work backwards problem solving strategy

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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 .

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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

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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2.5.3: Guess and Check, Work Backward

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Guess and Check, Work Backward

Suppose that you and your brother both play baseball. Last season, you had 12 more hits than 3 times the number of hits that your brother had. If you had 159 hits, could you figure out how many hits your brother had?

More Problem Solving Strategies

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.

Develop and Use the Strategy: Guess and Check

The strategy for the “guess and check” method is to guess a solution and use that guess in the problem to see if you get the correct answer. If the answer is too big or too small, then make another guess that will get you closer to the goal. You continue guessing until you arrive at the correct solution. The process might sound like a long one; however, the guessing process will often lead you to patterns that you can use to make better guesses along the way.

Let's use the guess and check method to solve the following problem:

Nadia takes a ribbon that is 48 inches long and cuts it in two pieces. One piece is three times as long as the other. How long is each piece?

We need to find two numbers that add to 48. One number is three times the other number.

Guess 5 and 15. The sum is 5+15=20, which is too small.

Guess bigger numbers 6 and 18. The sum is 6+18=24, which is too small.

However, you can see that the previous answer is exactly half of 48.

Multiply 6 and 18 by two.

Our next guess is 12 and 36. The sum is 12+36=48. This is correct.

Develop and Use the Strategy: Work Backward

The “work backward” method works well for problems in which a series of operations is applied to an unknown quantity and you are given the resulting value. The strategy in these problems is to start with the result and apply the operations in reverse order until you find the unknown. Let’s see how this method works by solving the following problem.

Let's solve the following problem by working backwards :

Anne has a certain amount of money in her bank account on Friday morning. During the day she writes a check for $24.50, makes an ATM withdrawal of $80, and deposits a check for $235. At the end of the day, she sees that her balance is $451.25. How much money did she have in the bank at the beginning of the day?

We need to find the money in Anne’s bank account at the beginning of the day on Friday. From the unknown amount, we subtract $24.50 and $80 and we add $235. We end up with $451.25. We need to start with the result and apply the operations in reverse.

Start with $451.25. Subtract $235, add $80, and then add $24.50.

451.25−235+80+24.50=320.75

Anne had $320.75 in her account at the beginning of the day on Friday.

Plan and Compare Alternative Approaches to Solving Problems

Most word problems can be solved in more than one way. Often one method is more straightforward than others. In this section, you will see how different problem-solving approaches compare when solving different kinds of problems.

Now, let's solve the following problem by using the both the guess and check method and the working backward method:

Nadia’s father is 36. He is 16 years older than four times Nadia’s age. How old is Nadia?

This problem can be solved with either of the strategies you learned in this section. Let’s solve the problem using both strategies.

Guess and Check Method:

We need to find Nadia’s age.

We know that her father is 16 years older than four times her age, or 4× (Nadia’s age) + 16.

We know her father is 36 years old.

Work Backward Method:

Nadia’s father is 36 years old.

To get from Nadia’s age to her father’s age, we multiply Nadia’s age by four and add 16.

Working backward means we start with the father’s age, subtract 16, and divide by 4.

Example 2.5.3.1

Earlier, you were told that you had 12 more hits than 3 times the number of hits that your brother had. If you had 159 hits, how many hits did your brother have?

Since we know how many hits you had, we can work backward to determine the number of hits that your brother had.

Because you had 12 more hits than 3 times the number of hits that your brother had, we do the opposite: subtract 12 and divide by 3.

159−12=147

147÷3=49

Your brother had 49 hits.

Example 2.5.3.2

Hana rents a car for a day. Her car rental company charges $50 per day and $0.40 per mile. Peter rents a car from a different company that charges $70 per day and $0.30 per mile. How many miles do they have to drive before Hana and Peter pay the same price for the rental for the same number of miles?

Hana’s total cost is $50 plus $0.40 times the number of miles.

Peter’s total cost is $70 plus $0.30 times the number of miles.

Guess the number of miles and use this guess to calculate Hana’s and Peter’s total cost.

Keep guessing until their total cost is the same.

Guess 50 miles.

Check $50+$0.40(50)=$70 $70+$0.30(50)=$85

Guess 60 miles.

Check $50+$0.40(60)=$74 $70+$0.30(60)=$88

Notice that for an increase of 10 miles, the difference between total costs fell from $15 to $14. To get the difference to zero, we should try increasing the mileage by 140 miles.

Guess 200 miles

Check $50+$0.40(200)=$130 $70+$0.30(200)=$130correct

• Nadia is at home and Peter is at school, which is 6 miles away from home. They start traveling toward each other at the same time. Nadia is walking at 3.5 miles per hour and Peter is skateboarding at 6 miles per hour. When will they meet and how far from home is their meeting place?
• Peter bought several notebooks at Staples for $2.25 each and he bought a few more notebooks at Rite-Aid for $2 each. He spent the same amount of money in both places and he bought 17 notebooks in total. How many notebooks did Peter buy in each store?
• Andrew took a handful of change out of his pocket and noticed that he was holding only dimes and quarters in his hand. He counted that he had 22 coins that amounted to $4. How many quarters and how many dimes does Andrew have?
• Anne wants to put a fence around her rose bed that is one-and-a-half times as long as it is wide. She uses 50 feet of fencing. What are the dimensions of the garden?
• Peter is outside looking at the pigs and chickens in the yard. Nadia is indoors and cannot see the animals. Peter gives her a puzzle. He tells her that he counts 13 heads and 36 feet and asks her how many pigs and how many chickens are in the yard. Help Nadia find the answer.
• Andrew invests $8000 in two types of accounts: a savings account that pays 5.25% interest per year and a more risky account that pays 9% interest per year. At the end of the year, he has $450 in interest from the two accounts. Find the amount of money invested in each account.
• There is a bowl of candy sitting on our kitchen table. This morning Nadia takes one-sixth of the candy. Later that morning Peter takes one-fourth of the candy that’s left. This afternoon, Andrew takes one-fifth of what’s left in the bowl and finally Anne takes one-third of what is left in the bowl. If there are 16 candies left in the bowl at the end of the day, how much candy was there at the beginning of the day?
• Nadia can completely mow the lawn by herself in 30 minutes. Peter can completely mow the lawn by himself in 45 minutes. How long does it take both of them to mow the lawn together?

Mixed Review

• Rewrite √500 as a simplified square root.
• To which number categories does −2/13 belong?
• Simplify 1/2|19−65|−14.
• Which property is being applied? 16+4c+11=(16+11)+4c
• Is {(4,2),(4,−2),(9,3),(9,−3)} a function?
• Write using function notation: y=(1/12)x−5.
• Jordyn spent $36 on four cases of soda. How much was each case?

Review (Answers)

To see the Review answers, open this PDF file and look for section 2.14.

Additional Resources

Activity: Guess and Check, Work Backward Discussion Questions

Practice: Guess and Check, Work Backward

Real World Application: Car Loan

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Working backward to solve problems - maurice ashley.

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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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Question: Jack walked from Santa Clara to Palo Alto. It took 1 hour 25 minutes to walk from Santa Clara to Los Altos. Then it took 25 minutes to walk from Los Altos to Palo Alto. He arrived in Palo Alto at 2:45 P.M. At what time did he leave Santa Clara? Strategy: 1) UNDERSTAND: What do you need to find? You need to find what the time was when Jack left Santa Clara. 2) PLAN: 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. This is the time it took to get from Los Altos to Palo Alto. Time is: 2:20 P.M. Subtract: 1 hour 25 minutes. This is the time it took to get from Santa Clara to Los Altos.. Jack left Santa Clara at 12:55 P.M.

Working Backwards: A Strategic Approach to Productivity

This guide will walk you through the essential elements of using working backwards - the productivity method to keep your team productive and engaged.

In today's fast-paced world, the concept of working backwards has gained significant attention as a strategic approach to productivity. In this comprehensive guide, we will explore the origin, utility, methods, as well as the pros and cons of working backwards, and provide a detailed step-by-step guide for implementing this approach effectively. Additionally, actionable tips, do's and dont's, and frequently asked questions will be addressed to ensure a thorough understanding of this concept. Whether you are an individual striving for personal efficiency, a team leader looking to streamline processes, or an organization aiming for innovation and growth, the principles of working backwards can be a valuable asset. Let's delve into this powerful methodology and uncover how it can revolutionize your approach to problem-solving, planning, and goal attainment.

What is Working Backwards in the Context of Productivity?

In the realm of productivity, the concept of working backwards entails beginning with the end goal in mind and then structuring the steps required to achieve it. This approach involves envisioning the desired outcome and systematically plotting the reverse steps necessary to reach that outcome. It underscores the significance of clear, well-defined objectives as a precursor to formulating the path leading up to them.

By utilizing this methodology, individuals and organizations can align their efforts, resources, and strategies in a manner that is directly linked to achieving the intended results. This approach is particularly pertinent in scenarios where the ultimate goal is clearly defined, but the means to attainment are open to exploration and refinement. Working backwards beckons a shift in perspective, cultivating a mindset that is oriented towards thoroughly analyzing and understanding the end goal before embarking on the journey towards it.

This novel approach to productivity has garnered attention not only in corporate settings but also in personal development, project management, and various aspects of problem-solving.

Origin of Working Backwards

The concept of working backwards finds its roots in diverse domains, particularly in problem-solving methodologies. It has been a fundamental aspect of various innovation and strategic planning processes across different industries. The origin of this approach can be traced back to the techniques employed in fields such as engineering, design thinking, Agile project management, and software development.

In addition, the methodology has been prominently featured in the operational strategies of renowned companies, notably exemplified by its integration into Amazon's product development and strategic decision-making processes. Amazon's adoption of the working backwards approach has propelled its innovative endeavors, playing a pivotal role in the company's success and global impact.

The concept's evolution as a foundational principle in strategic planning and execution underscores its versatile applicability and enduring relevance in diverse contexts.

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Who is Working Backwards For?

Working backwards is a versatile methodology that caters to a broad spectrum of individuals, teams, and organizations seeking to elevate their productivity, streamline their operations, and drive towards well-defined objectives. This approach is particularly beneficial for:

Innovators and Entrepreneurs : Individuals seeking to introduce groundbreaking products or pioneering solutions can benefit from the structured approach offered by working backwards, aiding in the comprehensive delineation of their vision.

Project Managers and Teams : Project managers and teams can leverage this approach to meticulously plan and execute projects, ensuring that every step aligns with the overall project goals.

Strategic Planners and Decision-makers : Professionals involved in strategic planning and decision-making can utilize this methodology to set clear, achievable targets and steer their organizations towards success.

Individuals Pursuing Personal Goals : The process of working backwards can be applied by individuals striving to achieve personal milestones, whether in terms of career progression, skill enhancement, or lifestyle transformations.

The widespread applicability of this approach underscores its relevance across various domains and its potential to drive impactful outcomes.

What are the Pros and Cons of Working Backwards?

Pros of working backwards.

The working backwards approach offers a multitude of benefits, making it an attractive productivity strategy for individuals and organizations alike. Some of the key advantages include:

Clarity and Precision : By commencing with a definitive end goal and working backwards, clarity and precision are fostered throughout the planning and execution phases, ensuring a clear trajectory towards the intended outcome.

Efficient Resource Allocation : This method enables the efficient allocation of resources by aligning them with the specific requirements and milestones identified during the working backwards process.

Risk Mitigation : Working backwards allows for a comprehensive analysis of potential pitfalls and challenges, thereby facilitating proactive risk mitigation strategies as part of the planning process.

Enhanced Innovation : The systematic approach of working backwards nurtures an environment conducive to innovation and unconventional thinking, often leading to breakthrough solutions and novel approaches.

Adaptability and Flexibility : The iterative nature of working backwards allows for adaptability and flexibility, empowering individuals and teams to adjust their strategies and tactics in response to evolving circumstances.

Cons of Working Backwards

While the working backwards methodology offers substantial advantages, it is imperative to consider potential drawbacks, including:

Complexity in Implementation : The detailed nature of this approach may result in a more intricate planning and execution process, potentially demanding additional time and resources.

Potential Over-analysis : There is a risk of over-analyzing the reverse steps, possibly leading to delays in the commencement of actions and initiatives.

Dynamic Environment Management : Adapting the planned steps to accommodate unexpected changes in a dynamic environment may necessitate ongoing evaluation and adjustment.

Striking a balance between the benefits and drawbacks is crucial for effectively implementing the working backwards methodology.

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How to Get Started with Working Backwards

Embarking on the journey of working backwards involves a deliberate and systematic approach, encompassing several key phases. The initial steps include defining the desired outcome, articulating the reverse steps, and committing to iterative refinement. Let's explore these fundamental stages in greater detail.

Step-by-Step Guide for Working Backwards

Step 1: define the end goal.

The primary phase of working backwards involves clearly defining the end goal or desired outcome. At this stage, it's imperative to articulate the specific objectives and results that are to be achieved. This pivotal step sets the foundation for the subsequent phases, guiding the formation of the reverse action plan.

Step 2: Identify Key Milestones

Once the end goal is defined, the next step entails identifying the key milestones and intermediate objectives that collectively lead to the attainment of the ultimate target. This stage involves delineating the critical stages and achievements that mark the progression towards the end result.

Step 3: Outline the Reverse Action Plan

With the end goal and milestones established, the reverse action plan is formulated, detailing the steps required to reach each milestone and, subsequently, the final objective. This involves structuring the sequence of actions in a reverse order, commencing from the last step and progressing towards the initial phase.

Step 4: Iterative Refinement

The iterative refinement stage involves continuous evaluation and refinement of the action plan based on feedback, insights, and evolving circumstances. This iterative process ensures that the plan remains adaptable and responsive to changes.

By systematically traversing through these sequential steps, individuals and teams can effectively embrace the working backwards approach, infusing precision and purpose into their endeavors.

Actionable Tips for Working Backwards

Incorporating working backwards into your productivity arsenal can be enhanced by integrating the following actionable tips:

Embrace Iterative Thinking : Cultivate a mindset that welcomes iterative thinking and planning, facilitating continuous improvement and adaptability.

Leverage Feedback Loops : Establish feedback loops within the planning process to solicit insights and perspectives that can drive refinement and enhancement.

Foster Open Communication : Encourage open communication and collaboration among team members to cultivate a holistic understanding of the working backwards methodology.

Maintain a Clear Vision : Uphold a clear and articulate vision of the end goal to channel efforts and resources effectively throughout the reverse planning process.

Do's and Dont's

Below is a concise representation of the essential do's and dont's to consider when embracing the concept of working backwards:

In conclusion, working backwards offers a powerful and systematic approach to aligning efforts and resources with the attainment of well-defined objectives. By crystallizing the end goal, mapping out the reverse steps, and embracing iterative refinement, individuals and organizations can navigate their journeys with purpose and precision. The methodology's versatility and adaptability render it a valuable asset in diverse domains, empowering innovators, project managers, strategic planners, and individuals pursuing personal goals. Embracing the principles of working backwards can enrich problem-solving, strategic planning, and goal attainment endeavors, charting a course towards impactful and enduring success.

1. What are the primary industries where working backwards is commonly applied?

The working backwards methodology finds extensive application in domains such as product development, strategic planning, project management, and innovation-driven industries.

2. How does working backwards foster innovation and unconventional thinking?

By encouraging a structured yet flexible approach, working backwards provides a conducive environment for nurturing innovative thinking, enabling individuals and teams to explore unconventional solutions and approaches.

3. Can working backwards be applied to personal goal setting?

Absolutely. The methodology can be leveraged by individuals pursuing personal goals, as it allows for a systematic approach to defining objectives and formulating the steps necessary to achieve them.

4. How does iterative refinement contribute to the effectiveness of working backwards?

Iterative refinement ensures that the reverse action plan remains adaptable and responsive to changes, thereby enhancing its relevance and efficacy in dynamic environments.

5. What pivotal role does clear communication play in the success of the working backwards approach?

Clear and open communication conduces to fostering a shared understanding and commitment to the predefined goals and action steps, catalyzing the collective efforts towards success.

By integrating these guidelines and insights into your projects and endeavors, you can harness the power of working backwards to catalyze your journey towards triumph and innovation.

Remember, success is not achieved by chance, but through deliberate strategy and purposeful execution. Embrace the principles of working backwards, and unlock the potential for transformative achievements and enduring excellence.

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Module 1: Problem Solving Strategies

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Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1

1. Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY

In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

First, you have to understand the problem.

After understanding, then make a plan.

Carry out the plan.

Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

Problem Solving Strategy 1 (Guess and Test)

Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution.

Mr. Jones has a total of 25 chickens and cows on his farm. How many of each does he have if all together there are 76 feet?

Step 1: Understanding the problem

We are given in the problem that there are 25 chickens and cows.

All together there are 76 feet.

Chickens have 2 feet and cows have 4 feet.

We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.

Step 2: Devise a plan

Going to use Guess and test along with making a tab

Many times the strategy below is used with guess and test.

Make a table and look for a pattern:

Procedure: Make a table reflecting the data in the problem. If done in an orderly way, such a table will often reveal patterns and relationships that suggest how the problem can be solved.

Step 3: Carry out the plan:

Notice we are going in the wrong direction! The total number of feet is decreasing!

Better! The total number of feet are increasing!

Step 4: Looking back:

Check: 12 + 13 = 25 heads

24 + 52 = 76 feet.

We have found the solution to this problem. I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.

Videos to watch:

1. Click on this link to see an example of “Guess and Test”

http://www.mathstories.com/strategies.htm

2. Click on this link to see another example of Guess and Test.

http://www.mathinaction.org/problem-solving-strategies.html

Check in question 1:

Place the digits 8, 10, 11, 12, and 13 in the circles to make the sums across and vertically equal 31. (5 points)

Check in question 2:

Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet . How many of each animal does he have? Make sure you use Polya’s 4 problem solving steps. (12 points)

Problem Solving Strategy 2 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric thinking visually can help!

Videos to watch demonstrating how to use "Draw a Picture".

1. Click on this link to see an example of “Draw a Picture”

2. Click on this link to see another example of Draw a Picture.

Problem Solving Strategy 3 ( Using a variable to find the sum of a sequence.)

Gauss's strategy for sequences.

last term = fixed number ( n -1) + first term

The fix number is the the amount each term is increasing or decreasing by. "n" is the number of terms you have. You can use this formula to find the last term in the sequence or the number of terms you have in a sequence.

Ex: 2, 5, 8, ... Find the 200th term.

Last term = 3(200-1) +2

Last term is 599.

To find the sum of a sequence: sum = [(first term + last term) (number of terms)]/ 2

Sum = (2 + 599) (200) then divide by 2

Sum = 60,100

Check in question 3: (10 points)

Find the 320 th term of 7, 10, 13, 16 …

Then find the sum of the first 320 terms.

Problem Solving Strategy 4 (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.

Videos to watch demonstrating of “Working Backwards”

https://www.youtube.com/watch?v=5FFWTsMEeJw

Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number?

1. We start with 11 and work backwards.

2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.

3. The opposite of doubling something is dividing by 2. 18/2 = 9

4. This should be our answer. Looking back:

9 x 2 = 18 -7 = 11

5. We have the right answer.

Check in question 4:

Christina is thinking of a number.

If you multiply her number by 93, add 6, and divide by 3, you obtain 436. What is her number? Solve this problem by working backwards. (5 points)

Problem Solving Strategy 5 (Looking for a Pattern)

Definition: A sequence is a pattern involving an ordered arrangement of numbers.

We first need to find a pattern.

Ask yourself as you search for a pattern – are the numbers growing steadily larger? Steadily smaller? How is each number related?

Example 1: 1, 4, 7, 10, 13…

Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19.

Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4.

So the next number would be

25 + 11 = 36

Example 3: 10, 7, 4, 1, -2… find the next 2 numbers.

In this sequence, the numbers are decreasing by 3. So the next 2 numbers would be -2 -3 = -5

-5 – 3 = -8

Example 4: 1, 2, 4, 8 … find the next two numbers.

This example is a little bit harder. The numbers are increasing but not by a constant. Maybe a factor?

So each number is being multiplied by 2.

16 x 2 = 32

1. Click on this link to see an example of “Looking for a Pattern”

2. Click on this link to see another example of Looking for a Pattern.

Problem Solving Strategy 6 (Make a List)

Example 1 : Can perfect squares end in a 2 or a 3?

List all the squares of the numbers 1 to 20.

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400.

Now look at the number in the ones digits. Notice they are 0, 1, 4, 5, 6, or 9. Notice none of the perfect squares end in 2, 3, 7, or 8. This list suggests that perfect squares cannot end in a 2, 3, 7 or 8.

How many different amounts of money can you have in your pocket if you have only three coins including only dimes and quarters?

Quarter’s dimes

0 3 30 cents

1 2 45 cents

2 1 60 cents

3 0 75 cents

Videos demonstrating "Make a List"

Check in question 5:

How many ways can you make change for 23 cents using only pennies, nickels, and dimes? (10 points)

Problem Solving Strategy 7 (Solve a Simpler Problem)

Geometric Sequences:

How would we find the nth term?

Solve a simpler problem:

1, 3, 9, 27.

1. To get from 1 to 3 what did we do?

2. To get from 3 to 9 what did we do?

Let’s set up a table:

Term Number what did we do

Looking back: How would you find the nth term?

Find the 10 th term of the above sequence.

Let L = the tenth term

Problem Solving Strategy 8 (Process of Elimination)

This strategy can be used when there is only one possible solution.

I’m thinking of a number.

The number is odd.

It is more than 1 but less than 100.

It is greater than 20.

It is less than 5 times 7.

The sum of the digits is 7.

It is evenly divisible by 5.

a. We know it is an odd number between 1 and 100.

b. It is greater than 20 but less than 35

21, 23, 25, 27, 29, 31, 33, 35. These are the possibilities.

c. The sum of the digits is 7

21 (2+1=3) No 23 (2+3 = 5) No 25 (2 + 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. Also we notice 25 is divisible by 5. By using the strategy elimination, we have found our answer.

Check in question 6: (8 points)

Jose is thinking of a number.

The number is not odd.

The sum of the digits is divisible by 2.

The number is a multiple of 11.

It is greater than 5 times 4.

It is a multiple of 6

It is less than 7 times 8 +23

What is the number?

Click on this link for a quick review of the problem solving strategies.

https://garyhall.org.uk/maths-problem-solving-strategies.html

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20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

• Draw a model
• Use different approaches
• Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

• The context
• What the key information is
• How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Similarly, you could draw a model to represent the objects in the problem:

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

• Understand the problem
• Devise a plan
• Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

How Third Space Learning improves problem-solving 

Resources .

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking. 

Explore the range of problem solving resources for 2nd to 8th grade students. 

One-on-one tutoring 

Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE : 8 Common Core math examples

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies of problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

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Differentiated Instruction: 9 Differentiated Curriculum And Instruction Strategies For Teachers 

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Working Backwards at KS2

Working backwards can be a very useful problem-solving skill.  These activities lend themselves to being tackled in this way.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Junior Frogs

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Would You Rather?

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

First Connect Three

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Multiplication Squares

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

What's in the Box?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Andy's Marbles

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

Can you go through this maze so that the numbers you pass add to exactly 100?

All the Digits

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Mystery Matrix

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Counting Cards

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Nice or Nasty

There are nasty versions of this dice game but we'll start with the nice ones...

Missing Multipliers

What is the smallest number of answers you need to reveal in order to work out the missing headers?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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How to work by working backwards (the Amazon method)

One of the most successful product organizations over the past 20 years is Amazon. As of 2022, the US census shows there are 131.2 million households in the US, and Amazon is estimated to have north of 150 million US-based members in its “Amazon Prime” membership program.

So how did they do it?

In this article, we’ll break down what working backwards, aka the Amazon method, is and how it became so successful. We’ll talk about how it works, how Amazon applies working backwards throughout their organization, and its benefits.

Background information

Working backwards is known interchangeably as the Amazon method. But their idea to work backwards had to start somewhere, right?

Amazon started this by turning to the advice of one of the best-selling nonfiction books of all time: Stephen Covey’s The 7 Habits of Highly Effective People . In particular, Amazon’s product organization leans hard on “Habit #2: Begin with the End in Mind.”

Beginning with the end in mind is designed to train individuals to “create” things twice: once in their imagination and then once in real life. It results in several benefits:

• A clearer vision
• An orientation set on a goal (vs. a solution or activity)
• Early thoughts on if the goal is achievable and how

“People are working harder than ever, but because they lack clarity and vision, they aren’t getting very far. They, in essence, are pushing a rope with all of their might” — Stephen Covey

How working backwards works

So how does one work backwards and begin with the end in mind? Stephen Covey presents a few ideas:

Define the end result

The delta between being a product manager and a product leader is this orientation. Product managers focus on efficiency. Product leaders focus on setting a strategic vision. Try asking yourself:

• What are we trying to accomplish?
• What do I hope we become?
• What business do I want to be in tomorrow? Five years from now, what do I hope they say about my product?

Then craft a mission statement

A well-written mission statement gives everyone the framework and the ability to autonomously make decisions aimed in the same direction. It should lay out why your product exists and what makes it different. Consider four elements:

• Value — what problem are you solving, and for whom?
• Purpose — what greater good will your product provide; what’s the meaning behind your work?
• Attainability — while the mission statement should be challenging, it must be perceived to be plausible
• Specificity — be equal parts broad and narrow; do not seek to be all things to all people, but leave it relatively open for pivots as you learn

Ensure that this is short, puts goals into focus, and charts a path to move the vision into reality.

How the Amazon method applies this guidance

Some companies practice product development by beginning with a solution, engineering it, then asking their marketing team to find customers for it. Amazon does the opposite.

They invest heavily in the upfront process of discovery , ensuring that the customer problem is intricately known and detailed — including the context around when the problem occurs and the benefit of solving it.

This results in the product manager writing a draft press release announcing the product they are pitching to create. Ian McCallister, the former director of Amazon Smile, shared some of the document’s requirements in a Quora post that’s since been taken down:

• Heading: name the product in a way the reader will understand
• Subheading: describe who the market for the product is and what benefit they get. Limit it to one sentence
• Problem: describe the problem your product solves
• Solution: describe how your product elegantly solves the problem
• Quote from you: a quote from a spokesperson in the company
• How to get started: describe how easy it is to get started
• Customer quote: provide a quote from a hypothetical customer that describes how they experienced the benefit
• Closing and call to action: wrap it up and give pointers on where the reader should go next

Typically, these documents are limited to one to one-and-a-half pages and are silently read at the beginning of meetings. The merits are debated, feedback is given, and product managers end up making multiple revisions to the press release. This saves Amazon time and money, as changing a Google Doc is a lot less expensive than changing code.

Amazon Kindle started as a press release, as did Amazon Prime and AWS.

The main benefit of working backwards

There’s one key benefit to this method, and it’s how it forces design thinking .

There’s an oft-shared quote in the startup world that has been attributed to way too many people to list: “Fall in love with the problem… not the solution.”

Most products fail because they begin with a solution and jump immediately to how to bring it to life and when.

The best products in the world are created when people start with a problem (the “why”) and end with the what, how, and when.

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Whichever orientation (solution versus problem) the team begins with is likely the one they’ll fall in love with. They’re likely to become attached to it and fail to refine details against it.

• If a team becomes attached to a customer problem, they’ll burn cycles trying to come up with a solution tied to it
• If a team becomes attached to a solution, they’ll burn cycles trying to come up with a customer problem tied to it

Potential troubles with working backwards

The benefit of working backwards — that it creates a destination — is also its Achilles’ heel. If the uncertainty is still high, it can cause premature convergence on a specific idea without enough time given to weigh alternatives. Be careful in employing this approach if either of these two factors are at play:

• Significant time pressure — speed can cause biases and premature convergence to enter your solution
• High degrees of uncertainty — specifying a set environment that is only moderately likely to happen can force rigidity that will cause your team to fail later

Working backwards, aka the Amazon method, changed the way product organizations run. By considering and implementing this method, you can be one of these best products by beginning with the end in mind — aka defining the problem to solve, the “why” — and following that with a well-crafted vision (aka press release) that inspires and guides a group of like-minded people to deliver that outcome to the world.

Working backwards ensures that you and your team have a clear alignment between intentions and a meaningful problem to solve.

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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.”

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.

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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