve shared before, there are many different ways to go about solving a math problem, and equipping kids to be successful problem solvers is just as important as teaching computation and algorithms. In my experience, students’ frustration often comes from not knowing where to start. Providing them with strategies enables them to at least get the ideas flowing and hopefully get some things down on paper. As in all areas of life, the hardest part is getting started! Today I want to explain how to teach  problem solving by working backwards .

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–>Pssst! Do your kids need help making sense of and solving word problems? You might like this set of editable word problem solving templates ! Use these with any grade level, for any type of word problem :

## Solve a Math Problem by Working Backwards:

Before students can learn to recognize when this is a helpful strategy, they must understand what it means. Working backwards is to start with the final solution and work back one step at a time to get to the beginning.

To help show your students what this looks like, you might start by thinking about directions. Write out some basic directions from home to school:

• Start: Home
• Turn right on Gray St.
• Turn left on Sycamore Ln.
• Turn left on Rose Dr.
• Turn right on Schoolhouse Rd.
• End: School

Ask students to then use this information to give directions from the school back home . Depending on the age of your students, you may even want to draw a map so they can see clearly that they have to do the opposite as they make their way back home from school. In other words, they need to “undo” each turn to get back, i.e. turn left on Schoolhouse Rd. and then right on Rose Dr. etc.

In math, these are called inverse operations . When using the “work backwards” strategy, each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backwards they will need to subtract. And if they multiply working forwards, they must divide when working backwards.

Once students understand inverse operations, and know that they must start with the solution and work back to the beginning, they will need to learn to recognize the types of problems that require working backwards.

In general, problems that list a series of events or a sequence of steps can be solved by working backwards.

## Here’s an example:

Sam’s mom left a plate of cookies on the counter. Sam ate 2 of them, his dad ate 3 of them and they gave 12 to the neighbor. At the end of the day, only 4 cookies were left on the plate. How many cookies did she make altogether?

In this case, we know that the final cookie amount is 4. So if we work backwards to “put back” all the cookies that were taken or eaten, we can figure out what number they started with.

Because cookies are being taken away, that denotes subtraction. Thus, to get back to the original number we have to do the opposite: add. If you take the 4 that are left and add the 12 given to the neighbors, and add the 3 that Dad ate, and then add the 2 that Sam ate, we find that Sam’s mom made 21 cookies .

You may want to give students a few similar problems to let them see when working backwards is useful, and what problems look like that require working backwards to solve.

Have you taught or discussed problem solving by working backwards  with your students? What are some other examples of when this might be useful or necessary?

## Don’t miss the other useful articles in this Problem Solving Series:

• Problem Solve by Drawing a Picture
• Problem Solve by Solving an Easier Problem
• Problem Solve with Guess & Check
• Problem Solve by Finding a Pattern
• Problem Solve by Making a List

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So glad to have come across this post! Today, word problems were the cause of a homework meltdown. At least tomorrow I’ll have a different strategy to try! #ThoughtfulSpot

I’m so glad to hear that! I hope you found some useful ideas!! Homework meltdowns are never fun!! Best of luck!

This is really a great help! We have just started using this method for some of my sons math problems and it helps loads. Thanks so much for sharing on the Let Kids Be Kids Linkup!

That’s great Erin! I hope this is a helpful method and makes things easier for your son! 🙂

I’ve not used this method before but sounds like a good resource to teach. Thanks for linking #LetKidsBeKids

I hope this proves to be helpful for you!

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## Let’s Begin…

Imagine where you want to be someday. Now, how did you get there? Retrograde analysis is a style of problem solving where you work backwards from the endgame you want. It can help you win at chess -- or solve a problem in real life. At TEDYouth 2012, chess grandmaster Maurice Ashley delves into his favorite strategy.

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## Chapter 4, Lesson 5: Problem-Solving Strategy: Work Backward

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## Chapter 4, Lesson 4: Problem-Solving Investigation: Work Backward

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1. Problem Solving by Working Backwards

Solve a Math Problem by Working Backwards: Before students can learn to recognize when this is a helpful strategy, they must understand what it means. Working backwards is to start with the final solution and work back one step at a time to get to the beginning.

2. Problem Solving (Working Backward)

This foundations of math video explains an example of the four-step process of problem solving using the method of working backward. We look at understanding...

3. Chapter 3, Lesson 4: Problem-Solving Investigation: Work Backward

Lesson Resources Extra Examples Group Activity Cards ... Home > Chapter 3 > Lesson 4. New York Math Connects: Concepts, Skills, and Problem Solving, Course 2. Chapter 3, Lesson 4: Problem-Solving Investigation: Work Backward. Extra Examples; Group Activity Cards; Personal Tutor; Self-Check Quizzes; Log In. The resource you requested requires ...

4. 2.5.3: Guess and Check, Work Backward

This lesson will expand your toolbox of problem-solving strategies to include guess and check and working backward. Let's begin by reviewing the four-step problem-solving plan: Step 1: Understand the problem. Step 2: Devise a plan - Translate. Step 3: Carry out the plan - Solve. Step 4: Look - Check and Interpret.

5. Working Backwards Method

The working backwards method is one technique for problem solving. The first step is to start with the final solution and work backwards to the beginning. Sometimes an end result is very...

6. Working Backwards to Solve Word Problems

To solve a problem by working backwards, we basically want to undo the problem step-by-step. We start at the end of the problem and work through to the beginning. In other words, we do...

7. Working Backward Problem Solving Teaching Resources

5.0 (2) \$1.00 PPTX This Power Point contains 10 engaging problems using the Work Backward strategy. Teachers can use the problems for whole group demonstrations or cooperative group work on the different problem solving strategies in mathematics. Best practices include problem solving every day.

8. 9.5 Problem Solving: Working Backwards

9.5 Problem Solving: Working BackwardsWe're learning how to draw models and work backwards to solve word problems.McGraw-Hill MyMath

9. Work Backwards Lesson Plans & Worksheets Reviewed by Teachers

In this math worksheet, students learn to solve word problems by working backwards. Students read the 20 word problems and solve them, choosing the best answer from 4 choices. There are helpful hints on the page to clue students to work... + Lesson Plan Curated OER Working Backwards For Teachers 3rd - 5th

10. Chapter 3, Lesson 4: Problem-Solving Investigation: Work Backward

Lesson Resources Extra Examples Group Activity Cards ... Home > Chapter 3 > Lesson 4. California Mathematics: Concepts, Skills, and Problem Solving, Grade 6. Chapter 3, Lesson 4: Problem-Solving Investigation: Work Backward. Extra Examples; Group Activity Cards; Personal Tutor; Self-Check Quizzes; Log In. The resource you requested requires you ...

11. Grade 3 Math: Problem Solving Strategy: Work Backward

McGraw Hill Math: Chapter 11 Lesson 7

12. Guess and Check, Work Backward ( Read )

Step 1. Understand the problem. Read the problem carefully. Then list all the components and data involved, and assign your variables. Step 2. Devise a plan - Translate. Come up with a way to solve the problem. Set up an equation, draw a diagram, make a chart or construct a table. Step 3.

13. Working backward to solve problems

Working backward to solve problems - Maurice Ashley 2,167,050 Views 6,444 Questions Answered TED Ed Animation Let's Begin… Imagine where you want to be someday. Now, how did you get there? Retrograde analysis is a style of problem solving where you work backwards from the endgame you want.

14. Work Backward to Problem Solve Lesson Plans & Worksheets

Working Backwards as a Problem-Solving Strategy. For Students 3rd. In this problem solving strategy worksheet, 3rd graders roll a dice three times and record the number in the hundreds, tens and ones place on the chart, then solve an addition and subtraction problem with that number. +. Worksheet.

15. Word Problems Work Backwards Lesson Plans & Worksheets

In this math worksheet, students learn to solve word problems by working backwards. Students read the 20 word problems and solve them, choosing the best answer from 4 choices. There are helpful hints on the page to clue students to work... + Worksheet Curated OER Number Word Problems: Working Backwards For Students 4th - 5th

16. grade 4 problem solving working backwards

Under \$5 \$5 - \$10 \$10 and up On Sale Resource Types Independent Work Packet Worksheets Results for grade 4 problem solving working backwards 321 results Sort: Relevance View: Grade 3 Envisions Math Topic 12 Common Core Version Inspired Power Point Lessons by

17. Work Backward Printable (4th Grade)

Grade: 4 Subjects: Word Problems Mathematics + show tags Excerpted from Compiled by the editors of TeacherVision ® The word-problem tips and worksheets in this printable book will help fourth-graders hone their problem-solving skills. They'll learn to analyze problems, choose the right strategy, and build problem-solving confidence.

18. Problem Solving: Work Backward Worksheet for 4th Grade

In this problem solving worksheet, 4th graders solve each of 6 word problems by working backwards. They use the strategy while working with money and decimals.

19. Chapter 4, Lesson 5: Problem-Solving Strategy: Work Backward

Lesson Resources Extra Examples Self-Check Quizzes Personal Tutor. Math Review ... Mathematics. Home > Chapter 4 > Lesson 5. California Algebra Readiness: Concepts, Skills, and Problem Solving. Chapter 4, Lesson 5: Problem-Solving Strategy: Work Backward. Extra Examples; Self-Check Quizzes; Log In.

20. Working Backwards

Chapter 3: Working Backwards. The very name of this strategy sounds confusing to most people. It is a very unnatural way of doing things. When most of us went to school, we were taught to solve mathematical problems in a direct, straightforward manner. And yet, working backwards is the way many real-life problems are often resolved.

21. Problem Solving Work Backward Lesson Plans & Worksheets

In this problem solving worksheet, 4th graders solve each of 6 word problems by working backwards. They use the strategy while working with money and decimals. + Lesson Plan Curated OER Word Clue and All About Me Problem Solving For Teachers 5th Fifth graders practice solving word problems using highlighted strategies.

22. Chapter 3, Lesson 4: Problem-Solving Investigation: Work Backward

Lesson Resources Extra Examples Group Activity Cards ... Mathematics. Home > Chapter 3 > Lesson 4. Oklahoma Math Connects Concepts, Skills, and Problem Solving Course 2. Chapter 3, Lesson 4: Problem-Solving Investigation: Work Backward. Extra Examples; Group Activity Cards; Personal Tutor; Self-Check Quizzes; Log In. The resource you requested ...

23. Chapter 4, Lesson 4: Problem-Solving Investigation: Work Backward

Home > Chapter 4 > Lesson 4. Texas Mathematics, Course 2. Chapter 4, Lesson 4: Problem-Solving Investigation: Work Backward. Extra Examples; Group Activity Cards; Personal Tutor; Self-Check Quizzes; Log In. ... To report a technical problem with this Web site, please contact the ...