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Math Strategies: 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 .

Help kids learn and apply this useful problem solving strategy: 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.

It may also be helpful for students to understand that this is useful in many aspects of life, not just solving math problems.

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

working backwards problem solving strategy

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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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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Primary 3 Working Backwards & Its Method

Math heuristics for problem solving, primary 3 working backwards & its method, what is working backwards in math.

The scenario occurs when the quantity data is insufficient to work from the beginning . Working Backwards is a problem-solving strategy in which you start with the end goal and work backward to figure out the steps needed to get there. In other words, instead of starting from the beginning and moving forward, you start from the end and move backward. This strategy is commonly used in math problems that ask you to find a starting value or figure out what happened before a given situation.

How to Solve Math Questions with Working Backwords Method?

Let's take a look at this primary 3 word problem example:.

Watch the tutorial for free!

Sarah had some pens. She bought 34 pens. She then threw away 29 pens as they were spoilt. In the end, she had 64 pens. How many pens did Sarah have at first?

Identify the Concept

We know this is a Working Backwards question as…

Workings Explained

Always remember when we work backwards, everything will be reversed. Example the 2nd sentence – “She bought 34 pens”. We know when we buy things, we will have more. We need to add. However, when we work backwards, instead of adding, we need to subtract.

  • We will start drawing the model from the end by drawing a box and label it “End”. Put the end amount “64” in the box.
  • Draw arrow to point to the left, draw another box. On top of the arrow write “+29” as “Sarah threw away 29 pens”. Instead of subtract, we need to add. In the box, write “93” (64+29=93).
  • Draw another arrow to point to the left, draw another box. On top of the arrow, write “-34” as Sarah bought 34 pens. Instead of adding, we need to subtract. In the box, write “59” (93-34=59). Label the box “At First” or “Before”.

Sarah had 59 pens at first.

We know this is a Working Backwards question as we were not told the number of pens Sarah had but were asked for the number of pens she had at first.

See other problem-solving strategies and methods

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Working backwards

For problems where you need to create a timeline, meet a deadline, or understand the steps needed to complete a task, working backwards can be a great problem-solving process. To do this, imagine that the task has already been completed or the problem has already been solved with a satisfactory outcome, and work backwards to see what steps were taken to reach that result and when those steps needed to be completed by. Check out the example below to see how this technique works.

The working backwards technique in action

Ruth works in the admin department at a hospital and has just been given an important project to work on. They’ve recently started using a new computer system for the storage of medical files at the hospital, and Ruth needs to develop a training course to teach employees how to use the new system.

To help her plan what steps she needs to take to complete the project, Ruth decides to use the working backwards technique. First, she imagines the course in its completed form. She thinks about what information staff members need to learn and how it would need to function for it to be an effective training tool.

Now, Ruth works backwards to think about the steps that need to be taken to get the course to the completed form that she’s imagined. She also assigns a due date to each of these tasks to help keep the project on track. She does this by taking the deadline she has been given by her boss and working backwards. Here’s the plan she comes up with:

working backwards problem solving strategy

Ruth has worked backwards to figure out how much time she can spend on each step. She now has a clear plan of the steps she will take to complete the project, which she can use to measure her progress along the way. Without a plan like this, Ruth might spend too much time on one step, and not be able to complete another important task, like testing the course for bugs, before handing over the finished product.

Here’s another example of how the working backwards technique can be used:

  • Do you like to plan things out ahead of time? Why? Why not?
  • For example, working out a budget to save for something or planning a social event.

Think about your particular discipline or area of professional interest — what kind of problems or tasks arise in your area that the working backwards approach could help solve?

  • For example, in the area of business sustainability, the problem could be product packaging that is damaging to the environment. A Sustainability Manager who is tasked with reducing the impact of a company’s product packaging would first envision the end goal of packaging with minimal environmental impact, then they’d use the working backwards strategy to develop a plan with all the steps in between. These steps could be things like designing a sustainable packaging strategy, sourcing eco-friendly materials, and implementing changes in the manufacturing line. 

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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. As a simple example, suppose you had to pick up your child from football practice at exactly 5:00 p.m. At what time should you leave? Well, let us say it take 30 minutes to get to the ballpark. We would better leave a 5-minute safety valve. Okay, then we need to leave 35 minutes earlier, or not later than 4:25 p.m. Without even thinking about it, we were working backwards! Of course, this is a very simple example of this strategy…

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Problem-Solving Strategies in Mathematics

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Why the Most Forward-Thinking Product Teams Work Backwards

You’ve probably heard the old adage “success is not a destination, but a journey.” Clearly its authors were not product managers. Product teams aren’t measured on the winding road and applauded for the many steps taken—it’s all about results. Yet, we’re often so consumed with the process, routine, and endless cycle of building that we can forget none of that matters if the end result doesn’t meet our goals.

That’s why the best plans start with the final outcome. Productivity gurus FranklinCovey even trademarked this as one of their seven habits: Begin with the end in mind.

Many innovative companies have adopted this working backwards mindset to keep people from being distracted during the development process and maintain a singular focus on the ultimate goal.

For example, Amazon starts every project with the product manager authoring a press release articulating the current problem. They explore why other solutions aren’t cutting it, and how they’re solving things for the customer with their not-yet-built product. Throughout the entire product development process, anyone can refer back to that document as a guidepost, ensuring everything they do is making that press release a reality.

What is working backwards?

Working backwards is all about starting with the desired end result in mind and then figuring out how to get there. Although everyone should already do this, there are plenty of times when this isn’t the case.

The key to working backwards is crystalizing where you want to end up. This means diving into the details of what the desired end result should be (more sales, happier customers, easier workflows, etc.), what the product must be capable of to achieve those goals, and what success would look like.

Looking at Apple’s slick and popular product line, it’s obvious they were listening when Steve Jobs said “you have to start with the customer experience and work backwards towards the technology.”

With an agreed upon vision, the product team can then break down all of the required steps to reach that final destination. This differs from taking a more exploratory, iterative, “let’s see where this takes us” approach, or simply building stuff for the sake of building it.

Why the best product teams work backwards

Working backwards creates a more efficient and focused product development process. With a clearly articulated endpoint in mind, teams don’t get distracted or build the wrong things as they fumble forward. Instead, they know exactly what the finished product must be capable of, so they’re far more likely to get it right the first time.

This approach also prevents the team from getting lost in the weeds and worrying about implementation instead of results. As we’ve heard many times from our engineering counterparts: “Don’t tell me HOW to build it, just tell me WHAT to build.”

When you’re working backwards, the WHAT has already been very well-defined and no one will have any questions about whether the final product meets expectations. This not only gives clear guidelines to product development; it also provides QA with precise things to look for during their testing and gives a head start for sales and marketing since they know what they’re getting.

Prioritization also benefits from this approach; if a particular item doesn’t move the product closer to the desired finish line, then it takes a backseat to the items that do. It hones everyone in on satisfying customers and delivering value accordingly.

How to get your team to work backwards

Working backwards may be a state of mind, but getting the rest of the team on board might require something a little more tangible to wrap their heads around. Here are three methods for hitting “rewind” instead of “fast forward.”

Starting with a press release

Made famous by Amazon, the working backwards strategy is a favorite among many product teams and thought leaders. A press release is usually the very last step in the product development and launch process. It tells the world: “Here I am, this is what I can do, and this is why you should care.”

Learn the Anatomy of a Product Launch ➜

To be effective, the author must step back from the technobabble trap and communicate in terms that resonate with the target customer.

“One important element of the press release is that it is written in so-called ‘Oprah-speak’. Or in other words, a way that is easy to understand,” says Nikki Gilliard of Econsultancy. “This essentially allows Amazon to cut through tech-jargon and any descriptions that would only confuse the customer, in order to deliver a mainstream product.”

The starting point for the product definition is a customer-centric document, unconcerned with implementation details, technology or user interface design. Then, the focus shifts to what encompasses a truly great solution for the customer. If the press release is compelling, then you’re onto something.

“Iterating on a press release is a lot quicker and less expensive than iterating on the product itself,” says Amazon’s Ian McAllister . “If the press release is hard to write, then the product is probably going to suck. Keep working at it until the outline for each paragraph flows.”

But struggling to get the press release right is part of the process—if you could bang it out in an afternoon then you haven’t done the homework and made it bulletproof enough to drive an entire product development cycle.

“I created a couple of them in the past and it took me a lot of time; several weeks or even months actually, as the amount of time you need to dedicate on research is high, and trying to explain your idea like you would to real customers requires a lot of effort and dedication,” says Andrea Marchiotto of Unilever.

And because the press release is intended to declare the company’s success with the product—not just its availability—there must be a significant business case for it as well, which matches Amazon’s approach to selecting new features. For example, 90% of Amazon Web Services roadmap is driven by broad customer requests , indicating advance knowledge of a clear demand.

Read the Essential Feature Kickoff Checklist ➜

Conducting a pre-mortem

A post-mortem (or after-the-fact review of everything that went right or wrong during a project) is a common method for organizations to learn from previous mistakes and successes to perform even better the next time around. It’s a group affair where representatives from the entire organization chime in on what worked well and what went astray.

A pre-mortem essentially places that same group of stakeholders in a time machine and asks them to imagine everything that could happen before a single line of code is written or design is mocked up. The goal is anticipating and wargaming the situation, spotting all possible scenarios so the team has already anticipated potential stumbling blocks and land mines.

These sessions begin by brainstorming every possible calamity that could befall your product, from total market rejection to compromising user data to sluggish performance and inability to scale. It’s a chance to surface every fear and doubt lurking in people’s minds and determining which are more likely to actually occur.

“Once you’ve collectively established your highest risks, you can start thinking about ways to mitigate these risks. Realistically, you might not be able to stop all risks from happening,” says Marc Abraham of Settled. “In these scenarios, you can still figure out how to best reduce the impact of a risk happening and come up with a ‘plan B’.”

If the mitigation strategy isn’t obvious, a sub-team can be assigned to each outstanding item. Then, the team can work out how to deal with it if it arises (or fully preventing it from occurring at all). And with all potential horror show endings in view, the product team can work backwards minimizing or avoiding as much as possible.

Believe it or not, this might even serve as a bonding exercise for the team, forced to identify and grapple with possible unpleasantness and tap their problem-solving skills.

Begin with your Product Hunt page

Similar to the press release tactic, this method also requires the product team to identify its ideal output and work backwards from there.

Product Hunt is one of the leading showcases for new products and a semi-meritorious platform for building buzz and traffic from early adopters. A Product Hunt page includes a 60-character-max tagline, a thumbnail image, a gallery, a two-sentence description, three or four topics that your product fits into and then finally a “maker comment,” which according to the Product Hunt blog should:

“Briefly introduce yourself, the team, and the problem that you’re solving. In a total of 3–4 sentences explain what the value prop is, what’s the use case, who its for, and why you are building it. If this is the second time you’re launching on PH (i.e. a big product update or huge feature announcement), explain what’s changed. Tip: Make it as easy as possible for people to care.”

In total, you’ve got about seven or eight sentences and a few visuals to communicate what your product does, who would want to use it, why they should use it and what makes your product and team so special. Distilling your grand product vision down to this tiny bit of text is not only a great exercise in editing and brevity, but it also forces the team to really lock in on what’s most important.

With your faux Product Hunt page already authored, this artifact can be used to gain consensus in the organization and serve as ongoing inspiration during the product development. It’s conciseness and focus on the customer experience and value proposition is a great point to work backwards from.

Regardless of how you bring a working backwards mentality to your product team, the ingredient pulling everything together is truly understanding what customers need before you begin working on everything. If you haven’t done your homework in that department then your perfect final product may miss the mark, leading to a post-mortem that doesn’t do the product team any favors.

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Effective Problem-Solving Techniques in Business

Problem solving is an increasingly important soft skill for those in business. The Future of Jobs Survey by the World Economic Forum drives this point home. According to this report, complex problem solving is identified as one of the top 15 skills that will be sought by employers in 2025, along with other soft skills such as analytical thinking, creativity and leadership.

Dr. Amy David , clinical associate professor of management for supply chain and operations management, spoke about business problem-solving methods and how the Purdue University Online MBA program prepares students to be business decision-makers.

Why Are Problem-Solving Skills Essential in Leadership Roles?

Every business will face challenges at some point. Those that are successful will have people in place who can identify and solve problems before the damage is done.

“The business world is constantly changing, and companies need to be able to adapt well in order to produce good results and meet the needs of their customers,” David says. “They also need to keep in mind the triple bottom line of ‘people, profit and planet.’ And these priorities are constantly evolving.”

To that end, David says people in management or leadership need to be able to handle new situations, something that may be outside the scope of their everyday work.

“The name of the game these days is change—and the speed of change—and that means solving new problems on a daily basis,” she says.

The pace of information and technology has also empowered the customer in a new way that provides challenges—or opportunities—for businesses to respond.

“Our customers have a lot more information and a lot more power,” she says. “If you think about somebody having an unhappy experience and tweeting about it, that’s very different from maybe 15 years ago. Back then, if you had a bad experience with a product, you might grumble about it to one or two people.”

David says that this reality changes how quickly organizations need to react and respond to their customers. And taking prompt and decisive action requires solid problem-solving skills.

What Are Some of the Most Effective Problem-Solving Methods?

David says there are a few things to consider when encountering a challenge in business.

“When faced with a problem, are we talking about something that is broad and affects a lot of people? Or is it something that affects a select few? Depending on the issue and situation, you’ll need to use different types of problem-solving strategies,” she says.

Using Techniques

There are a number of techniques that businesses use to problem solve. These can include:

  • Five Whys : This approach is helpful when the problem at hand is clear but the underlying causes are less so. By asking “Why?” five times, the final answer should get at the potential root of the problem and perhaps yield a solution.
  • Gap Analysis : Companies use gap analyses to compare current performance with expected or desired performance, which will help a company determine how to use its resources differently or adjust expectations.
  • Gemba Walk : The name, which is derived from a Japanese word meaning “the real place,” refers to a commonly used technique that allows managers to see what works (and what doesn’t) from the ground up. This is an opportunity for managers to focus on the fundamental elements of the process, identify where the value stream is and determine areas that could use improvement.
  • Porter’s Five Forces : Developed by Harvard Business School professor Michael E. Porter, applying the Five Forces is a way for companies to identify competitors for their business or services, and determine how the organization can adjust to stay ahead of the game.
  • Six Thinking Hats : In his book of the same name, Dr. Edward de Bono details this method that encourages parallel thinking and attempting to solve a problem by trying on different “thinking hats.” Each color hat signifies a different approach that can be utilized in the problem-solving process, ranging from logic to feelings to creativity and beyond. This method allows organizations to view problems from different angles and perspectives.
  • SWOT Analysis : This common strategic planning and management tool helps businesses identify strengths, weaknesses, opportunities and threats (SWOT).

“We have a lot of these different tools,” David says. “Which one to use when is going to be dependent on the problem itself, the level of the stakeholders, the number of different stakeholder groups and so on.”

Each of the techniques outlined above uses the same core steps of problem solving:

  • Identify and define the problem
  • Consider possible solutions
  • Evaluate options
  • Choose the best solution
  • Implement the solution
  • Evaluate the outcome

Data drives a lot of daily decisions in business and beyond. Analytics have also been deployed to problem solve.

“We have specific classes around storytelling with data and how you convince your audience to understand what the data is,” David says. “Your audience has to trust the data, and only then can you use it for real decision-making.”

Data can be a powerful tool for identifying larger trends and making informed decisions when it’s clearly understood and communicated. It’s also vital for performance monitoring and optimization.

How Is Problem Solving Prioritized in Purdue’s Online MBA?

The courses in the Purdue Online MBA program teach problem-solving methods to students, keeping them up to date with the latest techniques and allowing them to apply their knowledge to business-related scenarios.

“I can give you a model or a tool, but most of the time, a real-world situation is going to be a lot messier and more valuable than what we’ve seen in a textbook,” David says. “Asking students to take what they know and apply it to a case where there’s not one single correct answer is a big part of the learning experience.”

Make Your Own Decision to Further Your Career

An online MBA from Purdue University can help advance your career by teaching you problem-solving skills, decision-making strategies and more. Reach out today to learn more about earning an online MBA with Purdue University .

If you would like to receive more information about pursuing a business master’s at the Mitchell E. Daniels, Jr. School of Business, please fill out the form and a program specialist will be in touch!

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  1. 5-4 Problem-Solving Strategy Use Logical Reasoning

  2. Problem Solving Heuristic: Working Backwards

  3. How to do a cartwheel backwards walkover and some beginner skills

  4. National 5 Maths

  5. Working backwards to problem solve addition and subtraction equations

  6. Problem Solving Track

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  1. Math Strategies: Problem Solving 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. It may also be helpful for students to understand that this is useful in many aspects of life, not just solving math problems.

  2. Reverse Your Thinking: Unleash the Power of Working Backward ...

    Working backward is a problem-solving strategy where you start from the desired end result or goal and work your way back to the initial conditions or starting point.. It's a useful technique ...

  3. Working backward to solve problems

    View full lesson: http://ed.ted.com/lessons/working-backward-to-solve-problems-maurice-ashleyImagine where you want to be someday. Now, how did you get there...

  4. Working Backwards Method

    Working backwards is a solving process that can be used on word problems by starting at the end of the problem and undoing the problem one step at a time. There are many different ways to solve ...

  5. Working backward to solve problems

    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. Working backward to solve problems - Maurice Ashley. Watch on.

  6. PDF Working Backwards

    Most problems in this set require you to work backwards. Working backwards is a particularly useful method in situations when the end result of a problem is known, and one has to find the initial quantity. If you are new to any of the problem solving strategies, check out our complete overview of elementary problem solving strategies at https ...

  7. 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...

  8. How to Work Backwards to Solve Problems

    Learn how to solve a problem by working backwards.We hope you are enjoying this video! For more in-depth learning, check out Miacademy.co (https://www.parent...

  9. PDF Problem Solving Strategy: Working Backwards

    Problem Solving Strategy: Working Backwards Kevin went to a fair with his friends Matt and Colleen. Read each friend's story to determine how much money each of them took to the fair. Kevin spent $2 on a ferris wheel ride. He bought Colleen popcorn for $1 and played ball toss 4 times trying to win a prize. Each round of ball toss cost $1.

  10. 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.

  11. 1.5: Problem Solving

    Problem Solving Strategy 3 (Working Backwards) This is considered a strategy in many schools. If you are given an answer, and the steps that were taken to arrive at that answer, you should be able to determine the starting point. Example \(\PageIndex{3}\) Karen is thinking of a number. If you double it and subtract 7, you obtain 11.

  12. PDF Working Backwards

    You may use the work-backwards strategy to solve the following simple math problems as well as the story problems in this Math Challenge. Start with the end result and undo each step or reverse the operation on each step. If you are new to the Math Challenge, feel free to learn about the different problem-solving strategies at

  13. Working Backwards Problem-Solving: The Method & Examples

    The scenario occurs when the quantity data is insufficient to work from the beginning.Working Backwards is a problem-solving strategy in which you start with the end goal and work backward to figure out the steps needed to get there. In other words, instead of starting from the beginning and moving forward, you start from the end and move backward.

  14. Working backwards

    For problems where you need to create a timeline, meet a deadline, or understand the steps needed to complete a task, working backwards can be a great problem-solving process. To do this, imagine that the task has already been completed or the problem has already been solved with a satisfactory outcome, and work backwards to see what steps were ...

  15. 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.

  16. Working Backwards

    Elementary Math Problem Solving - Working BackwardsIn this video, we explore one of eight problem-solving strategies for the primary math student. Students a...

  17. Problem-Solving Strategies: Definition and 5 Techniques to Try

    In insight problem-solving, the cognitive processes that help you solve a problem happen outside your conscious awareness. 4. Working backward. Working backward is a problem-solving approach often ...

  18. Work Backwards

    How can you solve the problem? You can work backwards from the time Jack reached Palo Alto. Subtract the time it took to walk from Los Altos to Palo Alto. Then subtract the time it took to walk from Santa Clara to Los Altos. 3) SOLVE: Start at 2:45. This is the time Jack reached Palo Alto. Subtract 25 minutes.

  19. Welcome to CK-12 Foundation

    Develop and use the strategy "Guess and Check." Develop and use the strategy "Work Backward." Plan and compare alternative approaches to solving problems. Solve real-world problems using selected strategies as part of a plan. Introduction In this section, you will learn about the methods of Guess and Check and Working Backwards. These ...

  20. PDF Working Backward

    Welcome to the Math Challenge #7. In this challenge, most problems can be solved by using the "Working Backwards" strategy. You will need to start with the final solution and work back one step at a time to get to the beginning. In mathematics, when we use the 'working backward' strategy, we can reverse the operation or use the

  21. Working Backwards: Problem Solving Strategy 3

    Two players take turns at removing 1 to 4 coins from an original pile of 16 coins. Is there a winning strategy for either player? These short videos are mean...

  22. Work Backwards

    Word Problems Solving Strategies. ... Work Backwards. Example. Guess and Check. Example. Draw a Picture. Example. Make a List. Example: Write a Number Sentence. Example. Use Logical Reasoning ...

  23. Working Backwards: Why the Best Product Teams Use This Method

    Working backwards may be a state of mind, but getting the rest of the team on board might require something a little more tangible to wrap their heads around. Here are three methods for hitting "rewind" instead of "fast forward." Starting with a press release. Made famous by Amazon, the working backwards strategy is a favorite among ...

  24. Effective Problem-Solving Techniques in Business

    Problem solving is an increasingly important soft skill for those in business. The Future of Jobs Survey by the World Economic Forum drives this point home. According to this report, complex problem solving is identified as one of the top 15 skills that will be sought by employers in 2025, along with other soft skills such as analytical thinking, creativity and leadership.