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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

what is the definition of the word problem solving

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

what is the definition of the word problem solving

  • Identify the Problem
  • Define the Problem
  • Form a Strategy
  • Organize Information
  • Allocate Resources
  • Monitor Progress
  • Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

  • Asking questions about the problem
  • Breaking the problem down into smaller pieces
  • Looking at the problem from different perspectives
  • Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

  • Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
  • Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

  • Practicing brainstorming and coming up with multiple potential solutions to problems
  • Being open-minded and considering all possible options before making a decision
  • Breaking down problems into smaller, more manageable pieces
  • Asking for help when needed
  • Researching different problem-solving techniques and trying out new ones
  • Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Article • 7 min read

What Is Problem Solving?

By the Mind Tools Content Team

what is the definition of the word problem solving

We all spend a lot of our time solving problems, both at work and in our personal lives.

Some problems are small, and we can quickly sort them out ourselves. But others are complex challenges that take collaboration, creativity, and a considerable amount of effort to solve.

At work, the types of problems we face depend largely on the organizations we're in and the jobs we do. A manager in a cleaning company, for example, might spend their day untangling staffing issues, resolving client complaints, and sorting out problems with equipment and supplies. An aircraft designer, on the other hand, might be grappling with a problem about aerodynamics, or trying to work out why a new safety feature isn't working. Meanwhile, a politician might be exploring solutions to racial injustice or climate change.

But whatever issues we face, there are some common ways to tackle them effectively. And we can all boost our confidence and ability to succeed by building a strong set of problem-solving skills.

Mind Tools offers a large collection of resources to help you do just that!

How Well Do You Solve Problems?

Start by taking an honest look at your existing skills. What's your current approach to solving problems, and how well is it working? Our quiz, How Good Is Your Problem Solving? lets you analyze your abilities, and signposts ways to address any areas of weakness.

Define Every Problem

The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem – not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work. However, if you look a bit deeper, the real issue might be a general lack of training, or an unreasonable workload across the team.

Tools like 5 Whys , Appreciation and Root Cause Analysis get you asking the right questions, and help you to work through the layers of a problem to uncover what's really going on.

However, defining a problem doesn't mean deciding how to solve it straightaway. It's important to look at the issue from a variety of perspectives. If you commit yourself too early, you can end up with a short-sighted solution. The CATWOE checklist provides a powerful reminder to look at many elements that may contribute to the problem, keeping you open to a variety of possible solutions.

Understanding Complexity

As you define your problem, you'll often discover just how complicated it is. There are likely several interrelated issues involved. That's why it's important to have ways to visualize, simplify and make sense of this tangled mess!

Affinity Diagrams are great for organizing many different pieces of information into common themes, and for understanding the relationships between them.

Another popular tool is the Cause-and-Effect Diagram . To generate viable solutions, you need a solid understanding of what's causing the problem.

When your problem occurs within a business process, creating a Flow Chart , Swim Lane Diagram or a Systems Diagram will help you to see how various activities and inputs fit together. This may well highlight a missing element or bottleneck that's causing your problem.

Quite often, what seems to be a single problem turns out to be a whole series of problems. The Drill Down technique prompts you to split your problem into smaller, more manageable parts.

General Problem-Solving Tools

When you understand the problem in front of you, you’re ready to start solving it. With your definition to guide you, you can generate several possible solutions, choose the best one, then put it into action. That's the four-step approach at the heart of good problem solving.

There are various problem-solving styles to use. For example:

  • Constructive Controversy is a way of widening perspectives and energizing discussions.
  • Inductive Reasoning makes the most of people’s experiences and know-how, and can speed up solution finding.
  • Means-End Analysis can bring extra clarity to your thinking, and kick-start the process of implementing solutions.

Specific Problem-Solving Systems

Some particularly complicated or important problems call for a more comprehensive process. Again, Mind Tools has a range of approaches to try, including:

  • Simplex , which involves an eight-stage process: problem finding, fact finding, defining the problem, idea finding, selecting and evaluating, planning, selling the idea, and acting. These steps build upon the basic, four-step process described above, and they create a cycle of problem finding and solving that will continually improve your organization.
  • Appreciative Inquiry , which is a uniquely positive way of solving problems by examining what's working well in the areas surrounding them.
  • Soft Systems Methodology , which takes you through four stages to uncover more details about what's creating your problem, and then define actions that will improve the situation.

Further Problem-Solving Strategies

Good problem solving requires a number of other skills – all of which are covered by Mind Tools.

For example, we have a large section of resources to improve your Creativity , so that you come up with a range of possible solutions.

By strengthening your Decision Making , you'll be better at evaluating the options, selecting the best ones, then choosing how to implement them.

And our Project Management collection has valuable advice for strengthening the whole problem-solving process. The resources there will help you to make effective changes – and then keep them working long term.

Problems are an inescapable part of life, both in and out of work. So we can all benefit from having strong problem-solving skills.

It's important to understand your current approach to problem solving, and to know where and how to improve.

Define every problem you encounter – and understand its complexity, rather than trying to solve it too soon.

There's a range of general problem-solving approaches, helping you to generate possible answers, choose the best ones, and then implement your solution.

Some complicated or serious problems require more specific problem-solving systems, especially when they relate to business processes.

By boosting your creativity, decision-making and project-management skills, you’ll become even better at solving all the problems you face.

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Definition of 'problem-solving'

Problem-solving in british english.

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Examples of 'problem-solving' in a sentence problem-solving

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problem-solving noun & adjective

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What does the word problem-solving mean?

There are two meanings listed in OED's entry for the word problem-solving . See ‘Meaning & use’ for definitions, usage, and quotation evidence.

How common is the word problem-solving ?

Where does the word problem-solving come from.

Earliest known use

The earliest known use of the word problem-solving is in the 1850s.

OED's earliest evidence for problem-solving is from 1854, in Putnam's Monthly Magazine .

problem-solving is formed within English, by compounding.

Etymons: problem n.

Nearby entries

  • problemistic, adj. 1892–
  • problemize, v. 1844–
  • problemless, adj. 1865–
  • problemo, n. 1985–
  • problem of three bodies, n. 1814–
  • problem-orientated, adj. 1951–
  • problem-oriented, adj. 1946–
  • problem play, n. 1894–
  • problem-solve, v. 1956–
  • problem-solver, n. 1848–
  • problem-solving, n. & adj. 1854–
  • problem tape, n. 1948–
  • problem-wise, adv. a1859–
  • pro-Boarder, n. 1902–
  • pro-Boerism, n. 1899–
  • probole, n.¹ 1684–1880
  • probole, n.² 1696–
  • probolistic, adj. 1876–
  • pro bono, adv. & adj. 1774–
  • pro bono publico, adv. 1640–
  • proboscic, adj. 1835–

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Meaning & use

Entry history for problem-solving, n. & adj..

Originally published as part of the entry for problem, n.

problem, n. was revised in June 2007

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Earlier versions of problem, n. were published in:

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Definition of problem-solving noun from the Oxford Advanced Learner's Dictionary

problem-solving

  • to develop problem-solving skills and strategies

Questions about grammar and vocabulary?

Find the answers with Practical English Usage online, your indispensable guide to problems in English.

Nearby words

what is the definition of the word problem solving

What Is Problem Solving?

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches,…

What Is Problem Solving?

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches, so why do people need to organize these drives? It’s evident that despite advertising and posting anti-littering messages, some of us don’t follow the rules.

Temporary food stalls and shops make it even more difficult to keep the beaches clean. Since people can’t ask the shopkeepers to relocate or prevent every single person from littering, the clean-up drive is needed.  This is an ideal example of problem-solving psychology in humans. ( 230-fifth.com ) So, what is problem-solving? Let’s find out.

What Is Problem-Solving?

At its simplest, the meaning of problem-solving is the process of defining a problem, determining its cause, and implementing a solution. The definition of problem-solving is rooted in the fact that as humans, we exert control over our environment through solutions. We move forward in life when we solve problems and make decisions. 

We can better define the problem-solving process through a series of important steps.

Identify The Problem: 

This step isn’t as simple as it sounds. Most times, we mistakenly identify the consequences of a problem rather than the problem itself. It’s important that we’re careful to identify the actual problem and not just its symptoms. 

Define The Problem: 

Once the problem has been identified correctly, you should define it. This step can help clarify what needs to be addressed and for what purpose.

Form A Strategy: 

Develop a strategy to solve your problem. Defining an approach will provide direction and clarity on the next steps. 

Organize The Information:  

Organizing information systematically will help you determine whether something is missing. The more information you have, the easier it’ll become for you to arrive at a solution.  

Allocate Resources:  

We may not always be armed with the necessary resources to solve a problem. Before you commit to implementing a solution for a problem, you should determine the availability of different resources—money, time and other costs.

Track Progress: 

The true meaning of problem-solving is to work towards an objective. If you measure your progress, you can evaluate whether you’re on track. You could revise your strategies if you don’t notice the desired level of progress. 

Evaluate The Results:  

After you spot a solution, evaluate the results to determine whether it’s the best possible solution. For example, you can evaluate the success of a fitness routine after several weeks of exercise.

Meaning Of Problem-Solving Skill

Now that we’ve established the definition of problem-solving psychology in humans, let’s look at how we utilize our problem-solving skills.  These skills help you determine the source of a problem and how to effectively determine the solution. Problem-solving skills aren’t innate and can be mastered over time. Here are some important skills that are beneficial for finding solutions.

Communication

Communication is a critical skill when you have to work in teams.  If you and your colleagues have to work on a project together, you’ll have to collaborate with each other. In case of differences of opinion, you should be able to listen attentively and respond respectfully in order to successfully arrive at a solution.

As a problem-solver, you need to be able to research and identify underlying causes. You should never treat a problem lightly. In-depth study is imperative because often people identify only the symptoms and not the actual problem.

Once you have researched and identified the factors causing a problem, start working towards developing solutions. Your analytical skills can help you differentiate between effective and ineffective solutions.

Decision-Making

You’ll have to make a decision after you’ve identified the source and methods of solving a problem. If you’ve done your research and applied your analytical skills effectively, it’ll become easier for you to take a call or a decision.

Organizations really value decisive problem-solvers. Harappa Education’s   Defining Problems course will guide you on the path to developing a problem-solving mindset. Learn how to identify the different types of problems using the Types of Problems framework. Additionally, the SMART framework, which is a five-point tool, will teach you to create specific and actionable objectives to address problem statements and arrive at solutions. 

Explore topics & skills such as Problem Solving Skills , PICK Chart , How to Solve Problems & Barriers to Problem Solving from our Harappa Diaries blog section and develop your skills.

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Definition of problem

 (Entry 1 of 2)

Definition of problem  (Entry 2 of 2)

mystery , problem , enigma , riddle , puzzle mean something which baffles or perplexes.

mystery applies to what cannot be fully understood by reason or less strictly to whatever resists or defies explanation.

problem applies to a question or difficulty calling for a solution or causing concern.

enigma applies to utterance or behavior that is very difficult to interpret.

riddle suggests an enigma or problem involving paradox or apparent contradiction.

puzzle applies to an enigma or problem that challenges ingenuity for its solution.

Examples of problem in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'problem.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Middle English probleme , from Latin problema , from Greek problēma , literally, obstacle, from proballein to throw forward, from pro- forward + ballein to throw — more at pro- , devil

14th century, in the meaning defined at sense 1a

1894, in the meaning defined at sense 1

Phrases Containing problem

  • problem - solving
  • not someone's problem
  • not a problem
  • first world problem
  • drinking problem
  • what's someone's problem
  • word problem
  • have a problem with
  • attitude problem
  • therein lies the problem
  • drink problem

Articles Related to problem

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Dictionary Entries Near problem

problematic

Cite this Entry

“Problem.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/problem. Accessed 24 Feb. 2024.

Kids Definition

Kids definition of problem.

Kids Definition of problem  (Entry 2 of 2)

More from Merriam-Webster on problem

Nglish: Translation of problem for Spanish Speakers

Britannica English: Translation of problem for Arabic Speakers

Britannica.com: Encyclopedia article about problem

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Status.net

What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

  • Identify the issue : Recognize the problem that needs to be solved.
  • Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
  • Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
  • Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
  • Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
  • Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
  • Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

  • Brainstorming with others
  • Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
  • Analyzing cause and effect
  • Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

  • Creating a list of potential ideas to solve the problem
  • Grouping and categorizing similar solutions
  • Prioritizing potential solutions based on feasibility, cost, and resources required
  • Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

  • SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
  • Decision-making matrices
  • Pros and cons lists
  • Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

  • Communicating the solution to relevant parties
  • Setting timelines and milestones
  • Assigning tasks and responsibilities
  • Monitoring the solution and making adjustments as necessary
  • Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

  • Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
  • Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
  • SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
  • Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

  • Generate a diverse range of solutions
  • Encourage all team members to participate
  • Foster creative thinking

When brainstorming, remember to:

  • Reserve judgment until the session is over
  • Encourage wild ideas
  • Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

  • 5 Whys : Ask “why” five times to get to the underlying cause.
  • Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
  • Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

  • List your problem’s strengths, such as relevant resources or strong partnerships.
  • Identify its weaknesses, such as knowledge gaps or limited resources.
  • Explore opportunities, like trends or new technologies, that could help solve the problem.
  • Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

  • Write the problem in the center of a blank page.
  • Draw branches from the central problem to related sub-problems or contributing factors.
  • Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

  • Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
  • Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
  • Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

  • Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
  • Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
  • Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

  • Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
  • Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
  • Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
  • How to Resolve Employee Conflict at Work [Steps, Tips, Examples]
  • How to Write Inspiring Core Values? 5 Steps with Examples
  • 30 Employee Feedback Examples (Positive & Negative)
  • Problem solving
  • Skills & Tools

A problem is any unpleasant situation which prevents people from achieving what they want to achieve. Any activity to eliminate a problem is termed problem solving.

Problem solving skills refers to our ability to solve problems in an effective and timely manner without any impediments.

It involves being able to identify and define the problem, generating alternative solutions, evaluating and selecting the best alternative, and implementing the selected solution. Obtaining a feedback and responding to it appropriately is an essential aspect of problem solving skills too.

We face problems every time. However, some problems are more complex than others. But whether you face big problems or small ones, this skill helps solve it effectively.

Importance of problem solving skills

Obviously, every organization has problems and every individual has problems too. For this reason, the ability to solve problems is of great importance to individuals and organizations. Some of the benefits include:

  • Make the impossible possible.  Knowledge alone is not the key to solving problems but rather, complimenting it with systematic problem solving approaches makesthe difference. This helps individuals and organizations overcome perilous challenges.
  • Makes you a stand out.  People are trained to do the usual. They have acquired skills and knowledge in what they do. However, people can hardly solve problems when they are unexpected or unprecedented ones. If you become a regular problem solver at your workplace, you are easily noticed, recognized, and appreciated.
  • Increased confidence.  No matter where you work or what your profession is, having the ability to solve problems will boost your confidence level. Because you are sure of your ability to solve problems, you don’t spend time worrying about what you will do if a problem should arise.

How to improve upon problem solving skills

Just like any of the other skills, the art of problem solving can be learnt and improved upon. Below are few tips to help you improve this skill.

  • Detach yourself from the problem.  Don’t regard yourself as the problem itself and don’t presume you are incapacitated to solve the problem. See the problem as the enemy that has to be defeated by you.
  • Analyze it in parts and not as a whole.  Don’t see the problem as a whole big unit that needs to be fixed – That may deter you from attempting to solve it. Rather, break it into parts and tackle them step by step, and portion by portion. The little pieces you solve will add up to become the solution for the whole unit. For instance; if there’s turmoil in your organization, analyze the various aspects or departments of the organization. Choose one problematic area, such as communication, to start from. When that is fixed, you may move on to the other problematic areas.
  • Be inquisitive and investigative.  Being inquisitive and conducting thorough investigation and research helps you identify what the core of the problem is. In other words, it grants you access to the cause of the problem. Once the real cause of the problem is known, it becomes easier to solve it.
  • Be open to suggestions.  Other people’s contributions can be very helpful. It saves you the time of having to search for every piece of information that is needed.

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What is a word problem?

What are word problems?

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Word problems are seen as a crucial part of learning in the primary curriculum, because they require children to apply their knowledge of various different concepts to 'real-life' scenarios. 

Word problems also help children to familiarise themselves with mathematical language (vocabulary like fewer, altogether, difference, more, share, multiply, subtract, equal, reduced, etc.).

Teachers tend to try and include word problems in their maths lessons at least twice a week.  

what is the definition of the word problem solving

What is RUCSAC?

In the classroom children might be taught the acronym RUCSAC (Read, Understand, Choose, Solve, Answer, Check) to help them complete word problems.

By following the acronym step by step children learn to apply a structured, analytical strategy to their calculations. They will need to understand what the problem is asking them to find out by reading the question carefully, choosing the correct mathematical operation to help them solve the query and finally checking their answer by using the inverse operation .

Word problem examples for Years 1 to 6

The following are example word problems that apply to each primary year group.

In Year 1 a child would usually been given apparatus to help them with a problem (counters, plastic coins, number cards, number lines or picture cards).

Sarah wants to buy a teddy bear costing 30p. How many 10p coins will she need?

Brian has 3 sweets. Tom has double this number of sweets. How many sweets does Tom have?

In Year 2, children continue to use apparatus to help them with problem-solving.

Faye has 12 marbles. Her friend Louise has 9 marbles. How many marbles do they both have altogether?

Three children are each given 5 teddy bears. How many teddy bears do they have altogether?

In Year 3, some children may use apparatus, but on the whole children will tend to work out word problems without physical aids. Teachers will usually demonstrate written methods for the four operations (addition, subtraction, multiplication and division) to support children in their working out of the problems.

A jumper costs £23. How much will 4 jumpers cost?

Sarah has 24 balloons. She gives a quarter of them away to her friend. How many balloons does she give away?

Children will also start to do two-step problems in Year 3. This is a problem where finding the answer requires two separate calculations, for example:

I have £34. I am given another £26. I divide this money equally into four different bank accounts. How much money do I put in each bank account?

  • In this case, the first step would be to add £34 and £26 to make £60.
  • The second step would be to divide £60 by 4 to make £15.

Children should feel confident in an efficient written method for each operation at this stage. They will continue to be given a variety of problems and have to work out which operation and method is appropriate for each. They will also be given two-step problems. 

I have 98 marbles. I share them equally between 6 friends. How many marbles does each friend get? How many marbles are left over?

Children will continue to do one-step and two-step problems. They will start to carry out problem-solving involving decimals . 

My chest of drawers is 80cm wide and my table is 1.3m wide. How much wall space do they take up when put side by side?

There are 24 floors of a car park. Each floor has room for 45 cars. How many cars can the car park fit altogether?

In Year 6 children solve 'multi-step problems' and problems involving fractions , decimals and percentages . 

Sarah sees the same jumper in two different sales: In the first sale, the original price of the jumper is £36.15, but has been reduced by a third. In the second sale, the jumper was priced at £45, but now has 40% off. How much does each jumper cost and which one is the cheapest?

In the past, calculators were sometimes used for solving two-step problems like the one above, but the new curriculum does not include the use of calculators at any time during primary school.

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Word Problems Explained For Elementary School Teachers & Parents

Sophie bartlett.

Solving word problems in elementary school is an essential part of the math curriculum. Here are over 30 math word problems to practice with children, plus expert guidance on how to solve them.

This blog is part of our series of blogs designed for teachers, schools, and parents supporting home learning .

What is a word problem?

Isn’t brilliant arithmetic enough, mastery helps children to explore math in greater depth, how to teach children to solve word problems , math word problems for kindergarten to grade 5, topic based word problems.

A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a ‘real-life’ scenario. 

This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem. 

For example:

Vocabulary Used In Word Problems

Word Problems Grade 4 Number and Base 10

11 grade 4 number and base 10 questions to develop your students' reasoning and problem solving skills.

In short, no. Students need to build good reading comprehension, even in math. Overtime math problems become increasingly complex and require students to possess deep conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. 

As students progress through their mathematical education, they will need to be able to apply mathematical reasoning and develop mathematical arguments and proofs using math language. They will also need to be dynamic, applying their math knowledge to a variety of increasingly sophisticated problems. 

To support this schools are adopting a ‘mastery’ approach to math

“Teaching for mastery”, is defined with these components: 

  • Math teaching for mastery rejects the idea that a large proportion of people ‘just can’t do math’.  
  • All students are encouraged by the belief that by working hard at math they can succeed. 
  • Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other. 
  • Significant time is spent developing deep knowledge of the key ideas that are needed to support future learning. The structure and connections within the mathematics are emphasized, so that students develop deep learning that can be sustained.

(The Essence of Maths Teaching for Mastery, 2016)

Fluency in arithmetic is important; however, with this often lies the common misconception that once a child has learned the number skills appropriate to their grade level/age, they should be progressed to the next grade level/age of number skills. 

The mastery approach encourages exploring the breadth and depth of these math concepts (once fluency is secure) through reasoning and problem solving. 

Here are two simple strategies that can be applied to many word problems before solving them.

  • What do you already know?
  • How can this problem be drawn/represented pictorially?

Let’s see how this can be applied to word problems to help achieve the answer.

Solving a simple word problem

There are 28 students in a class.

The teacher has 8 liters of orange juice.

She pours 225 milliliters of orange juice for every student.

How much orange juice is left over?

1. What do you already know?

  • There are 1,000ml in 1 liter
  • Pours = liquid leaving the bottle = subtraction
  • For every = multiply
  • Left over = requires subtraction at some point

2. How can this problem be drawn/represented pictorially?

The bar model , also known as strip diagram , is always a great way of representing problems. However, if you are not familiar with this, there are always other ways of drawing it out. 

Read more: What is a bar model

For example, for this question, you could draw 28 students (or stick man x 28) with ‘225 ml’ above each one and then a half-empty bottle with ‘8 liters’ marked at the top.

Now to put the math to work. This is a 5th grade multi-step problem, so we need to use what we already know and what we’ve drawn to break down the steps.

quantity word problem

Solving a more complex, mixed word problem

Mara is in a bookshop.

She buys one book for $6.99 and another that costs $3.40 more than the first book.

She pays using a $20 bill.

What change does Mara get? (What is the remainder?)

  • More than = add
  • Using decimals means I will have to line up the decimal points correctly in calculations
  • Change from money = subtract

See this example of bar modelling for this question:

money word problem

Now to put the math to work using what we already know and what we’ve drawn to break down the steps.

Mara is in a bookshop. 

She buys one book for $6.99 and another that costs $3.40 more than the first book. 1) $6.99 + ($6.99 + $3.40) = $17.38

What change does Mara get? 2) $20 – $17.38 = $2.62

The more children learn about math as they go through elementary school, the trickier the word problems they face will become.

Below you will find some information about the types of word problems your child will be coming up against on a year by year basis, and how word problems apply to each elementary grade. 

Word problems in kindergarten

Throughout kindergarten a child is likely to be introduced to word problems with the help of concrete resources (manipulatives, such as pieces of physical apparatus like coins, cards, counters or number lines) to help them understand the problem.

An example of a word problem for kindergarten would be

Chris has 3 red bounce balls and 2 green bounce balls. How many bounce balls does Chris have in all?

Word problems in 1st grade

First grade is a continuation of kindergarten when it comes to word problems, with children still using concrete resources to help them understand and visualize the problems they are working on

An example of a word problem for first grade would be:

A class of 10 children each have 5 pencils in their pencil cases. How many pencils are there in total?

Word problems in 2nd grade

In second grade, children will move away from using concrete resources when solving word problems, and move towards using written methods. Teachers will begin to demonstrate the adding and subtracting within 100, adding up to 4- two-digit numbers at a time.

This is also the year in which 2-step word problems will be introduced. This is a problem which requires two individual calculations to be completed.

2nd grade word problem: geometry properties of shape

Shaun is making shapes out of plastic straws.

At the vertices where the straws meet, he uses blobs of modeling clay to fix them together

Here are some of the shapes he makes:

One of Sean’s shapes is a triangle. Which is it? Explain your answer.

Answer: shape B as a triangle has 3 sides (straws) and 3 vertices, or angles (clay)

2nd grade word problem: statistics

2nd grade is collecting pebbles. This pictogram shows the different numbers of pebbles each group finds.

Second grade word problem: Statistics

Word problems in 3rd grade

At this stage of their elementary school career, children should feel confident using the written method for addition and subtraction. They will begin multiplying and dividing within 100. 

This year children will be presented with a variety of problems, including 2-step problems and be expected to work out the appropriate method required to solve each one. 

3rd grade word problem: number and place value

My number has four digits and has a 7 in the hundreds place.

The digit which has the highest value in my number is 2.

The digit which has the lowest value in my number is 6.

My number has 3 fewer tens than hundreds.

What is my number?

Answer: 2,746

Word problems in 4th grade

One and two-step word problems continue in fourth grade, but this is also the year that children will be introduced to word problems containing decimals.

4th grade word problem: fractions and decimals

Stan, Frank and John are washing their cars outside their houses.

Stan has washed 0.5 of his car.

Frank has washed 1/5 of his car.

Norm has washed 2/5 of his car.

Who has washed the most?

Explain your answer.

Answer: Stan (he has washed 0.5 whereas Frank has only washed 0.2 and Norm 0.4)

Word problems in 5th grade

In fifth grade children move on from 2-step word problems to multi-step word problems . These will include fractions and decimals.

Here are some examples of the types of math word problems in fifth grade will have to solve.

5th grade word problem: ratio and proportion

The Angel of the North is a large statue in England. It is 20 meters tall and 54 meters wide. 

Ally makes a scale model of the Angel of the North. Her model is 40 centimeters tall. How wide is her model?

Answer: 108cm

5th grade word problem: algebra

Amina is making designs with two different shapes.

She gives each shape a value.

algebra question for 5th grade

Calculate the value of each shape.

Answer: 36 (hexagon) and 25. 

5th grade word problem: measurement

Answer: 1.7 liters or 1,700ml

The following examples give you an idea of the kinds of math word problems your child will encounter in elementary school

4th grade word problem: place value

This machine subtracts one hundredth each time the button is pressed. The starting number is 8.43. What number will the machine show if the button is pressed six times? Answer: 8.37

Download free number and place value word problems for grades 2, 3, 4 and 5

2nd grade word problem: addition and subtraction

Sam has 64 sweets. He gets given 12 more. He then gives 22 away. How many sweets is he left with? Answer: 54

Download free addition and subtraction word problems for for grades 2, 3, 4 and 5

2nd grade word problem: addition

Sammy thinks of a number. He subtracts 70. His new number is 12. What was the number Sammy thought of? Answer: 82

5th grade word problem: subtraction

The temperature at 7pm was 4oC. By midnight, it had dropped by 9 degrees. What was the temperature at midnight? Answer: -5oC

3rd grade word problem: multiplication

Eggs are sold in boxes of 12. The egg boxes are delivered to stores in crates. Each crate holds 9 boxes. How many eggs are in a crate? Answer: 108

Download free multiplication word problems for grades 2, 3, 4 and 5. 

5th grade word problem: division

A factory produces 3,572 paint brushes every day. They are packaged into boxes of 19. How many boxes does the factory produce every day? Answer: 188

Download free division word problems for grades 2, 3, 4 and 5. 

Free resource: Use these four operations word problems to practice addition, subtraction, multiplication and division all together.

4th grade word problem: fractions

At the end of every day, a chocolate factory has 1 and 2/6 boxes of chocolates left over. How many boxes of chocolates are left over by the end of a week? Answer: 9 and 2/6 or 9 and 1/3

Download free fractions and decimals word problems for grades 2, 3, 4 and 5. 

2nd grade word problem: money

Lucy and Noor found some money on the playground at recess. Lucy found 2 dimes and 1 penny, and Noor found 2 quarters and a dime. How many cents did Lucy and Noor find? Answer: Lucy = $0.21, Noor = $0.60; $0.21 + $0.61 = $0.81

3rd grade word problem: area

A rectangle measures 6cm by 5cm.

area maths questions

What is its area? Answer: 30cm2

3rd grade word problem: perimeter

The swimming pool at the Sunshine Inn hotel is 20m long and 7m wide. Mary swims around the edge of the pool twice. How many meters has she swum? Answer: 108m

5th grade word problem: ratio (crossover with measurement)

A local council has spent the day painting double yellow lines. They use 1 pot of yellow paint for every 100m of road they paint. How many pots of paint will they need to paint a 2km stretch of road? Answer: 20 pots

5th grade word problem: PEMDAS

Draw a pair of parentheses in one of these calculations so that they make two different answers. What are the answers?

50 – 10 × 5 =

5th grade word problem: volume

This large cuboid has been made by stacking shipping containers on a boat. Each individual shipping container has a length of 6m, a width of 4m and a height of 3m. What is the volume of the large cuboid? Answer: 864m3

Remember: The word problems can change but the math won’t 

It can be easy for children to get overwhelmed when they first come across word problems, but it is important that you remind them that while the context of the problem may be presented in a different way, the math behind it remains the same. 

Word problems are a good way to bring math into the real world and make math more relevant for your child. So help them practice, or even ask them to turn the tables and make up some word problems for you to solve. 

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

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Check out this guide featuring practical examples, tips and strategies to successfully embed metacognition across your school to accelerate math growth.

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We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

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This is a guide on how to solve word problems!

Definition of a Word Problem:

Before you start to solve word problems, it is important to understand what a word problem is. A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved. A good way to solve word problems is by using the method called “GRASS.” GRASS is an acronym for Given, Required, Analysis, Solution, and Statement. You can use GRASS, step by step, to break down a word problem, making it easier to solve.

Given : Identify the given information in the question. What values are given and what do they represent? It may be helpful to know the following terms that are sometimes used in math questions and what they mean:

Required : Look at what the question is actually asking you to find. Whatever it is, represent it with a variable e.g., x.

Analysis : If applicable, draw a sketch if one is not already provided. Decide on the appropriate math techniques to use and the formulas that relate the different quantities of interest. Whenever possible, use one variable only. For example, if you're looking for two numbers that differ by 5, then let x, and x+5 (or x and x-5) represent the two numbers, NOT x and y. Alternatively, you may be able to use some information presented in the question to help you rewrite your equation in terms of one variable only.

Solution : Solve the equation or find the answer you're looking for. You’ll have to think hard about the various math techniques you’ve learned in your courses to figure out which ones work for this particular question. Make sure your solution(s) makes sense in the context of the application—e.g., a negative area doesn't make any sense.

Statement : Finish off with a concluding statement to make clear the answer to the question. If applicable, include units in your answer.

Here is a simple example to show how GRASS is used to solve a word problem.

The perimeter of a rectangular park is 26 m. If the length of the park is 5m, what is the width of the park?

Given : In this question, we are given the perimeter of the rectangular park as 26 m. We are also told that the length of the park is 5 m. So, P= 26m and L= 5m.

Required : The question asks: “What is the width of the park?” From this we know we have to find the width. Find: w = ?

Analysis : We can draw a sketch of the rectangular park to find out what formulas we might have to use to find the width.

Note: The longer sides are the lengths and the shorter sides are the widths.

Word Problem Sketch

So from this sketch, we can see that we need the formula for the perimeter of a rectangle.

If we rearrange the equation for w, then we get

w = (P – 2L) ÷ 2

The simplified equation is,

w = P/2 - L

Solution : So now that we have our equation, we can solve for the unknown variable w by subbing in our known variables, P and L.

w = (26m)/2   -  5m

w = 13m - 5m

w = 8m 

Statement : We found that the width is 8 metres. So now write your final answer from your solution in words.

Therefore, the width of the rectangular park is 8 metres.

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Our next-generation model: Gemini 1.5

Feb 15, 2024

The model delivers dramatically enhanced performance, with a breakthrough in long-context understanding across modalities.

SundarPichai_2x.jpg

A note from Google and Alphabet CEO Sundar Pichai:

Last week, we rolled out our most capable model, Gemini 1.0 Ultra, and took a significant step forward in making Google products more helpful, starting with Gemini Advanced . Today, developers and Cloud customers can begin building with 1.0 Ultra too — with our Gemini API in AI Studio and in Vertex AI .

Our teams continue pushing the frontiers of our latest models with safety at the core. They are making rapid progress. In fact, we’re ready to introduce the next generation: Gemini 1.5. It shows dramatic improvements across a number of dimensions and 1.5 Pro achieves comparable quality to 1.0 Ultra, while using less compute.

This new generation also delivers a breakthrough in long-context understanding. We’ve been able to significantly increase the amount of information our models can process — running up to 1 million tokens consistently, achieving the longest context window of any large-scale foundation model yet.

Longer context windows show us the promise of what is possible. They will enable entirely new capabilities and help developers build much more useful models and applications. We’re excited to offer a limited preview of this experimental feature to developers and enterprise customers. Demis shares more on capabilities, safety and availability below.

Introducing Gemini 1.5

By Demis Hassabis, CEO of Google DeepMind, on behalf of the Gemini team

This is an exciting time for AI. New advances in the field have the potential to make AI more helpful for billions of people over the coming years. Since introducing Gemini 1.0 , we’ve been testing, refining and enhancing its capabilities.

Today, we’re announcing our next-generation model: Gemini 1.5.

Gemini 1.5 delivers dramatically enhanced performance. It represents a step change in our approach, building upon research and engineering innovations across nearly every part of our foundation model development and infrastructure. This includes making Gemini 1.5 more efficient to train and serve, with a new Mixture-of-Experts (MoE) architecture.

The first Gemini 1.5 model we’re releasing for early testing is Gemini 1.5 Pro. It’s a mid-size multimodal model, optimized for scaling across a wide-range of tasks, and performs at a similar level to 1.0 Ultra , our largest model to date. It also introduces a breakthrough experimental feature in long-context understanding.

Gemini 1.5 Pro comes with a standard 128,000 token context window. But starting today, a limited group of developers and enterprise customers can try it with a context window of up to 1 million tokens via AI Studio and Vertex AI in private preview.

As we roll out the full 1 million token context window, we’re actively working on optimizations to improve latency, reduce computational requirements and enhance the user experience. We’re excited for people to try this breakthrough capability, and we share more details on future availability below.

These continued advances in our next-generation models will open up new possibilities for people, developers and enterprises to create, discover and build using AI.

Context lengths of leading foundation models

Highly efficient architecture

Gemini 1.5 is built upon our leading research on Transformer and MoE architecture. While a traditional Transformer functions as one large neural network, MoE models are divided into smaller "expert” neural networks.

Depending on the type of input given, MoE models learn to selectively activate only the most relevant expert pathways in its neural network. This specialization massively enhances the model’s efficiency. Google has been an early adopter and pioneer of the MoE technique for deep learning through research such as Sparsely-Gated MoE , GShard-Transformer , Switch-Transformer, M4 and more.

Our latest innovations in model architecture allow Gemini 1.5 to learn complex tasks more quickly and maintain quality, while being more efficient to train and serve. These efficiencies are helping our teams iterate, train and deliver more advanced versions of Gemini faster than ever before, and we’re working on further optimizations.

Greater context, more helpful capabilities

An AI model’s “context window” is made up of tokens, which are the building blocks used for processing information. Tokens can be entire parts or subsections of words, images, videos, audio or code. The bigger a model’s context window, the more information it can take in and process in a given prompt — making its output more consistent, relevant and useful.

Through a series of machine learning innovations, we’ve increased 1.5 Pro’s context window capacity far beyond the original 32,000 tokens for Gemini 1.0. We can now run up to 1 million tokens in production.

This means 1.5 Pro can process vast amounts of information in one go — including 1 hour of video, 11 hours of audio, codebases with over 30,000 lines of code or over 700,000 words. In our research, we’ve also successfully tested up to 10 million tokens.

Complex reasoning about vast amounts of information

1.5 Pro can seamlessly analyze, classify and summarize large amounts of content within a given prompt. For example, when given the 402-page transcripts from Apollo 11’s mission to the moon, it can reason about conversations, events and details found across the document.

Reasoning across a 402-page transcript: Gemini 1.5 Pro Demo

Gemini 1.5 Pro can understand, reason about and identify curious details in the 402-page transcripts from Apollo 11’s mission to the moon.

Better understanding and reasoning across modalities

1.5 Pro can perform highly-sophisticated understanding and reasoning tasks for different modalities, including video. For instance, when given a 44-minute silent Buster Keaton movie , the model can accurately analyze various plot points and events, and even reason about small details in the movie that could easily be missed.

Multimodal prompting with a 44-minute movie: Gemini 1.5 Pro Demo

Gemini 1.5 Pro can identify a scene in a 44-minute silent Buster Keaton movie when given a simple line drawing as reference material for a real-life object.

Relevant problem-solving with longer blocks of code

1.5 Pro can perform more relevant problem-solving tasks across longer blocks of code. When given a prompt with more than 100,000 lines of code, it can better reason across examples, suggest helpful modifications and give explanations about how different parts of the code works.

Problem solving across 100,633 lines of code | Gemini 1.5 Pro Demo

Gemini 1.5 Pro can reason across 100,000 lines of code giving helpful solutions, modifications and explanations.

Enhanced performance

When tested on a comprehensive panel of text, code, image, audio and video evaluations, 1.5 Pro outperforms 1.0 Pro on 87% of the benchmarks used for developing our large language models (LLMs). And when compared to 1.0 Ultra on the same benchmarks, it performs at a broadly similar level.

Gemini 1.5 Pro maintains high levels of performance even as its context window increases. In the Needle In A Haystack (NIAH) evaluation, where a small piece of text containing a particular fact or statement is purposely placed within a long block of text, 1.5 Pro found the embedded text 99% of the time, in blocks of data as long as 1 million tokens.

Gemini 1.5 Pro also shows impressive “in-context learning” skills, meaning that it can learn a new skill from information given in a long prompt, without needing additional fine-tuning. We tested this skill on the Machine Translation from One Book (MTOB) benchmark, which shows how well the model learns from information it’s never seen before. When given a grammar manual for Kalamang , a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person learning from the same content.

As 1.5 Pro’s long context window is the first of its kind among large-scale models, we’re continuously developing new evaluations and benchmarks for testing its novel capabilities.

For more details, see our Gemini 1.5 Pro technical report .

Extensive ethics and safety testing

In line with our AI Principles and robust safety policies, we’re ensuring our models undergo extensive ethics and safety tests. We then integrate these research learnings into our governance processes and model development and evaluations to continuously improve our AI systems.

Since introducing 1.0 Ultra in December, our teams have continued refining the model, making it safer for a wider release. We’ve also conducted novel research on safety risks and developed red-teaming techniques to test for a range of potential harms.

In advance of releasing 1.5 Pro, we've taken the same approach to responsible deployment as we did for our Gemini 1.0 models, conducting extensive evaluations across areas including content safety and representational harms, and will continue to expand this testing. Beyond this, we’re developing further tests that account for the novel long-context capabilities of 1.5 Pro.

Build and experiment with Gemini models

We’re committed to bringing each new generation of Gemini models to billions of people, developers and enterprises around the world responsibly.

Starting today, we’re offering a limited preview of 1.5 Pro to developers and enterprise customers via AI Studio and Vertex AI . Read more about this on our Google for Developers blog and Google Cloud blog .

We’ll introduce 1.5 Pro with a standard 128,000 token context window when the model is ready for a wider release. Coming soon, we plan to introduce pricing tiers that start at the standard 128,000 context window and scale up to 1 million tokens, as we improve the model.

Early testers can try the 1 million token context window at no cost during the testing period, though they should expect longer latency times with this experimental feature. Significant improvements in speed are also on the horizon.

Developers interested in testing 1.5 Pro can sign up now in AI Studio, while enterprise customers can reach out to their Vertex AI account team.

Learn more about Gemini’s capabilities and see how it works .

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Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi . We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Strings but also build up problem-solving skills.

In this problem, we are given a string A and a dictionary of n words B, to find out if A can be segmented into a space-separated sequence of dictionary words. Return 1 if it is possible to break A into a sequence of dictionary words, else return 0.

Note: From the dictionary B each word can be taken any number of times and in any order.

Input: n = 6 B = { "i", "like", "sam", "sung", "samsung", "mobile"} A = "ilike" Output: 1 Explanation: The string can be segmented as "i like".

Give the problem a try before going through the video. All the best!!! Problem Link: https://www.geeksforgeeks.org/problems/word-break1352/1

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  6. Word Problem Solving Help

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VIDEO

  1. What type of problem is this ?

  2. Calculus Word Problem Solving

  3. Word problems

COMMENTS

  1. Problem-solving Definition & Meaning

    noun : the process or act of finding a solution to a problem Let's do some problem-solving and see if we can't figure out what to do. problem-solving skills Examples of problem-solving in a Sentence

  2. PROBLEM-SOLVING

    noun [ U ] HR, MANAGEMENT uk us Add to word list the process of finding solutions to problems: problem-solving abilities/skills/strategies The programme offers training in basic problem-solving strategies and is suitable for all levels. problem-solver noun [ C ] He is considered a troubleshooter and a problem-solver.

  3. Problem solving

    Definition. The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific ...

  4. PROBLEM-SOLVING definition

    noun [ U ] HR, MANAGEMENT uk us Add to word list Add to word list the process of finding solutions to problems: problem-solving abilities/skills/strategies The programme offers training in basic problem-solving strategies and is suitable for all levels. problem-solver noun [ C ] He is considered a troubleshooter and a problem-solver.

  5. What exactly do we mean by the term 'problem solving'?

    Just like creativity, problem solving is a key skill required across all sectors and at all levels. However, while the word 'creativity' can seem to refer to a very broad range of meanings, the term 'problem solving' can, in contrast, seem overly narrow. A well-defined problem can be understood, agreed upon and then solved, often using approaches that are familiar or well-practiced.

  6. The Problem-Solving Process

    Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation.

  7. What Is Problem Solving?

    Define Every Problem. The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem - not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work.

  8. PROBLEM-SOLVING definition and meaning

    the act or process of finding solutions to problems, esp by using a scientific or analytical approach Problem-solving is often carried on by processes of visualization. an approach to problem-solving Collins English Dictionary. Copyright © HarperCollins Publishers Derived forms problem-solver noun Examples of 'problem-solving' in a sentence

  9. problem-solving noun & adjective

    The earliest known use of the word problem-solving is in the 1850s. OED's earliest evidence for problem-solving is from 1854, in Putnam's Monthly Magazine. problem-solving is formed within English, by compounding. n. 1946-.

  10. problem-solving noun

    /ˈprɒbləm sɒlvɪŋ/ /ˈprɑːbləm sɑːlvɪŋ/ [uncountable] the act of finding ways of dealing with problems to develop problem-solving skills and strategies Oxford Collocations Dictionary Join us Join our community to access the latest language learning and assessment tips from Oxford University Press!

  11. What is Problem Solving? Steps, Process & Techniques

    Quality Glossary Definition: Problem solving Problem solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution. The problem-solving process Problem solving resources Problem Solving Chart The Problem-Solving Process

  12. Word problem Definition & Meaning

    noun : a mathematical problem expressed entirely in words typically used as an educational tool Examples of word problem in a Sentence

  13. Word problem (mathematics education)

    Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.As most word problems involve a narrative of some sort, they are ...

  14. What Are Problem-Solving Skills? Definitions and Examples

    Creativity. Communication. Decision-making. Team-building. Problem-solving skills are important in every career at every level. As a result, effective problem-solving may also require industry or job-specific technical skills. For example, a registered nurse will need active listening and communication skills when interacting with patients but ...

  15. What is Problem Solving

    At its simplest, the meaning of problem-solving is the process of defining a problem, determining its cause, and implementing a solution. The definition of problem-solving is rooted in the fact that as humans, we exert control over our environment through solutions. We move forward in life when we solve problems and make decisions.

  16. Problem Definition & Meaning

    1 a : a question raised for inquiry, consideration, or solution b : a proposition in mathematics or physics stating something to be done 2 a : an intricate unsettled question b : a source of perplexity, distress, or vexation c : difficulty in understanding or accepting I have a problem with your saying that problem 2 of 2 adjective 1

  17. What Are Problem-Solving Skills? Definition and Examples

    Problem-Solving: The Bottom Line Problem-Solving Skills Definition Problem-solving skills are the ability to identify problems, brainstorm and analyze answers, and implement the best solutions.

  18. What is Problem Solving? (Steps, Techniques, Examples)

    Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease.

  19. Problem Solving

    Any activity to eliminate a problem is termed problem solving. Problem solving skills refers to our ability to solve problems in an effective and timely manner without any impediments.

  20. What is a word problem?

    A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation. Word problems are seen as a crucial part of learning in the primary curriculum, because they require children to apply their knowledge of various different concepts to 'real-life' scenarios.

  21. Word Problems Explained For Elementary School

    Word Problems Explained For Elementary School Teachers & Parents. Solving word problems in elementary school is an essential part of the math curriculum. Here are over 30 math word problems to practice with children, plus expert guidance on how to solve them. This blog is part of our series of blogs designed for teachers, schools, and parents ...

  22. PDF Glossary of Problem-Solving Terms

    a problem. In other words, problem solving is the process of figuring out what to do about a problem. Problem Space That area wherein the problem state can be said to reside. This "area" might be conceptual, physical or logical. Problem State The situation requiring action, including all the reasons action is required.

  23. Word Problems

    A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved. A good way to solve word problems is by using the method called "GRASS." GRASS is an acronym for Given, Required, Analysis, Solution, and Statement.

  24. Introducing Gemini 1.5, Google's next-generation AI model

    Relevant problem-solving with longer blocks of code. 1.5 Pro can perform more relevant problem-solving tasks across longer blocks of code. When given a prompt with more than 100,000 lines of code, it can better reason across examples, suggest helpful modifications and give explanations about how different parts of the code works.

  25. PROBLEM OF THE DAY : 20/02/2024

    Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi.We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Strings but also build up problem-solving skills.. In this problem, we are given a string A and a dictionary of n words B, to find out if A can be segmented into a ...