rucsac method for problem solving

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Operation Maths: A Unique Approach to Problem-Solving

• February 27, 2017

Tags : About Operation Maths Problem Solving

Category : About Operation Maths

In this post, we will look specifically at the Operation Maths approach to problem-solving in the senior end books (3rd to 6th classes). In a subsequent post, we will look at how this approach develops in the junior end books (infants to second classes).

Presenting children with an abundance of mathematical problems does not automatically transform them into competent and confident problem-solvers. Rather, the children must be explicitly taught a range of problem-solving strategies and they must be facilitated in applying and practising the strategies repeatedly in a range of different contexts. Operation Maths has an integral multilayered approach to problem-solving throughout the 3rd to 6th class books:

• A variety of key problem-solving strategies is introduced, explored and applied to various real-life contexts in a developmental and spiral way through the classes (i.e. bar model drawing, empty number lines, T-charts , branching etc)
• Regular Work It Out! sections throughout the chapters in the pupils books provide the children with opportunities to apply and hone their problem-solving skills.
• Let’s Investigate! sections at the end of the Pupils’ Books where the focus is on open-ended problems
• Thematic revision spreads with a strong problem-solving focus.
• Extra problem-solving in Early Finisher photocopiables.

All of this happens as part of a larger problem-solving approach based on the acronym RUCSAC. This approach, which can be used as a whole school problem-solving approach, is also reinforced and explained for both children and parents on a convenient French flap/bookmark on the Discovery Book (see images from flaps below), which encourages the children to use RUCSAC as an aid when problem-solving.

Problem-solving skills

The ability to reason mathematically is fundamental to being able to solve mathematical problems. However, reasoning mathematically requires not just one, but a number of mathematical skills e.g. being able to • Work through a problem in a systematic way • Predict an answer • Identify the relevant information and understand what type of answer is being sought • Visualise the problem mentally or being able to represent the components of the problem in either a pictorial or abstract (using only numbers and symbols) way. • Plan or decide what approach to take • Work to get an answer • Check that the answer is suitable and accurate.

What is fundamentally different about the Operation Maths approach to problem solving is that the children are being taught specific strategies to develop the aforementioned skills, in a spiral and progressive way, in order to equip the children with the necessary skills for them to become capable and confident problem-solvers.

Central to the Operation Math approach to problem solving is RUCSAC. This clear, sequential approach enables the children to work through problems in a systematic way, while simultaneously utilising the mathematical skills that are being developed with and throughout the chapters.

RUCSAC and the Specific Strategies taught in Operation Maths

RUCSAC is an acronym, where each letter represents one of the six distinct phases of this problem-solving approach (see below). However, this more than just a clever mnemonic, as each of these phases is supported by the development of specific strategies throughout the programme, which support this approach.  These specific strategies are as follows:

• Reasonable answer: Would you predict a bigger or smaller answer? How many digits would you expect in the answer
• Front-end estimation: Look at the digits at the front of the numbers
• Rounding: Round each number to the place of the highest value digit e.g. tens, hundreds, thousands.
• Rounding to fives: (only in OM6): Usually we round to the nearest tenth, unit, ten, etc. But if the number(s) involved are approximately in the middle, it is more efficient to round them to the nearest five tenths, 5, 50 etc. to get a more accurate estimate. (OM6, Pupils Book p 30)

Underline – Colour coding operational vocabulary:

• Identifying specific phrases, colour coding them, and recording them on in the Discovery Book. This forces the child to engage with the language of problems and to decode them. However, this only suits word problems which contain obvious operational vocabulary or that which can be easily inferred.

Create – Creating visual representation to show the information in the problem, as part of a CPA approach :

• Using concrete materials (e.g. counters, cubes, children etc.)
• Using bar model drawings
• Using empty number lines
• Using T-charts (OM4 to OM6)
• Making/completing a table, grid, list etc.
• Creating number sentences (and/or equations with variables in OM6)

Select – Selecting a suitable and efficient approach:

• Using a mental method, e.g. petitioning, sequencing, compensating etc.
• Using a written method e.g. a formal algorithm, jottings, branching
• Using guess and test

Answer – Answering the question:

• The teaching panels demonstrate how to layout and position work clearly and sequentially
• Children are encouraged to “show your thinking”

Check – Checking answer(s):

• Comparing the answer to the estimate, e.g. does it look reasonable?
• Using the inverse to check.

Furthermore, as part of this approach, specific visual strategies are introduced and repeatedly used where appropriate:

• Empty Number lines

Empty Number Line (ENL)

Simply, a horizontal line, initially with no numbers or markings that helps develop a child’s number sense, their ability to visualise numbers and to compute mentally. Also known as a blank or open number line, empty number lines can be used to show elapsed time, operations, skip counting, fractions, decimals, measures, money (making change) and much more (see image below).

While, strictly speaking the number line should initially start empty (i.e. no numbers or markings), in Operation Maths, some of the required numbers and/or markings have been provided, to act as scaffolding for the child. Ultimately, it in envisaged, that as the child grows more confident of this structure, he/she should be able to construct an empty number line from scratch in order to help solve other problems. I is also hope that through using this structure the child would be able to develop this ability to visualise numbers in such a way and, in doing so, enhance their ability to compute mentally.

These are simply drawing(s) that resemble bars, (like that seen in bar graphs), that are used to illustrate number relationships. There are two main types, part-whole bar models and comparison bar models.

Part-whole model: which can represent a whole amount that is subdivided into smaller parts. In Operation Maths these are used to represent:

• Addition/subtraction: where a whole amount has been subdivided into two or three amounts/parts and either the value of one of the parts or the whole/total is required
• Multiplication/division: where a whole amount has been subdivided into equal amounts/parts and either the value of one/some of the parts or the whole amount is required
• Fractions, ratios, decimals and percentages: Where a whole amount has been subdivided into equal amounts/parts and either the value of one/some of the parts or the whole amount is unknown.

Comparison models :  which are used when comparing two or more quantities. In Operation Maths these can be used to represent:

• Addition/subtraction and Multiplication/division: where two amounts are being compared and the value of one of the amounts or the difference between the amounts or the total value of the amounts is being sought.
• Fractions, ratios, decimals and percentages: Where two or three amounts are being compared and the value of some of the amounts, the difference between the amounts or the total is unknown. This can also be a very effective way to calculate selling price and cost price when given percentage profit/loss

A T-chart is simply a table, usually divided into two columns, giving it a T-shape. They can be used as a means to aid calculations and/or to identify patterns and connections within problems .

Other strategies

Other strategies used in Operation Maths which promote the visualising and decoding of problems include: • Using number bonds and branching • Making lists • Using “guess and test” (also known as Trial & Error) • Using the process of elimination (e.g. logic problems)

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Effects of the Six Thinking Hats Method in Creative Problem Solving among Undergraduate Honors Students

Cultivating problem-solving in highly motivated university students remains a persistent priority in higher education. These highly motivated students often enroll in honors programs to engage in small group discussions with their like-minded peers to enhance creative problem-solving skills; however, limited empirical research exists on the effectiveness of creative thinking interventions in creative problem-solving among introverted university honors students. This study focused on how the Six Thinking Hats method, a creative thinking tool designed to encourage individuals to think in parallel with those of others through six metaphoric Hats, increases creative problem-solving in introverted honors students.

A quantitative single-case multiple baseline design across four introverted university honors students was used to examine a functional relation between the Six Thinking Hats and creative problem-solving. The dependent variables were: (a) total number of Hats, (b) total number of topic-related participation units, (c) total number of creative ideas, and (d) total number of words per Hat. Results indicated a functional relation between the STH method and Hats (i.e., perspectives), but no functional relation existed for topic-related participation units, creative ideas, and words per Hat. The social validity data, confirmed through thematic analysis, revealed three themes regarding the STH method: (a) awareness of metacognition, (b) meaningfulness of the intervention, and (c) application to problem-solving situations. This study offers a first step in contributing to the small body of experimental research on the effectiveness of the Six Thinking Hats method in promoting multiple perspectives among undergraduate honors students.

26 Expert-Backed Problem Solving Examples – Interview Answers

Published: February 13, 2023

Interview Questions and Answers

Actionable advice from real experts:

Biron Clark

Former Recruiter

Contributor

Dr. Kyle Elliott

Career Coach

Hayley Jukes

Editor-in-Chief

Biron Clark , Former Recruiter

Kyle Elliott , Career Coach

Hayley Jukes , Editor

As a recruiter , I know employers like to hire people who can solve problems and work well under pressure.

 A job rarely goes 100% according to plan, so hiring managers are more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical.

But how do they measure this?

Hiring managers will ask you interview questions about your problem-solving skills, and they might also look for examples of problem-solving on your resume and cover letter. 

In this article, I’m going to share a list of problem-solving examples and sample interview answers to questions like, “Give an example of a time you used logic to solve a problem?” and “Describe a time when you had to solve a problem without managerial input. How did you handle it, and what was the result?”

• Problem-solving involves identifying, prioritizing, analyzing, and solving problems using a variety of skills like critical thinking, creativity, decision making, and communication.
• Describe the Situation, Task, Action, and Result ( STAR method ) when discussing your problem-solving experiences.
• Tailor your interview answer with the specific skills and qualifications outlined in the job description.
• Provide numerical data or metrics to demonstrate the tangible impact of your problem-solving efforts.

What are Problem Solving Skills? 

Problem-solving is the ability to identify a problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation. 

Problem-solving encompasses other skills that can be showcased in an interview response and your resume. Problem-solving skills examples include:

• Critical thinking
• Analytical skills
• Decision making
• Research skills
• Technical skills
• Communication skills
• Adaptability and flexibility

Why is Problem Solving Important in the Workplace?

Problem-solving is essential in the workplace because it directly impacts productivity and efficiency. Whenever you encounter a problem, tackling it head-on prevents minor issues from escalating into bigger ones that could disrupt the entire workflow. 

Beyond maintaining smooth operations, your ability to solve problems fosters innovation. It encourages you to think creatively, finding better ways to achieve goals, which keeps the business competitive and pushes the boundaries of what you can achieve. 

Effective problem-solving also contributes to a healthier work environment; it reduces stress by providing clear strategies for overcoming obstacles and builds confidence within teams. 

Examples of Problem-Solving in the Workplace

• Correcting a mistake at work, whether it was made by you or someone else
• Overcoming a delay at work through problem solving and communication
• Resolving an issue with a difficult or upset customer
• Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
• Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
• Troubleshooting and resolving technical issues
• Handling and resolving a conflict with a coworker
• Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
• Taking initiative when another team member overlooked or missed something important
• Taking initiative to meet with your superior to discuss a problem before it became potentially worse
• Solving a safety issue at work or reporting the issue to those who could solve it
• Using problem solving abilities to reduce/eliminate a company expense
• Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
• Changing how a process, team, or task is organized to make it more efficient
• Using creative thinking to come up with a solution that the company hasn’t used before
• Performing research to collect data and information to find a new solution to a problem
• Boosting a company or team’s performance by improving some aspect of communication among employees
• Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem-Solving Examples for Recent Grads/Entry-Level Job Seekers

• Coordinating work between team members in a class project
• Reassigning a missing team member’s work to other group members in a class project
• Adjusting your workflow on a project to accommodate a tight deadline
• Speaking to your professor to get help when you were struggling or unsure about a project
• Asking classmates, peers, or professors for help in an area of struggle
• Talking to your academic advisor to brainstorm solutions to a problem you were facing
• Researching solutions to an academic problem online, via Google or other methods
• Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

How To Answer “Tell Us About a Problem You Solved”

When you answer interview questions about problem-solving scenarios, or if you decide to demonstrate your problem-solving skills in a cover letter (which is a good idea any time the job description mentions problem-solving as a necessary skill), I recommend using the STAR method.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them. 

Start by briefly describing the general situation and the task at hand. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact. Finally, describe the positive result you achieved.

Note: Our sample answers below are structured following the STAR formula. Be sure to check them out!

EXPERT ADVICE

Dr. Kyle Elliott , MPA, CHES Tech & Interview Career Coach caffeinatedkyle.com

How can I communicate complex problem-solving experiences clearly and succinctly?

Before answering any interview question, it’s important to understand why the interviewer is asking the question in the first place.

When it comes to questions about your complex problem-solving experiences, for example, the interviewer likely wants to know about your leadership acumen, collaboration abilities, and communication skills, not the problem itself.

Therefore, your answer should be focused on highlighting how you excelled in each of these areas, not diving into the weeds of the problem itself, which is a common mistake less-experienced interviewees often make.

Tailoring Your Answer Based on the Skills Mentioned in the Job Description

As a recruiter, one of the top tips I can give you when responding to the prompt “Tell us about a problem you solved,” is to tailor your answer to the specific skills and qualifications outlined in the job description. 

Once you’ve pinpointed the skills and key competencies the employer is seeking, craft your response to highlight experiences where you successfully utilized or developed those particular abilities. 

For instance, if the job requires strong leadership skills, focus on a problem-solving scenario where you took charge and effectively guided a team toward resolution. 

By aligning your answer with the desired skills outlined in the job description, you demonstrate your suitability for the role and show the employer that you understand their needs.

Amanda Augustine expands on this by saying:

“Showcase the specific skills you used to solve the problem. Did it require critical thinking, analytical abilities, or strong collaboration? Highlight the relevant skills the employer is seeking.”  

Interview Answers to “Tell Me About a Time You Solved a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” or “Tell me about a time you solved a problem,” since you’re likely to hear different versions of this interview question in all sorts of industries.

The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate.

1. Analytical Thinking

Situation: In my previous role as a data analyst , our team encountered a significant drop in website traffic.

Task: I was tasked with identifying the root cause of the decrease.

Action: I conducted a thorough analysis of website metrics, including traffic sources, user demographics, and page performance. Through my analysis, I discovered a technical issue with our website’s loading speed, causing users to bounce. 

Result: By optimizing server response time, compressing images, and minimizing redirects, we saw a 20% increase in traffic within two weeks.

2. Critical Thinking

Situation: During a project deadline crunch, our team encountered a major technical issue that threatened to derail our progress.

Task: My task was to assess the situation and devise a solution quickly.

Action: I immediately convened a meeting with the team to brainstorm potential solutions. Instead of panicking, I encouraged everyone to think outside the box and consider unconventional approaches. We analyzed the problem from different angles and weighed the pros and cons of each solution.

Result: By devising a workaround solution, we were able to meet the project deadline, avoiding potential delays that could have cost the company $100,000 in penalties for missing contractual obligations.

3. Decision Making

Situation: As a project manager , I was faced with a dilemma when two key team members had conflicting opinions on the project direction.

Task: My task was to make a decisive choice that would align with the project goals and maintain team cohesion.

Action: I scheduled a meeting with both team members to understand their perspectives in detail. I listened actively, asked probing questions, and encouraged open dialogue. After carefully weighing the pros and cons of each approach, I made a decision that incorporated elements from both viewpoints.

Result: The decision I made not only resolved the immediate conflict but also led to a stronger sense of collaboration within the team. By valuing input from all team members and making a well-informed decision, we were able to achieve our project objectives efficiently.

4. Communication (Teamwork)

Situation: During a cross-functional project, miscommunication between departments was causing delays and misunderstandings.

Task: My task was to improve communication channels and foster better teamwork among team members.

Action: I initiated regular cross-departmental meetings to ensure that everyone was on the same page regarding project goals and timelines. I also implemented a centralized communication platform where team members could share updates, ask questions, and collaborate more effectively.

Result: Streamlining workflows and improving communication channels led to a 30% reduction in project completion time, saving the company $25,000 in operational costs.

5. Persistence 

Situation: During a challenging sales quarter, I encountered numerous rejections and setbacks while trying to close a major client deal.

Task: My task was to persistently pursue the client and overcome obstacles to secure the deal.

Action: I maintained regular communication with the client, addressing their concerns and demonstrating the value proposition of our product. Despite facing multiple rejections, I remained persistent and resilient, adjusting my approach based on feedback and market dynamics.

Result: After months of perseverance, I successfully closed the deal with the client. By closing the major client deal, I exceeded quarterly sales targets by 25%, resulting in a revenue increase of $250,000 for the company.

Tips to Improve Your Problem-Solving Skills

Throughout your career, being able to showcase and effectively communicate your problem-solving skills gives you more leverage in achieving better jobs and earning more money .

So to improve your problem-solving skills, I recommend always analyzing a problem and situation before acting.

 When discussing problem-solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Don’t just say you’re good at solving problems. Show it with specifics. How much did you boost efficiency? Did you save the company money? Adding numbers can really make your achievements stand out.

To get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t.

Think about how you can improve researching and analyzing a situation, how you can get better at communicating, and deciding on the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem-solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem-solving ability.

More Interview Resources

• 3 Answers to “How Do You Handle Stress?”
• How to Answer “How Do You Handle Conflict?” (Interview Question)
• Sample Answers to “Tell Me About a Time You Failed”

About the Author

Biron Clark is a former executive recruiter who has worked individually with hundreds of job seekers, reviewed thousands of resumes and LinkedIn profiles, and recruited for top venture-backed startups and Fortune 500 companies. He has been advising job seekers since 2012 to think differently in their job search and land high-paying, competitive positions. Follow on Twitter and LinkedIn .

Read more articles by Biron Clark

About the Contributor

Kyle Elliott , career coach and mental health advocate, transforms his side hustle into a notable practice, aiding Silicon Valley professionals in maximizing potential. Follow Kyle on LinkedIn .

About the Editor

Hayley Jukes is the Editor-in-Chief at CareerSidekick with five years of experience creating engaging articles, books, and transcripts for diverse platforms and audiences.

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Problem Solving (RUCSAC)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

22 February 2018

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Solving optimal electric vehicle charger deployment problem.

1. Introduction

• Building a comprehensive mathematical framework accommodating the particular complexity,
• Demonstrating our numerical computational framework for solving the facility location problem (FLP) representing the optimal location;
• Laying out an extensive comparative study among the optimization solving techniques as an effort to find the most efficient solver;
• Applying the findings to two real-world case studies representing an average and high density of EVs.

2. Related Work

2.1. problem formulation approaches, 2.1.1. facility location problem (flp), 2.1.2. distance optimization, 2.1.3. weight assignment techniques, 2.1.4. machine learning techniques, 2.2. solving techniques, 3. problem formulation, 3.1. spatial setup, 3.2. formulation to capacitated flp.

• i and j are indexes for an EV charging facility and a demanding area (or, equivalently, a customer), respectively.
• v i j gives the variable cost to obtain the electricity supplied to serve customer j .
• d j gauges the demand from customer j .
• y i j quantifies the fraction of the demand made by customer j and fulfilled by facility i .
• x i indicates whether facility i opens or not .
• s i denotes the sunken cost (also known as “fixed” cost) of opening a charging facility i .
• E i , j defines the equity achieved at customer j via service from facility i .
• C i and C min indicate the capacity of facility i and the required minimum capacity of any facility, respectively, both in the unit of kWh.

3.3. Unique Challenges

• C1:   Large search spaces for domain and other variables;
• C2:   Inexistence of polynomial-time numerical solving. techniques

4. Solving Techniques Development

4.1. unique challenges and proposed approaches, 4.2. comparison among solving techniques, 4.3. alternative techniques, 5. case study 1: region with average ev density, 5.1. case-specific refinement of solving method, 5.2. results and discussion.

6. Case Study 2: Region with High EV Density

6.1. case-specific refinement of solving method, 6.1.1. data collection and preprocessing, 6.1.2. data integration, 6.1.3. training methods.

• Data Preparation: The collected and merged dataset undergoes preprocessing to ensure its suitability for training, including handling missing values, data normalization, and feature engineering.
• Model Selection: The decision tree (DT) [ 67 ], support vector machine (SVM) [ 68 ], and random forest (RF) [ 69 ] models are considered as potential candidates for training due to their widespread usage in site selection problems.
• Training Process: Each selected model is trained using the prepared dataset, which is divided into training and validation sets. Performance evaluation metrics such as accuracy, precision, recall, and F1 score are utilized to assess the model’s performance during training.
• Model Evaluation: After training, the models are evaluated using the validation set to assess their predictive capabilities. The evaluation metrics are used to compare the models’ performance and identify the model with the highest accuracy or other desired performance metrics.
• Model Selection: Based on the evaluation results, the model demonstrating the best performance is selected as the final machine learning model for the site selection task.

6.2. Results and Discussions

• Installation criteria differ between DC fast chargers and level-2 chargers. Significant differences in consistency are observed when training separately based on each charging station type or when training with both types together. Consequently, it can be concluded that chargers have been installed at locations that meet their respective criteria for both DC fast chargers and level-2 chargers.
• Non-uniform distribution of reference data does not significantly affect training results. There is no significant difference in consistency between training based on non-uniformly distributed chargers and training based on grid points uniformly distributed at regular intervals. Thus, it can be concluded that the non-uniform distribution of data does not impact the training results.
• Buffer size influences data consistency. Decreasing the buffer size results in increased consistency. The reason for the decrease in consistency at buffer sizes below 125 m is that the polygon data used for learning is 250 m × 250 m grid data, resulting in buffers that do not contain data from the 125 m radius buffer size. This problem can be solved by using smaller grid data than 250 m × 250 m grid data during data preprocessing. In conclusion, this result shows that larger buffer sizes increase data redundancy and affect consistency.

7. Conclusions and Future Work

Author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

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Kim, S.; Jeong, Y.; Nam, J.-W. Solving Optimal Electric Vehicle Charger Deployment Problem. Appl. Sci. 2024 , 14 , 5092. https://doi.org/10.3390/app14125092

Kim S, Jeong Y, Nam J-W. Solving Optimal Electric Vehicle Charger Deployment Problem. Applied Sciences . 2024; 14(12):5092. https://doi.org/10.3390/app14125092

Kim, Seungmo, Yeonho Jeong, and Jae-Won Nam. 2024. "Solving Optimal Electric Vehicle Charger Deployment Problem" Applied Sciences 14, no. 12: 5092. https://doi.org/10.3390/app14125092

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