blake education problem solving working backwards

Fun teaching resources & tips to help you teach math with confidence

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 .

* Please Note : This post contains affiliate links which help support the work of this site. Read our full disclosure here .*

–>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!

• Pingback: 6th Grade Week 11: Monks, Mosques, and Minecraft • The Sunny Patch

Comments are closed.

Similar Posts

Division Debate: Do Kids Need Long Division?

Sidewalk Chalk Jumping Maze Math Challenge

Have You Checked Out Noodle Education?

Multiplying Large Numbers with a Table: Building Number Sense

Pythagorean Theorem Lego Proof

Number Bond Rainbows

Find more resources to help make math engaging, join 165k+ parents & teachers.

Who learn new tips and strategies, as well as receive engaging resources to make math fun!

• Privacy Policy

All Formats

Resource types, all resource types.

• Rating Count
• Price (Ascending)
• Price (Descending)
• Most Recent

Problem solving working backwards

Work Backwards Problem Solving PowerPoint, Task Cards and Worksheet

Working Backwards Strategy Problem Solving

• Google Apps™

Blake's Topic Bank - Problem Solving : Working Backwards

Problem Solving Unit 5: Work Backwards

Everyday Math 2: 8 - Problem Solving - Working Backwards

Problem Solving Strategies - Work Backwards

Working Backwards : Problem Solving with Maze Puzzles

Working Backwards Problem Solving Strategy-Chevron

Multistep Problem Solving Using the Skill of: Working Backwards

• Word Document File

Working Backwards : Problem Solving Strategy Cards-Brush Strokes

Problem Solving Strategy - Working Backwards

Problem Solving - Working Backwards

Working Backwards Problem Solving

Math Problems ? No Problem ! (Grade 5-6): problem - solving questions and strategies

Problem Solving Strategy Posters

Problem Solving : Classroom Display

Spooky Halloween Math Problems | Math Problem Solving Activities

Math Problems ? No Problem ! (Grade 5-8 Bundle) - problem solving questions

Math Problem Solving Strategies Anchor Chart

Math Problems ? No Problem ! (Set 3): problem - solving questions and strategies

Problem Solving Strategies for Math Poster

Problem Solving Strategies Posters

Problem Solving Strategies Posters- Solve it like a Superhero!!

Math Problem Solving Strategies Posters, Set of 9

• We're hiring
• Help & FAQ
• Privacy policy
• Student privacy
• Terms of service
• Tell us what you think

Working Backwards: Strategic Approach to Challenges

In the fast-paced and ever-evolving world we inhabit, challenges are as constant as the ticking of a clock. The Working Backwards Strategy is a beacon of hope amidst the formidable waves of complexity that confront individuals and organizations alike. In essence, this strategic approach is a clarion call to begin where most end – the desired outcome. By flipping conventional problem-solving on its head, this strategy empowers us to navigate through the murky waters of uncertainty and forge a clear path towards our goals.

The relevance of the Working Backwards Strategy can hardly be overstated - it imparts a robust framework to individuals and enterprises for overcoming challenges that may at first appear insurmountable. This article illuminates the intricate cogs and wheels that constitute the strategic approach to problem-solving, thereby equipping readers with an arsenal of tactics to conquer the obstacles that beset their paths.

As we embark on this enlightening journey through the annals of the Working Backwards Strategy , we will dissect its historical underpinnings, explore its mechanics, and glean insight from real-world applications. This expedition promises not just theoretical knowledge but also practical wisdom, aiding our understanding of how this approach dovetails seamlessly with innovative thinking to produce remarkable results.

The Genesis of Working Backwards Strategy

The Working Backwards Strategy is more than a mere tactic; it is a paradigm shift that has its roots firmly planted in a historical context. Its origin can be traced back to the stoic philosophers, who often emphasized the significance of visualizing the end to make sense of the present. Fast forward to the modern era, and we observe that this strategy has been honed and tailored to address the complexities of contemporary problems, particularly in business and technology.

Innovation has become the lifeblood of today's corporate giants and disruptive startups. The Working Backwards Strategy is paramount in this arena as it encourages an outcome-oriented outlook. When the endpoint is clear and immovable, the path to reach it can be crafted with precision and agility, aligning perfectly with the demands for creative and divergent thinking.

Not only does the strategy align with the forces of change propelling today's markets, but it also synergizes with the kind of innovative thinking that paves the way for groundbreaking advances. Even in a world that venerates forward-thinking, looking backwards from the future to the present offers the clarity needed to cut through the noise and home in on what truly matters.

Understanding the Mechanics of Working Backwards

Central to the Working Backwards Strategy are several core principles that guide its disciplined application. This strategy necessitates a departure from linear planning and proffers a more cyclic and iterative model of strategy development. It asks us to start with the customer experience and work our way to the minimum set of creative solutions needed to meet that experience.

Step 1: Identifying the ideal end-state

The inception of this journey demands a clear definition of the ultimate goal. This vision serves as a lighthouse, guiding all subsequent decisions and strategies. By envisioning the ideal end-state, one can crystallize their objectives and garner insight into the expectations that need fulfillment. Understanding the final destination is crucial as it underpins the entire process that follows.

Step 2: Establishing key milestones

Once a clear endpoint is discerned, the next phase involves charting out significant milestones. These act as checkpoints that help track progress and ensure that all efforts are congruent with the ultimate goal. Milestones define the critical junctures in the journey to success and lay out the high-level strategy that must be followed.

Step 3: Creating a reverse action plan

The creation of a reverse action plan is where the strategy takes tangible form. This plan draws directly from the identified milestones and sketches a backward path to the present. Each step is scrutinized through the lens of necessity and efficaciousness, with the primary criterion being its contribution to reaching the end goal.

This tactical phase is also where innovative thinking comes into full play. Understanding that the desired future state might require unprecedented solutions, practitioners of this strategy are encouraged to adopt an explorative mindset, entertain unconventional ideas, and remain adaptable in their approach.

Application in Various Contexts

Overcoming challenges in business development.

Example: Product development in tech companies

In the realm of technology, the strategy has proven instrumental in navigating the turbulent waters of product development. Take, for instance, the creation of a new software platform. Working Backwards entails envisioning the complete, seamless user experience before writing a single line of code. By focusing on the desired utility and ease of use, tech companies can reverse engineer the process to ensure each development phase contributes directly to the end user's needs.

Example: Marketing strategies in startups

For startups, crafting a marketing strategy can be a daunting task with resource limitations. Working Backwards from the client acquisition targets can help startups prioritize high-impact marketing efforts and optimize the allocation of their limited resources. This approach allows them to carve a niche in the market while ensuring sustainability and growth.

Problem-Solving Techniques in Personal Goals

Example: Career advancement planning

Working Backwards is not confined to the corporate and technological spheres - it's equally applicable to personal development areas such as career planning. By starting with the end goal of a desired job position, one can delineate the certifications, skills, and experiences required to achieve it. Opting for a problem solving course or an online mba course might emerge as pivotal steps in this tailored plan.

Example: Educational achievements

Students aiming for high academic achievement can also benefit from this strategy. By picturing their names on the dean's list, they can craft a detailed study schedule that revolves around this goal, carefully selecting the courses and extracurricular activities that align with their academic aspirations.

The Working Backwards Strategy has cemented itself as an essential component of the problem-solver's toolkit, offering a robust and strategic scaffold for surmounting challenges across a spectrum of domains. In reflecting on its utility, the strategy's penchant for fostering innovative thinking and meticulous goal orientation stands out as particularly compelling.

As we draw this exploration to a close, it becomes evident that the Working Backwards Strategy beckons individuals and organizations to re-evaluate traditional paradigms in favor of a more outcome-centric and proactive approach to problem-solving. It is a call to action, urging us to adopt this strategy with a view toward fostering innovation and strategic growth in our respective endeavors.

Now is the moment to harness the transformative power of the Working Backwards Strategy . Embrace this strategic approach in your professional pursuits, educational goals, or personal development plans. Tackle your current challenges with an innovative lens and backward vision. For those seeking to delve deeper into the intricacies of strategic problem-solving, resources abound; extending from literature to problem solving courses and online MBA courses designed to inculcate the principles of this efficacious strategy.

Equip yourself with the knowledge and tools necessary to convert your aspirations into achievements. Remember, the journey to success is often charted by looking to the end and crafting your pathway backward.

What is the conceptual framework of the working backwards approach to problem-solving?

The working backwards approach: a conceptual framework.

The working backwards approach stands as a revered method in problem-solving. It starts with the desired outcome. This involves envisioning the ideal solution or end-point before anything else. After defining the end goal, one must then deconstruct it, breaking down the steps that lead to this outcome, in reverse. This retrospective path mapping distinguishes the working backwards strategy from other techniques.

Core Principles of Working Backwards

Identify the end goal first . Clarity of the objective remains paramount. Without a clear target, the process loses direction.

Deconstruct the problem . Break it down into smaller, manageable segments. Each segment acts as a milestone. Experts agree on the efficacy of this subdivision.

Reverse engineer the process . Working from the end backwards, the solver identifies the prerequisites for each milestone. This allows for a clear roadmap of actions.

Avoid assumptions . Each step must rest on solid, verifiable facts. False assumptions can derail the entire process.

Iterative refinement . Solutions often require tweaking. With each iteration, the solution becomes more precise.

Advantages of Working Backwards

- Enhanced clarity . Visualizing the end state brings focus.

- Reduction of complexity . Breaking down the problem simplifies it.

- Strategic insight . Recognizing dependencies becomes straightforward.

- Encourages creativity . Solutions may emerge in counter-intuitive ways.

Implementation in Different Fields

In software development, Amazon pioneered this approach. They write the press release before product development. Educators also apply this approach. They define learning outcomes before creating teaching plans. In research, scientists determine the desired discovery, then design experiments accordingly.

Challenges and Considerations

Resource constraints may limit the applicability. Adjusting the goal can sometimes be necessary. Solvers must remain cognizant of potential roadblocks . They might encounter stages where progression is not evident in reverse.

Theoretical Underpinnings

Cognitive science supports the working backwards method. It aligns with how the human brain problem-solves. The temporal structure of human cognition suggests a natural affinity for retrospective organization. Thus, working backwards proves not just effective, but intuitive.

The working backwards strategy offers a structured path to problem-solving. Begin with the end. Deconstruct to comprehend. Engage with facts. Refine rigorously. Recognize its potential across disciplines but remain aware of challenges. Anchored in cognitive theory, it mirrors our inherent reasoning processes. In sum, it presents a robust framework for tackling complex problems.

How can the concept of working backwards enhance strategic decision-making in challenging situations?

Working backwards to enhance decision-making.

Strategic decision-making often involves complex problems. These problems can overwhelm decision-makers. When faced with such challenges, working backwards can clarify objectives and illuminate the path to achieving them.

Begin with the End in Mind

The mantra "begin with the end in mind" is central here. It compels leaders to envision the desired outcome first. This future state acts as a North Star, guiding all subsequent decisions and actions.

Set Clear Objectives

It is crucial to set clear, measurable objectives. These targets help assess decisions. They act as benchmarks throughout the process. Decision-makers can ensure alignment with the final goal by continually referencing these objectives.

Map the Steps Reversely

Mapping steps from the end goal to the present is a reverse chronology. This action breaks down the path to success into manageable sections. Each step becomes smaller, more tangible. It simplifies the process of identifying what actions to take and when.

Identify Key Milestones

Key milestones mark progress. They provide structure to the journey. Recognizing these milestones allows teams to celebrate small wins. This boosts morale and keeps focus sharp.

Anticipate Potential Obstacles

Working backwards forces foresight of obstacles. Anticipated issues can be tackled proactively. Solutions become embedded in the plan from the start.

Allocate Resources Wisely

Knowing the end goal helps allocate resources wisely. It becomes clear where to invest time, money, and effort. Scarce resources are conserved for critical paths.

Adjust with Flexibility

Even the best plans need adjustments. With a clear end goal, decision-makers can pivot with confidence. They remain flexible without losing sight of the objective.

Foster a Strategic Mindset

The backward approach fosters a strategic mindset. This thought process values proactive planning. It involves considering long-term impact over short-term gains.

Enhance Team Communication

Clear benchmarks improve team communication. Everyone understands the direction and their role in it. This alignment reduces misunderstandings and enhances collective performance.

Encourage Analytical Thinking

Working backwards encourages analytical thinking. Decision-makers must dissect the goal into its parts. They learn to understand the mechanisms that drive success.

Working backwards is not just a tactic. It is a strategic philosophy. It simplifies complex decision-making. Clarity, foresight, and structured planning are its byproducts. In challenging situations, this method can be a game-changer. Strategic leadership demands such innovative approaches. It stands as a testament to the virtue of thoughtful, reverse-engineered problem-solving.

Can you provide an example of how employing a "working backwards" strategy has been successful in a real life complex challenge?

The virtue of working backwards.

Success often stems from innovative strategy. Employing 'working backwards' illustrates this point. This approach demands starting from the end goal. One then maps out the path to that goal. This ensures efficiency and focus.

Consider Amazon's approach to product development. They start with customer needs. They create the press release first. This defines the desired outcome. They write about the product's release. This draft press release centers on the customer experience. It covers benefits and customer challenges. Amazon then engineers the product backwards. They develop features to fulfill the press release claims. This ensures the final product delights customers.

Real-Life Success Stories

This strategy thrives across various industries. Look at software development, for instance. Successful teams don't start coding immediately. They first define the user's end experience. Features then get planned. Every feature must serve the user's needs. Only after meticulous planning does coding begin.

Apple also embraces this mindset. They begin with the user experience. Product design comes next. Engineering follows to meet these specifications.

The 'Working Backwards' Framework

This strategy can be broken down into steps:

- Identify the ultimate goal.

- Craft the final outcome's narrative.

- Pinpoint essential success metrics.

- Develop milestones working backwards from the goal.

- Execute the plan, ensuring alignment at each step.

Critical Evaluation

While powerful, 'working backwards' is not infallible. It requires deep customer understanding. It demands that the end goal remains clear. Teams must adopt a customer-centric vision. Assumptions need constant testing. The strategy thrives on flexibility.

In summary, 'working backwards' breeds innovation. It demands a customer-first approach. It enforces clarity and focus throughout a project. Both Amazon and Apple showcase its success. Adopting this tactic means aligning with customer value. It ultimately leads to products that resonate in the market.

He is a content producer who specializes in blog content. He has a master's degree in business administration and he lives in the Netherlands.

5 Whys: Analyzing Root Causes for Effective Decision Making

Mastering Problem Solving Skills: How Thinking Aloud Works

Design Sprint 2.0: Streamline Innovative Solutions

Unlock Problem Solving: Activeness is Key

PROBLEM SOLVING – Blake’s Guide to Maths Problem Solving

This guide is a vital tool for all middle and upper primary students who want to be successful maths problem solvers. The book is divided into three sections.

• Why Solve Problems? Explains which personal skills help you solve problems and what a problem solving cycle looks like.
• Common Problem Solving Strategies The 8 suggested strategies are: Visualise it, Make a table or graph, Guess and check, Break it into smaller parts, Work backwards, Look for a pattern, Eliminate possibilities.
• Types of Problems More than 140 sample problems include 1-step, 2-step, more than 2-step, multiple choice and open-ended problems.

The book includes detailed, suggested strategies, as well as TRY THIS and CHALLENGE activities to test your understanding. Answers are at the back of the book. It is suitable for students, teachers and parents working with Stage 2 or 3 students. This Guide is packed full of easy-to-understand explanations, real-life photographs and graphics. The book includes curriculum correlation charts. The book also showcases 7 outstanding male and female problem-solvers from across the world.

Click here to buy a copy directly from the publisher or to view sample pages.

Attention! Your ePaper is waiting for publication!

By publishing your document, the content will be optimally indexed by Google via AI and sorted into the right category for over 500 million ePaper readers on YUMPU.

This will ensure high visibility and many readers!

Your ePaper is now published and live on YUMPU!

You can find your publication here:

Share your interactive ePaper on all platforms and on your website with our embed function

Problem Solving: Working Backwards - Blake Education

• www.blake.com.au

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

<strong>Problem</strong> <strong>Solving</strong><br />

<strong>Working</strong> <strong>Backwards</strong><br />

Sharon Shapiro Upper Primary<br />

THE PROBLEM<br />

SOLVING PROCESS<br />

It is important that students follow a logical and<br />

systematic approach to their problem solving. Following<br />

these four steps will enable students to tackle<br />

problems in a structured and meaningful way.<br />

STEP 1: UNDERSTANDING<br />

❖ Encourage students to read the problem<br />

carefully a number of times until they fully<br />

understand what is wanted.They may need to<br />

discuss the problem with someone else or<br />

rewrite it in their own words.<br />

❖ Students should ask internal questions such as,<br />

what is the problem asking me to do, what<br />

information is relevant and necessary for solving<br />

the problem.<br />

❖ They should underline any unfamiliar words and<br />

find out their meanings.<br />

❖ They should select the information they know<br />

and decide what is unknown or needs to be<br />

discovered.They should see if there is any<br />

unnecessary information.<br />

❖ A sketch of the problem often helps their<br />

understanding.<br />

STEP 2: STUDENTS SHOULD<br />

DECIDE ON A STRATEGY OR PLAN<br />

Students should decide how they will solve the<br />

problem by thinking about the different strategies<br />

that could be used.They could try to make<br />

predictions, or guesses, about the problem. Often<br />

these guesses result in generalisations which help<br />

to solve problems. Students should be discouraged<br />

from making wild guesses but they should be<br />

encouraged to take risks.They should always think<br />

in terms of how this problem relates to other<br />

problems that they have solved.They should keep<br />

a record of the strategies they have tried so that<br />

they don’t repeat them.<br />

Some possible strategies include:<br />

❖ Drawing a sketch, graph or table.<br />

❖ Acting out situations, or using concrete<br />

materials.<br />

❖ Organising a list.<br />

❖ Identifying a pattern and extending it.<br />

❖ Guessing and checking.<br />

❖ <strong>Working</strong> backwards.<br />

❖ Using simpler numbers to solve the problem,<br />

then applying the same methodology to the<br />

real problem.<br />

❖ Writing a number sentence.<br />

❖ Using logic and clues.<br />

❖ Breaking the problem into smaller parts.<br />

STEP 3: SOLVING THE PROBLEM<br />

❖ Students should write down their ideas as they<br />

work so they don’t forget how they approached<br />

❖ Their approach should be systematic.<br />

❖ If stuck, students should reread the problem<br />

and rethink their strategies.<br />

❖ Students should be given the opportunity to<br />

orally demonstrate or explain how they reached<br />

an answer.<br />

STEP 4: REFLECT<br />

❖ Students should consider if their answer makes<br />

sense and if it has answered what was asked.<br />

❖ Students should draw and write down their<br />

thinking processes, estimations and approach, as<br />

this gives them time to reflect on their<br />

practices.When they have an answer they<br />

should explain the process to someone else.<br />

❖ Students should ask themselves ‘what if’ to link<br />

this problem to another.This will take their<br />

exploration to a deeper level and encourage<br />

their use of logical thought processes.<br />

❖ Students should consider if it is possible to do<br />

the problem in a simpler way.<br />

© <strong>Blake</strong> <strong>Education</strong>—<strong>Problem</strong> <strong>Solving</strong>: <strong>Working</strong> <strong>Backwards</strong><br />

• More documents
• Recommendations

<strong>Problem</strong> <strong>Solving</strong> <strong>Working</strong> <strong>Backwards</strong> Sharon Shapiro Upper Primary THE PROBLEM SOLVING PROCESS It is important that students follow a logical and systematic approach to their problem solving. Following these four steps will enable students to tackle problems in a structured and meaningful way. STEP 1: UNDERSTANDING THE PROBLEM ❖ Encourage students to read the problem carefully a number of times until they fully understand what is wanted.They may need to discuss the problem with someone else or rewrite it in their own words. ❖ Students should ask internal questions such as, what is the problem asking me to do, what information is relevant and necessary for solving the problem. ❖ They should underline any unfamiliar words and find out their meanings. ❖ They should select the information they know and decide what is unknown or needs to be discovered.They should see if there is any unnecessary information. ❖ A sketch of the problem often helps their understanding. STEP 2: STUDENTS SHOULD DECIDE ON A STRATEGY OR PLAN Students should decide how they will solve the problem by thinking about the different strategies that could be used.They could try to make predictions, or guesses, about the problem. Often these guesses result in generalisations which help to solve problems. Students should be discouraged from making wild guesses but they should be encouraged to take risks.They should always think in terms of how this problem relates to other problems that they have solved.They should keep a record of the strategies they have tried so that they don’t repeat them. Some possible strategies include: ❖ Drawing a sketch, graph or table. ❖ Acting out situations, or using concrete materials. ❖ Organising a list. ❖ Identifying a pattern and extending it. ❖ Guessing and checking. ❖ <strong>Working</strong> backwards. ❖ Using simpler numbers to solve the problem, then applying the same methodology to the real problem. ❖ Writing a number sentence. ❖ Using logic and clues. ❖ Breaking the problem into smaller parts. STEP 3: SOLVING THE PROBLEM ❖ Students should write down their ideas as they work so they don’t forget how they approached the problem. ❖ Their approach should be systematic. ❖ If stuck, students should reread the problem and rethink their strategies. ❖ Students should be given the opportunity to orally demonstrate or explain how they reached an answer. STEP 4: REFLECT ❖ Students should consider if their answer makes sense and if it has answered what was asked. ❖ Students should draw and write down their thinking processes, estimations and approach, as this gives them time to reflect on their practices.When they have an answer they should explain the process to someone else. ❖ Students should ask themselves ‘what if’ to link this problem to another.This will take their exploration to a deeper level and encourage their use of logical thought processes. ❖ Students should consider if it is possible to do the problem in a simpler way. © <strong>Blake</strong> <strong>Education</strong>—<strong>Problem</strong> <strong>Solving</strong>: <strong>Working</strong> <strong>Backwards</strong> 1

Teaching Notes <strong>Working</strong> <strong>Backwards</strong> The strategy of working backwards is used to solve problems that include a number of linked factors or events, where some of the information has not been provided, usually at the beginning of the problem. To solve these problems it is usually necessary to start with the answer and work methodically backwards to fill in the missing information. This strategy is extremely useful in dealing with a situation or a sequence of events.The events occur one after the other and each stage, or piece of information, is affected by what comes next. Students begin at the end, with the final action, and work through the process in reverse order to establish what happened in the original situation. In order to use the strategy of working backwards effectively, students will need to develop the following skills and understanding. USING THE OPPOSITE OPERATION WHEN WORKING BACKWARDS When you are solving a problem by starting at the end and working backwards, any mathematical operations you come across will have to be reversed. This means that if the problem requires you to add something, then when working backwards you must subtract it, or if multiplying when working forwards, you must divide when working backwards. So if the problem the correct way round is – ÷ 8 x 2 = 14 then backwards it will be – Or ? 14 ÷ 2 x 8 = 56 Jack is 35 years younger than Karen. Frank is half of Jack’s age. Jennifer is 17 years older than Frank. If Jennifer is 35 years old, how old is Karen? Jennifer is 35. She is 17 years older than Frank. So using the opposite operation plus becomes minus. So Frank is 35 – 17 = 18 Frank is half Jack’s age so the opposite operation is 18 x 2 = 36 Jack is 35 years younger than Karen so 36 + 35 = 71 Therefore Karen is 71 years old. STARTING WITH THE ANSWER AND WORKING BACKWARDS In a problem where you know the final outcome but don’t know the starting point, beginning at the end of the problem and working backwards is the best way of arriving at a solution. For example, in a dancing competition all the contestants started dancing together.After three minutes half the people were eliminated. During the next ten minutes half of the remaining were eliminated.At the 15 minute mark, half again were eliminated, and at the 20 minute mark, half of those still remaining were eliminated. In the last two minutes one more contestant was eliminated leaving a winner of the competition. How many dancers were there in the beginning? You know that there is one winner and that the number of contestants was halved at certain intervals. Using this information, it is possible to work backwards and find out how many dancers entered the competition. Start with the winner 1 person dancing Last 2 minutes 1+1 = 2 dancers After 20 minutes Double = 4 dancers After 15 minutes Double = 8 dancers After 10 minutes Double = 16 dancers After 3 minutes Double = 32 dancers 32 dancers started. © <strong>Blake</strong> <strong>Education</strong>—<strong>Problem</strong> <strong>Solving</strong>: <strong>Working</strong> <strong>Backwards</strong> 2

• Page 1: Blake’s Topic Bank Problem Solvin
• Page 5 and 6: Teaching Examples Working Backwards
• Page 7 and 8: BLM Working Backwards ★ Understan
• Page 9 and 10: PROBLEM SOLVING TASK CARDS -Working
• Page 11 and 12: PROBLEM SOLVING TASK CARDS -Working
• Page 13 and 14: PROBLEM SOLVING TASK CARDS -Working
• Page 15: Problem 10 Working backwards, Chris

Extended embed settings

Inappropriate

You have already flagged this document. Thank you, for helping us keep this platform clean. The editors will have a look at it as soon as possible.

Mail this publication

Delete template.

Are you sure you want to delete your template?

DOWNLOAD ePAPER

This ePaper is currently not available for download. You can find similar magazines on this topic below under ‘Recommendations’.

Save as template?

• Help & Support
• tuxbrain.com
• ooomacros.org
• nubuntu.org
• Terms of service
• Privacy policy
• Cookie policy
• Cookie settings

Choose your language

Main languages

Further languages

• Bahasa Indonesia

Performing this action will revert the following features to their default settings:

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!

• Arts & Humanities

Acting it Out - Blake Education

Related documents

Study collections

Add this document to collection(s).

You can add this document to your study collection(s)

Add this document to saved

You can add this document to your saved list

Suggest us how to improve StudyLib

(For complaints, use another form )

Input it if you want to receive answer

• Targeting Comprehension
• Targeting General Capabilities
• Targeting HASS
• Targeting Maths
• Targeting Phonics
• Targeting STEM
• Mathematics
• Business Studies
• HSIE & SOSE
• PDHPE & Life Skills
• Technology & Design
• Free to Download
• Subscribe & save
• FOR SCHOOLS

--> FLASH SALE: SAVE 20% OFF STOREWIDE! *T&C's apply. --> Learn more

Back-to-School Sale: Save 25% on your next order!* Learn more

BLACK FRIDAY SALE: USE CODE BFCM30 FOR 30% OFF STOREWIDE! *T&C's apply.--> --> -->