problem solving different word

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Synonyms and antonyms of problem-solving in English

Problem-solving.

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skip out on something

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to avoid doing something that you should do; to leave someone when they need your help

It’s not really my thing (How to say you don’t like something)

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verb as in answer, resolve

Strongest matches

clarify , clear up , deal with , decide , determine , do , explain , figure out , fix , have , iron out , settle , work out

Strong matches

break , construe , crack , decipher , decode , disentangle , divine , elucidate , enlighten , expound , fathom , get , hit , illuminate , interpret , lick , puzzle , reason , unfold , unlock , unravel , untangle , work

Weak matches

find out , get right , get to the bottom , hit upon , make a dent , make out , pan out , put two and two together , think out , unriddle

Example Sentences

We know more than ever about how students reason, process information and solve problems.

I always think about what my favorite creators are building in their homes and what problems they are trying to solve.

Whoever’s fault it is, we either all chip in to solve it or we all suffer.

I was only looking for a generic term that helps me to solve my most immediate problem, which is to create a logo.

She wants them to think about different ways to solve a problem.

But one extra trick would instantly solve the problem of crashes that occur over water.

This is the first study of its kind in Turkey and raises the possibility that a private solution could solve a public problem.

To solve the problem, we need to study a lot more comets and meteorites.

Is there anyone who thinks the urgent problem we need to solve in Washington, D.C. is how to allow more spending on campaigns?

“I doubt you can solve range and the need for a large magazine with the same missile,” he said.

To solve this one I stopped on the tavern steps, leaned against a pillar, and gazed through the dozing village.

But, though a capital sabreur, he was evidently not made to solve questions in diplomacy.

In the preceding chapter we have endeavoured to solve the question what are the qualities that constitute good tone.

The meetings were held secretly behind closed doors because of the grave problems which the convention had to solve.

To solve this problem, is to know the remedy; and to know it, is but necessary, in order successfully to apply it.

Related Words

Words related to solve are not direct synonyms, but are associated with the word solve . Browse related words to learn more about word associations.

verb as in bring to successful conclusion; reach a goal

• bring about
• bring to pass
• carry through
• follow through
• see-through

verb as in reply, react

• acknowledge
• answer back
• back at you
• be in touch
• counterclaim
• field the question
• get back at
• get back to
• give a snappy comeback

verb as in figure out code

Viewing 5 / 30 related words

From Roget's 21st Century Thesaurus, Third Edition Copyright © 2013 by the Philip Lief Group.

Look up a word, learn it forever.

Problem solving.

• noun the thought processes involved in solving a problem see more see less types: show 14 types... hide 14 types... enquiry , inquiry , research a search for knowledge calculation , computation , figuring , reckoning problem solving that involves numbers or quantities nature study the study of animals and plants in the natural world (usually at an elementary level) experiment , experimentation the testing of an idea empirical research an empirical search for knowledge investigation , probe an inquiry into unfamiliar or questionable activities canvass , opinion poll , poll , public opinion poll , survey an inquiry into public opinion conducted by interviewing a random sample of people heraldry the study and classification of armorial bearings and the tracing of genealogies extrapolation (mathematics) calculation of the value of a function outside the range of known values interpolation (mathematics) calculation of the value of a function between the values already known conversion a change in the units or form of an expression: "conversion from Fahrenheit to Centigrade" approximation , estimate , estimation , idea an approximate calculation of quantity or degree or worth derivative , derived function , differential , differential coefficient , first derivative the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx integral the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x) type of: cerebration , intellection , mentation , thinking , thought , thought process the process of using your mind to consider something carefully
• noun the area of cognitive psychology that studies the processes involved in solving problems see more see less type of: cognitive psychology an approach to psychology that emphasizes internal mental processes

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Overview of the Problem-Solving Mental Process

• 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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7 Problem Solving Skills That Aren’t Just Buzzwords (+ Resume Example)

• Júlia Mlčúchova , 
• Updated April 8, 2024 9 min read

Problem-solving skills are something everybody should include on their resume, yet only a few seem to understand what these skills actually are. If you've always felt that the term "problem-solving skills" is rather vague and wanted to know more, you've come to the right place.

In this article, we're going to explain what problem-solving skills really mean. We'll talk about what makes up good problem-solving skills and give you tips on how to get better at them. You'll also find out how to make your problem-solving abilities look more impressive to those who might want to hire you.

Sounds good, right? Curious to learn more? 

In this article we’ll show you:

• What are problem solving skills;
• Why are they important; 
• Specific problem solving skills examples;
• How to develop your problem solving skills;
• And, how to showcase them on your resume.

Table of Contents

Click on a section to skip

What are problem solving skills?

Why are problem solving skills important, the best 7 problem solving skills examples, how to develop problem solving skills, problem solving skills resume example, key takeaways: problem solving skills.

First of all, they're more than just a buzzword!

Problem-solving skills are a set of specific abilities that allow you to deal with unexpected situations in the workplace, whether it be job related or team related. 

It's a complex process that involves several “sub skills” or “sub steps,” namely:

• Recognizing and identifying the issue at hand.
• Breaking the problem down into smaller parts and analyzing how they relate to one another. 
• Creating potential solutions to the problem, evaluating them and picking the best one.  
• Applying the chosen solution and assessing its outcome. 
• Learning from the whole process to deal with future problems more effectively. 

As you can see, it's not just about solving problems that are right in front of us, but also about predicting potential issues and being prepared to deal with them before they arise.  

Despite what you may believe, problem-solving skills aren't just for managers . 

Think about it this way: Why do employers hire employees in the first place? To solve problems for them!

And, as we all know, problems don't discriminate. In other words, it doesn't matter whether you're just an intern, an entry-level professional, or a seasoned veteran, you'll constantly face some kind of challenges. And the only difference is in how complex they will get.

This is also reflected in the way employers assess suitability of potential job candidates. 

In fact, research shows that the ability to deal with unexpected complications is prioritized by an overwhelming 60% of employers across all industries, making it one of the most compelling skills on your resume.

So, regardless of your job description or your career level, you're always expected to find solutions for problems, either independently or as a part of a team. 

And that's precisely what makes problem-solving skills so invaluable and universal ! 

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As we've said before, problem-solving isn't really just one single skill. 

Instead, your ability to handle workplace issues with composure depends on several different “sub-skills”. 

So, which specific skills make an employee desirable even for the most demanding of recruiters? 

In no particular order, you should focus on these 7 skills : 

• Analytical skills
• Research skills
• Critical thinking 
• Decision-making
• Collaboration
• Having a growth mindset

Let's have a look at each of them in greater detail!

#1 Analytical skills

Firstly, to truly understand complex problems, you need to break them down into more manageable parts . Then, you observe them closely and ask yourself: “ Which parts work and which don't,” How do these parts contribute to the problem as a whole,” and "What exactly needs to be fixed?” In other words, you gather data , you study it, and compare it - all to pinpoint the cause of the issue as closely as possible.

#2 Research skills

Another priceless tool is your research skills (sometimes relying on just one source of information isn't enough). Besides, to make a truly informed decision , you'll have to dig a little deeper. Being a good researcher means looking for potential solutions to a problem in a wider context. For example: going through team reports, customer feedback, quarterly sales or current market trends.  

#3 Critical thinking

Every employer wants to hire people who can think critically. Yet, the ability to evaluate situations objectively and from different perspectives , is actually pretty hard to come by. But as long as you stay open-minded, inquisitive, and with a healthy dose of skepticism, you'll be able to assess situations based on facts and evidence more successfully. Plus, critical thinking comes in especially handy when you need to examine your own actions and processes. 

 #4 Creativity

Instead of following the old established processes that don't work anymore, you should feel comfortable thinking outside the box. The thing is, problems have a nasty habit of popping up unexpectedly and rapidly. And sometimes, you have to get creative in order to solve them fast. Especially those that have no precedence. But this requires a blend of intuition, industry knowledge, and quick thinking - a truly rare combination. 

#5 Decision-making

The analysis, research, and brainstorming are done. Now, you need to look at the possible solutions, and make the final decision (informed, of course). And not only that, you also have to stand by it ! Because once the train gets moving, there's no room for second guessing. Also, keep in mind that you need to be prepared to take responsibility for all decisions you make. That's no small feat! 

#6 Collaboration

Not every problem you encounter can be solved by yourself alone. And this is especially true when it comes to complex projects. So, being able to actively listen to your colleagues, take their ideas into account, and being respectful of their opinions enables you to solve problems together. Because every individual can offer a unique perspective and skill set. Yes, democracy is hard, but at the end of the day, it's teamwork that makes the corporate world go round. 

#7 Having a growth mindset

Let's be honest, no one wants their work to be riddled with problems. But facing constant challenges and changes is inevitable. And that can be scary! However, when you're able to see these situations as opportunities to grow instead of issues that hold you back, your problem solving skills reach new heights. And the employers know that too!

Now that we've shown you the value problem-solving skills can add to your resume, let's ask the all-important question: “How can I learn them?”

Well…you can't. At least not in the traditional sense of the word. 

Let us explain: Since problem-solving skills fall under the umbrella of soft skills , they can't be taught through formal education, unlike computer skills for example. There's no university course that you can take and graduate as a professional problem solver. 

But, just like other interpersonal skills, they can be nurtured and refined over time through practice and experience. 

Unfortunately, there's no one-size-fits-all approach, but the following tips can offer you inspiration on how to improve your problem solving skills:

• Cultivate a growth mindset. Remember what we've said before? Your attitude towards obstacles is the first step to unlocking your problem-solving potential. 
• Gain further knowledge in your specialized field. Secondly, it's a good idea to delve a little deeper into your chosen profession. Because the more you read on a subject, the easier it becomes to spot certain patterns and relations.  
• Start with small steps. Don't attack the big questions straight away — you'll only set yourself up for failure. Instead, start with more straightforward tasks and work your way up to more complex problems. 
• Break problems down into more digestible pieces. Complex issues are made up of smaller problems. And those can be further divided into even smaller problems, and so on. Until you're left with only the basics. 
• Don't settle for a single solution. Instead, keep on exploring other possible answers.
• Accept failure as a part of the learning process. Finally, don't let your failures discourage you. After all, you're bound to misstep a couple of times before you find your footing. Just keep on practicing. 

How to improve problem solving skills with online courses

While it’s true that formal education won’t turn you into a master problem solver, you can still hone your skills with courses and certifications offered by online learning platforms :

• Analytical skills. You can sharpen your analytical skills with Data Analytics Basics for Everyone from IBM provided by edX (Free); or Decision Making and Analytical Thinking: Fortune 500 provided by Udemy (＄21,74).
• Creativity. And, to unlock your inner creative mind, you can try Creative Thinking: Techniques and Tools for Success from the Imperial College London provided by Coursera (Free).
• Critical thinking. Try Introduction to Logic and Critical Thinking Specialization from Duke University provided by Coursera (Free); or Logical and Critical Thinking offered by The University of Auckland via FutureLearn.  
• Decision-making. Or, you can learn how to become more confident when it's time to make a decision with Decision-Making Strategies and Executive Decision-Making both offered by LinkedIn Learning (1 month free trial).
• Communication skills . Lastly, to improve your collaborative skills, check out Communicating for Influence and Impact online at University of Cambridge. 

The fact that everybody and their grandmothers put “ problem-solving skills ” on their CVs has turned the phrase into a cliche. 

But there's a way to incorporate these skills into your resume without sounding pretentious and empty. Below, we've prepared a mock-up resume that manages to do just that.

FYI, if you like this design, you can use the template to create your very own resume. Just click the red button and fill in your information (or let the AI do it for you).

Problem solving skills on resume example

This resume was written by our experienced resume writers specifically for this profession.

Why this example works?

• Firstly, the job description itself is neatly organized into bullet points .  
• Instead of simply listing soft skills in a skills section , you can incorporate them into the description of your work experience entry.  
• Also, the language here isn't vague . This resume puts each problem-solving skill into a real-life context by detailing specific situations and obstacles. 
• And, to highlight the impact of each skill on your previous job position, we recommend quantifying your results whenever possible. 
• Finally, starting each bullet point with an action verb (in bold) makes you look more dynamic and proactive.

To sum it all up, problem-solving skills continue gaining popularity among employers and employees alike. And for a good reason!

Because of them, you can overcome any obstacles that stand in the way of your professional life more efficiently and systematically. 

In essence, problem-solving skills refer to the ability to recognize a challenge, identify its root cause, think of possible solutions , and then implement the most effective one. 

Believing that these skills are all the same would be a serious misconception. In reality, this term encompasses a variety of different abilities , including:

In short, understanding, developing, and showcasing these skills, can greatly boost your chances at getting noticed by the hiring managers. So, don't hesitate and start working on your problem-solving skills right now!

Julia has recently joined Kickresume as a career writer. From helping people with their English to get admitted to the uni of their dreams to advising them on how to succeed in the job market. It would seem that her career is on a steadfast trajectory. Julia holds a degree in Anglophone studies from Metropolitan University in Prague, where she also resides. Apart from creative writing and languages, she takes a keen interest in literature and theatre.

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Problem-Solving vs Word Problems

I remember preparing for an interview for my first teaching position in the 90’s. I was told that I would likely be asked to explain my approach to teaching problem-solving. I jumped on the Internet to research problem-solving and craft my response. What I found was that problem-solving in math basically meant teaching students to solve word problems. I ended up getting the job and, for a number of years, taught what I  thought was problem-solving. What I’ve come to find out, however, is that while we certainly need to teach students strategies for solving word problems, problem-solving is so much more than solving word problems.

Problem-Solving > Word Problems

Think for a minute about a problem you’ve solved recently. I’ll give you a personal example. My current car lease ends next month, and I have to decide what to do. Usually, I just turn in my old car and lease another one. This year, however, is different. We are in the midst of an unprecedented shortage of new cars, driving new car prices way up. Not the best time to buy or lease a new car. At the same time, used car prices are surging and many used cars are selling at close to their original MSRP. Once again I jumped on the Internet to research the situation. I found out that I might be able to purchase my car at lease-end and turn around and sell it at a higher price! But that would leave me without a car. So, I have decided to purchase my car at lease-end and hold onto it until new car prices start to come back down. I should still get a trade-in value on my current car higher than what it will cost me to purchase it at lease-end. Of course, all this sounds great in theory and seems to be the right decision based on the data, but I won’t really know if I made the best decision until sometime next year.

This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.

I think you’d agree that what I described was some heavy-duty problem-solving with pretty significant consequences. Yet not a word problem in sight. You see, true problem-solving is messy and goes way beyond solving word problems.

George Polya is often called the Father of Problem-Solving. In 1945, he outlined a 4-step process for solving problems in his ground-breaking book  How to Solve It .  You can see the four steps pictured below.

Now think about the process I went through while solving my car problem. Don’t you see the four steps in what I did?

The problem is that well-intentioned teachers have tried to turn the problem-solving process, which is inherently messy, into an algorithm—if you do these steps, then you can easily solve problems. This is why we see students boxing numbers, underlining questions, and looking for “key” words, all shortcuts that basically give students permission to not read and understand word problems.

So how do we teach students to become problem solvers? Well, it might sound simplistic, but we give them rich problems to solve and get out of the way. Again, with the best of intentions, teachers often provide too much support and students come to depend on it.

I recently facilitated a book study on the book Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance , by John J. SanGiovanni, Susie Katt, and Kevin J. Dykema. It is a fabulously useful and easy-to-read book, chock full of implementable ideas. In other words, it’s a book you will  use and not just read. It’s no coincidence that the first three chapters all deal with creating a climate where productive struggle can thrive. Let’s face it, many math classrooms still run on the premise that math is about regurgitating a memorized procedure. Not much thinking involved. First, we as teachers need to embrace the idea of teaching through productive struggle. Then, we need to set students up for success as we introduce struggle into our lessons. 

One way to increase productive struggle and thinking in our classroom is to flip the sequence of our instruction. Rather than the traditional direct teaching approach of I do, We do, and You do , we flip the process so students are given a problem to solve before direct instruction.

Here’s an example. Say students have been using a part/whole diagram to represent join/result unknown word problems . So they have been practicing identifying if each number in a word problem represents one of the parts or the whole and creating part/whole diagrams, such as this one. By looking at the diagram, you can probably construct the word problem they were solving, right?

Now you would like to introduce a new structure—join/change unknown. It’s a more complicated type of problem. Here’s an example of this type of problem.

Mariana had $20. Her grandmother gave her some money for her birthday. Now Mariana has $28. How much money did Mariana’s grandmother give her for her birthday?

I could proceed to teach this new structure with a scripted lesson:  Boys and girls, you have been using a diagram to solve join/result unknown problems. Today, I’m going to show you how to use the diagram to solve a new structure—Join/change unknown.  I would model a problem or two, we would work a couple together, and then they could practice more on their own. A typical I do, We do, You do lesson.

But instead, what if we read the new problem out loud together, and then I commented, Huh. This problem sounds a little different. Work with a partner to see if you can solve it using your part/whole diagram.  In other words, the You do comes first! Would every pair of students be successful in solving the problem? Probably not. But after all students have the opportunity to struggle with it, think of the rich discussions we can have. It’s likely that at least some students will determine that it’s a new structure and then I can come along behind and put a name to it.

So I hope you will commit to thinking of problem-solving as something beyond just solving word problems and give students the opportunity to productively struggle in your classroom. I think you’ll see engagement soar!

If you want more information on addition/subtraction structures check out this post .

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Cy Fair does model drawing!! It works

Howdy, neighbor! Yes, model drawing is so powerful. I’m looking forward to next year when this whole group comes up knowing it!

I’ve been using model drawing with my first graders and it’s been powerful to see how they understand what’s happening in the problem, especially those tricky missing addend problems. This is the most confident I’ve felt with first graders and problems in a very long time!

I totally agree, Nilda! It really helps them to visualize the math that is happening in the story!

Looks like a great lesson!

Tara The Math Maniac

Thanks, Tara!

Hi Donna I am a math coach in Massachusetts and want institute bar models in all grade levels, K-5, for the 2017-2018 school year. Can you recommend a resource for me to use for research prior to professional development? Thanks Meg

A book that I have used and think is a great resource is Char Forsten’s book on model drawing .

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Grab my Math Problem-Solving Sampler Pack!

This handy download includes a variety of resources to help your students master word problems! You’ll find the ready-to-go Small Group Planner, the Problem-Solving Rounds Cheat Sheet, the printable Thinking Mat for any word problem, plus unique options for practice. Get it now when you sign up for free resources and teaching tips from Teacher Trap!

5 Unique Word Problem Solving Strategies That Get Results

Word problems are a special kind of math challenge. Not only do they require computation skills, but they also test students’ reading comprehension and problem-solving abilities. This can be the perfect storm of frustration for many kids. But it doesn’t have to be so hard! Today, I’m sharing easy word problem solving strategies for helping students finally master the word problem!

Word Problem Solving Strategies That Work

Commonly taught word problem solving strategies usually include memorizing a rote set of steps such as circling important information or underlining keywords. These are helpful steps, but they do not address the more complex thinking required for word problems.

Feel free to teach those handy habits, but for better student outcomes, focus on building comprehension, critical thinking skills, and mathematical reasoning.

Reading Comprehension as a Word Problem Strategy

Many people think of math and reading as completely separate skills. But with word problems, reading comprehension plays a crucial role in attacking the problem. Kids have a bad habit of reading word problems like they are just passing through words to get to the numbers. Blah, blah, blah. 127! Blah, blah, blah, 52! They search for numbers and then rush to DO something with those numbers. 

If our students are going to find success with word problems, they need to use their good reading strategies! Teach your students to:

Reread: Slow down and reread as many times as needed

Visualize: Imagine what is taking place in the problem. What is the order of events?

Ask questions: What do I know? What do I need to find out?

Make predictions: What would be a reasonable result? Do I expect the answer to be more or less than the numbers I’m given?

Teach a Word Problem-Solving Routine

Help students form effective thinking habits by teaching and practicing a problem-solving process. Rather than a rote set of steps like CUBES (Circle the numbers, Underline the question, Box key words, etc.) build a THINKING routine that helps the child learn the critical thinking skills involved in solving real problems. 

The routine itself uses powerful word problem solving strategies as students begin to internalize this process and become confident with each step.

I’ve found a simple PLAN, SOLVE, CHECK format works best. With young children, the biggest issue I find is that they simply skip (or struggle with) one of these steps, which causes a breakdown in their ability to solve the problem. 

In my classroom, I use Guided Math Groups that are formed based on students’ success in each of those those three categories (planning strategies, solving strategies, checking strategies.) **You can grab a FREE Word Problem Thinking Mat along with Winter themed problems in my Winter Word Problem Solving Sampler Pack .

Compare Word Problem Structures

One of my favorite word problem solving strategies is something I call “Side-by-Sides.” This is simply where we solve two different problems and then compare the structure of the problem and the operation used. 

When students model, solve, and compare the different problem types, they grow a deeper understanding of how word problems work. This is a  powerful way to help students compare the different operations (addition, subtraction, multiplication, division) or compare the different formats of problems that use the same operation (such as subtracting as comparison vs subtracting as a decrease.)

**You can grab FREE samples of side-by-side problems  in the Preview File of my Side-by-Side Word Problems Pack or grab  a FREE Side-by-Side Mat in the Preview File of my Tiered Word Problems Pack for 2nd Grade or 3rd Grade .

Start With the Easy Version of the Word Problem

Differentiation isn’t just for reading!  Many students get overwhelmed when they see large numbers in word problems, so why not meet them where they are?  I use what I call “Tiered Word Problems” to help students understand word problem structures and grow confidence before tackling the on-level version.

In my Word Problem Solving Bundle , I provide all kinds of leveled word problems – Tiered Problem Pages, Task Cards, Side-by-Sides, Exit Tickets, and more, all increasing in challenge from first through fifth grade. This allows for scaffolding of instruction by student need, and throughout the school year.

Use Word Problem-Solving Rounds

Problem-Solving Rounds changed my math instruction forever!  This dynamic routine encourages students to move through the problem-solving process I mentioned at the beginning of this post, to explain their thinking, and to reflect on other possible strategies and solutions. 

Since using Problem-Solving Rounds, my students are more confident with word problems, have a deeper understanding of problem-types, and are better able to tackle new and challenging tasks.

The basic structure of the rounds follows the Problem-Solving Process I shared above.  

In Round 1, students read and discuss the problem with a focus on UNDERSTANDING.  In Round 2, they turn to a partner and explain how they PLAN to solve the problem. They SOLVE the problem independently in Round 3, and in Round 4 they work with a partner and as a whole class to CHECK and reflect on their work. For a detailed guide to this process, check out my blog post all about Problem-Solving Rounds .

I’d love to hear from you! Comment below with your favorite word problem solving strategies?

You might also like:

How to Fix Your Daily Math Review

Problem Solving Rounds for Word Problems

Mastering Multi-Step Word Problem

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Word Problems and Problem-Solving

Today’s challenge is all about reflecting on problem-solving–how we teach it AND how we make it accessible to students.  I am hoping something in this post resonates with you–and if it does, please consider dropping into the Facebook group and sharing your thoughts!

Word Problems As Problem-Solving Warm Ups

I do this in a few different ways…see if any seem like they could work for you.

• Try projecting one problem on the board and students first talk about it, then solve independently, then share solutions and thinking.
• Each student gets a copy of the problem to glue into their math notebook. They work to solve independently, then share in pairs or bring it back to the whole class for a discussion.
• Provide a problem (maybe a task card, maybe projected) where a small group first discusses strategies that would work (no paper and pencil!) and then students go back to try it on their own.
• Students work to solve a problem on their own and then different students share their strategies with the class or under a document camera.  This can also be a great time for students who organized their work really well to showcase that!
• Solve a problem as a whole class and then send students off to try writing a similar problem.
• Use a problem that has blanks instead of numbers and then give three choices of numbers to use…students can pick their level of challenge
• And so many more!

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3 Word Problem Solving Strategies To Improve Word Problem Performance

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The ability to solve word problems doesn’t necessarily come easily to all students. We can improve our students’ ability to solve story problems with a few simple word problem-solving strategies. When it comes to comprehending, understanding, and solving word problems, sometimes it is helpful to move beyond traditional word problems and try a new word problem type that is designed to support students in tackling these tricky skills!

In order to solve word problems, students need to be able to:

• Comprehend the action or context of a word problem
• Understand the question or missing piece of information
• Develop a mathematically sound plan for solving for the missing information.
• Accurately calculate to find their solution.

It’s a balance between comprehension, an understanding of math concepts, and an ability to carry out math concepts. Identifying which of these steps are strengths or needs for your students can help you to choose a strategy that will best improve their word problem performance.

Word Problem Solving Strategy #1: Numberless Word Problems

Who is this strategy for? If your students are struggling to understand the action, context or question in a story problem, discussion and numberless word problems will be a word problem-solving strategy that can help your students tremendously! This strategy also helps your “number pluckers” who see numbers, pluck and add together regardless of context! Numberless word problems slow your students down!

Using a tool such as numberless word problems can help your students in their understanding precisely because the numberless word problem strategy emphasizes discussion every step of the way!

How do I use this strategy? As you solve numberless word problems you begin with a problem with no numbers at all and ask a variety of questions as you discuss and slowly add information back into the problem.

Reagan picked flowers for a bouquet! She picked both roses and carnations.

When you initially present the problem, ask your students questions such as

• Who is the story problem about?
• What is happening in this story?
• What are you wondering about?

Reagan picked flowers for a bouquet! She picked 7 roses and also some carnations.

• What new information do we have?
• What do you think we might learn next?
• What *could* be the number of carnations in the bouquet? What might make sense?

Reagan picked flowers for a bouquet! She picked 7 roses and 8 carnations.

• What new information do we know?
• What do you know about the story?
• What happened in the story?
• Could we draw a picture or diagram to match the story?
• What might we be wondering about the bouquet?
• What questions could we answer about the bouquet?

Reagan picked flowers for a bouquet! She picked 7 roses and 8 carnations. How many flowers are in the bouquet in all?

• What is the question wondering?
• Do we have enough information to answer that question?
• Where do we see the 7 roses in our diagram?
• Where do we see the 8 carnations in our diagram?
• How can we use the diagram to answer the question of how many flowers are in the bouquet in all?

DONE FOR YOU NUMBERLESS WORD PROBLEMS

Kindergarten | 1st Grade | 2nd Grade | 3rd Grade | 4th Grade

Word Problem Solving Strategy #2: Guided Visual Models

Who is this strategy for? Visual models help your students to organize the information they know as well as to visualize the missing piece of information. Drawing visual models helps lead your students to an equation. This strategy is ideal for students who understand what a word problem is asking but have difficulty connecting the action of a word problem to an equation.

A visual model might include:

• A math drawing (simple circles or an organic representation)
• A number bond (number bonds can be used beyond addition and subtraction! Adding more “parts” can help to visualize multiplication and division as well!)
• Tape diagrams

How can I use this strategy? As you are supporting your students in using these visual models, continually ask questions and draw connections between the word problem and their diagram.

Frank built a tower using 16 blocks. He took 7 blocks off of his tower and gave them to Declan so he could build a tower as well. How many blocks does Frank have left?

• Could you draw a picture that shows what happened?
• Frank had 16 blocks. Was that all of the blocks in the story or part of them? Where would we put the total in our number bond?
• Frank gave away 7 blocks. Was that all of the blocks or a part of the blocks? Where would we put the part in our number bond?
• And we’re wondering how many blocks Frank has left. Where is the missing part in our number bond? Could we write a question mark in that part?

If your students are familiar with number bonds or tape diagrams, knowing that they are missing a part will lead them to writing a subtraction equation or a missing addend addition equation to solve.

**If your students are not familiar with how to find a missing part or missing whole in an equation this is a topic that needs to be addressed as well! Your students are missing foundational math understandings that are critical to their word problem-solving strategy. Additional practice with both fact families and missing numbers in an equation will be helpful to your students!

Word Problem Strategy #3: Problem Sorts

Who is this strategy for? This strategy is for ALL students! When your students examine problems to help understand the underlying structures and problem types , solving word problems becomes easier.

If you were to be asked to cook dinner for a group of people at the drop of a hat, you would likely have a much easier time putting together a pizza than you would a complicated curry dish. You understand the underlying structure of a pizza- crust, sauce, cheese, toppings- and because you know this structure, given any different type of pizza (BBQ, Traditional, Garlic, Buffalo Chicken) you would be able to use the structure to come up with a recipe quickly and easily.

Understanding and recognizing problem types can do the same thing for our students! Understanding that in a “put together” problem there are going to be parts and that those parts can be put together using addition makes these problems much easier to solve!

How can I use this strategy? One way to help your students to recognize and understand problem types is to sort word problems. In a problem sort, you aren’t attending to the matter of solving the problem at all . Instead, you are reading the problems and sorting them based on whether the problem is missing a part or missing the total. If you are working on multiplication and division word problems you might sort based on whether the problem is missing the total , missing the number of groups or missing the group size. Other problem types will lend themselves to different sorting activities.

Additional Word Problem Resources

Using different types of word problem resources can help you to support your students in different ways.

Word Problem Sort Cards   can be a useful tool when you want your students to attend to the structure of math problems. Sort the cards based on problem type or based on the operation your students would use to solve. After sorting, solve the problems together. Reuse the sort as a math center!

Word Problem Notebooks  are a useful tool when you want your students to draw models and visual representations of word problems and to connect these models to an equation.

Numberless Word Problems   help get to the heart of the action or context of a word problem. Because you start with no numbers and employ a great deal of conversation these problems are simple to differentiate and give all students a point of access into the activity.

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“Problem-Solving” Or “Problem Solving”? Learn If It Is Hyphenated

Is it problem-solving or problem solving? Hyphenation rules seem to be a little confusing when you’re first picking up a language. Don’t worry, though. They’re not nearly as complicated as the language may have led you to believe!

Problem-Solving Or Problem Solving – Hyphenated Or Not?

When we discuss the problem-solving hyphen rule, we learn that problem-solving is hyphenated when used to modify a noun or object in a sentence. We keep the two words separated when using them as their own noun and not modifying anything else in the sentence.

Examples Of When To Use “Problem-Solving”

Now that we’re into the whole debate of problem-solving vs problem solving, let’s look through some examples of how we can use “problem-solving” with a hyphen. As stated above, we use “problem-solving” when modifying a noun or object in a sentence. It’s the most common way to write “problem-solving.” Even the spelling without a hyphen is slowly being pushed out of common language use!

• This is a problem-solving class.
• I hold a problem-solving position at my workplace.
• My manager put me in charge of the problem-solving accounts.
• They say I have a problem-solving mind.
• We’re known as problem-solving children.

Examples Of When To Use “Problem Solving”

Though much less common to be seen written as a phrase noun, it is still worth mentioning. It’s grammatically correct to use “problem solving” at the end of a sentence or clause without a hyphen. However, as we stated above, many people are beginning to prefer the ease of sticking to the hyphenated spelling, meaning that it’s slowly phasing out of existence even in this form.

• I’m good at problem solving.
• This requires a lot of problem solving.
• We are all trained in problem solving.
• My job asks for problem solving.
• Did you say you were good at problem solving?

Is Problem-Solving Hyphenated AP Style?

Have you had a look through the rules in the AP stylebook before? Even if you haven’t, there’s a good explanation for hyphens there. As we stated above, we use hyphens when linking close words that modify a noun or object in a sentence. They’re used to help a reader better understand what is going on through the modification of the clause.

Should I Capitalize “Solving” In The Word “Problem-Solving”?

The question of “is problem-solving hyphenated” was answered, but now we’ve got a new question. What happens to capitalization rules when we add a hyphen to a title. It depends on your own title choices, so let’s look a little further into the three potential options. The first option capitalizes only the first word and any proper nouns in a title. In this case, neither word in “problem-solving” is capitalized.

The second option capitalizes all words except for short conjunctions, short prepositions, and articles. In this case, you will always capitalize “problem” but always leave “solving” uncapitalized. The final option capitalizes every single word in a title. No matter what, you’ll capitalize both words in “problem-solving” when using this style to write your titles.

Does The Rule Also Apply To “Problem Solver” Vs “Problem-Solver”?

The same rule does apply when we use “problem solver” instead of “problem solving.” However, it’s not often that we’ll see a “problem-solver” modifying a noun or object (unless it’s a problem-solver robot or something). So, it’s most likely you’ll write “problem solver.”

Alternatives To “Problem-Solving”

If you’re still struggling with the hyphen rule of whether it’s problem solving or problem-solving, there’s one last thing we can help you with. We can give you some alternatives that have the same meanings but don’t require a hyphen. This way, you can be safe in your own knowledge without having to worry about getting the rules wrong.

• interpretive

Quiz – Problem-Solving Or Problem Solving?

We’ll finish with a quiz to see how much you’ve learned from this article. The answers are all multiple choice, so you should have a blast with them! We’ll include the answers at the end to reference as well.

• I’ve been told that I’m good at (A. problem-solving / B. problem solving).
• I hold my (A. problem-solving / B. problem solving) skills close to my heart.
• We aren’t great at (A. problem-solving / B. problem solving).
• These are all the best (A. problem-solving / B. problem solving) subjects.
• Can we have a go at a (A. problem-solving / B. problem solving) puzzle?

Quiz Answers

Martin holds a Master’s degree in Finance and International Business. He has six years of experience in professional communication with clients, executives, and colleagues. Furthermore, he has teaching experience from Aarhus University. Martin has been featured as an expert in communication and teaching on Forbes and Shopify. Read more about Martin here .

• Full time or Full-time? Learn if “Full time” is hyphenated
• “Well written” or “Well-written”? Learn If “Well written” Is Hyphenated
• “On-Time” Or “On Time”? Learn If “On Time” Is Hyphenated
• Year round or Year-round? (Hyphen Rule Explained)

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Team-Building Activities for In-Person Teams

Last week, we outlined team-building activities for remote and hybrid teams. But what about when you work in person? Here are some proven ways to bring people closer—even when they’re already working together every day. Recurring lunches. Sharing a meal fosters relaxed interactions, signaling the organization’s investment in unscripted, enjoyable team time. Exchanging expertise. Implement […]

Last week, we outlined team-building activities for remote and hybrid teams. But what about when you work in person? Here are some proven ways to bring people closer—even when they’re already working together every day.

Source: This tip is adapted from “17 Team-Building Activities for In-Person, Remote, and Hybrid Teams,” by Rebecca Knight

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A Donor Math Problem: How to Grow Donor Lifetime Value Using Blackbaud Raiser’s Edge NXT®

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Raiser’s Edge NXT and Blackbaud Merchant Services can help your organization secure, steward, and manage more recurring donors. Here are a few ways your software can help your organization extend donor lifetime value and build loyal donors.

I have a confession to make: I love the back-to-school season and math word problems with the pictogram illustrations. A brand new sharpened yellow No. 2 pencil and some fresh scratch paper still makes my day!

Calculating Donor Lifetime Value has a lot in common with these word problems I love. Let’s walk through this really useful exercise together:

The setup: In January, Tommy pledged $200 to your annual fund and committed to send the funds before the end of the year. At the same time, Susie commits to a recurring gift of $25 monthly.

Your challenge: Assume neither Tommy nor Susie makes an additional gift beyond the one-time pledge and monthly sustainer gifts. In December, how much will your organization have received from Tommy? From Susie?

The answer: In December, your organization will have received $200 from Tommy and $300 from Susie.

The takeaway: Don’t be fooled by the size of the gift. Susie’s seemingly smaller monthly gift can lead to a greater lifetime value for her as a donor. As a functional expert at Blackbaud, I've seen countless <$1,000 pledges — paid and unpaid — in hundreds of databases. Pledges, with the pledge reminders and processing effort often required to collect on them, can be administratively costly and time consuming. Nobody's anti-pledge here, but I would love more donors like Susie in my revenue pyramid, wouldn't you?

Leaning into this little lesson on potential lifetime value (and level of effort), with your team investing some energy into automation and stewardship, imagine if Susie were to give $25 a month for two years (or more). Your organization would receive $600 (24 months x $25) in just two years! That's $200 more than you would receive from Tommy if he pledged the exact same amount two years in a row. Research suggests that specific segments of the population are more likely to give on a recurring basis.

How You Can Start Building Lifetime Value Today

Let’s sharpen our pencils and take some notes on ways Raiser’s Edge NXT and Blackbaud Merchant Services can help your organization build more loyal donors like Susie and benefit from this surprising lifetime value equation for recurring giving:

Begin collecting automated recurring gifts with Raiser’s Edge NXT donation forms. Are you still manually processing recurring gift payments in the database view? The time may be right to switch to web view donation forms to build a more automated sustainer program, saving your team time.

For a recurring gift given via a web view donation form, all subsequent recurring gift payments (or Recurring Gift Pay-Cash in database view) are automatically charged when they are due, after the recurring gift has been approved.

As subsequent recurring gift payments are on the due date, a new gift batch is created in gift management in the web view.

Build a strategic stewardship plan for recurring donors.

Start by using the gift receipting option for recurring gifts on the donation form. Once Susie's recurring gift is approved, she will receive the customized e-receipt designated on the donation form.

Susie's name might not be engraved on your donor wall but think of some cost-effective ways to thank her. Use workflow designer to automate quarterly actions or special emails for recurring donors.

If you need ideas on how to say thank you, enroll in Fundraising: Stewarding Sustaining Givers / Organizational Best Practices from Blackbaud University.

Turn on the Blackbaud pays, recurring gift upsell, and first payment processes today options on your donation form.

With Blackbaud pays (also known as Complete Cover ), Blackbaud pays the processing fee on one-time and recurring gifts made via credit card (or US direct debit where available) up to $3,000. This means 100% of Susie's recurring gift payments go right into your organization's piggy bank.

The recurring gift upsell feature on the Standard donation form displays a pop-up, gently nudging one-time donors to consider giving $35 a month versus a one-time donation of $100.

Then, toggle on the first payment processes today radio button. Why wait a whole month or until next quarter? Start processing those gifts today!

Fine-tune your recurring gifts and use Portal features to save your team even more time.

In Raiser’s Edge NXT, you can designate the number of retries for a recurring gift payment transaction.

Minimize disruptions to your sustainer revenue flow with the Credit Card Updater service, included with Blackbaud Merchant Services in the United States and Canada. This service automatically updates credit card numbers when available for cards that expire or get replaced by the card holder.

Spending some preparation time beforehand to create operational workflows for failed payments and tracking changes weekly or daily can also give you some time back. Blackbaud Merchant Services and Raiser's Edge NXT can streamline your reconciliation with reliable disbursement schedules and reporting.

Invite donors with automated recurring gifts to your organization's donor portal . Donors can see their giving history, hold/skip payments, update payment methods, and adjust the frequency or amount of the recurring gift.

Promote your recurring giving option. I've seen organizations add a “Give Monthly” button in their Raiser’s Edge NXT emails, which takes donors directly to a Standard donation form with only recurring giving options. Or they use the QR Code feature to create "Give Monthly" signage in and around buildings or to display in presentations and slideshows.

Save even more time. Did you know that you can use AI acknowledgments (available now in the US, globally within the next few weeks) or an acknowledgment letter application from the Blackbaud Marketplace to send a customized email with a link to the portal where doors can manage their automated recurring gift? .

Just five donors like Susie can yield $1,500 a year. This word problem is an easy one! Definitely, let’s keep the pledges coming, but also be strategic about expanding donor lifetime value by capturing new recurring donations.

Raiser’s Edge NXT and Blackbaud Merchant Services can help your organization secure, steward, and manage more recurring donors. So, what's your team waiting for? Start revamping your recurring giving plan and drop your questions for me in the comments below!

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What is JUMP Math, and why are some teachers raving about it? Try 13 of its brain-teasing problems to find out

Michelle Jones says her students have been far more engaged since she started using the JUMP Math method at Jarvis Traditional Elementary School in Delta, B.C. Try the quiz at the end of this article to see whether you could solve the problems that Ms. Jones's Grade 6 students are expected to handle. Jennifer Gauthier/The Globe and Mail

In her more than two decades in front of a classroom, Michelle Jones has used five different math textbooks and, until recently, had grown increasingly frustrated in her inability to reach many of her students.

The story-based math problems that filled those textbooks left most of the children either checked out or confused. She’d draw on videos and other materials to supplement her lessons, but it didn’t feel like that was enough to help her students build their confidence in the subject.

Then, three years ago, her board – the Delta School District in Delta, B.C. – piloted a program that incorporated JUMP Math, a resource originally developed by John Mighton, an accomplished playwright and entrepreneur in Toronto. The program, run by a charity established in 2002, emphasizes students rehearsing basic arithmetic operations so they can see patterns and break problems down into smaller parts, gradually raising the level of difficulty. “We were just ready for a shift, to try something different,” said Ms. Jones, who teaches Grades 6 and 7 at Delta’s Jarvis Traditional Elementary School.

John Mighton helps Grade 4 pupils practice JUMP techniques at a Toronto school in 2007, five years after he developed the method. Deborah Baic/The Globe and Mail

For Ms. Jones, using JUMP Math – JUMP stands for Junior Undiscovered Math Prodigies – represented a sea change.

She is now armed with new strategies to teach the subject and has been able to reintroduce some rote learning so that students can engage with the material more quickly. The students use whiteboards, check in with their partners and practise on their own. As a result, she’s noticed they are less anxious and take more risks in class.

“In my experience, I have never seen students so engaged, relaxed and enjoying a math lesson,” she said.

The pilot at Delta has since expanded: In 14 of the district’s 24 elementary schools, most of the teachers are now using JUMP.

Focusing on math fact fluency may seem like an obvious recipe for success, but the way math is taught in schools has been the subject of a long-standing and divisive debate, much like reading.

On one side, some experts and educators believe rote learning creates anxiety and dread, and that children should approach the subject with playfulness and curiosity by learning through problem solving, pattern discovery and open-ended exploration.

Others have advocated for a so-called back-to-basics approach and pushed governments to initiate curriculum changes so students have the ability to quickly recall addition, subtraction, multiplication and division through repetition and memorization. Rote learning shouldn’t be considered a dirty phrase, they argue.

The debate comes at a critical time: Although Canada performs well compared with other countries globally, Canadian students’ scores on an international test administered by the Organization for Economic Co-operation and Development have been slipping for almost two decades – and the latest results from late last year show that slide continuing.

Neil Stephenson, director of learning services at Delta, brought in JUMP Math because he felt something needed to change in his district.

Educators were doing a “hodgepodge of things” to help students meet curriculum expectations, he said, which put an incredible strain on them to find and build lesson plans.

After doing some research and finding JUMP, he approached an elementary school that hadn’t been scoring well on provincial tests to see if any teachers there would try the program. Around three-quarters of them raised their hands – and assessments at the end of that school year showed that several students had progressed multiple grade-levels, and teacher confidence in how they approach the subject rose, he said.

“Absolutely we want kids to be doing creative work and solving interesting questions and synthesizing their knowledge. But there has to be some building up of that knowledge somewhere else first,” Mr. Stephenson said.

In Jarvis Elementary's district, more than half the schools now use JUMP for math education. Jennifer Gauthier/The Globe and Mail

That is heartening to JUMP’s founder.

Mr. Mighton didn’t fare well in math in school and nearly failed first-year calculus in university. But he slowly overcame his own math anxiety and, as a playwright trying to make a living, started tutoring the subject later in life. Teaching children encouraged him to break down difficult concepts into smaller parts, and, in turn, grasp the subject better. He relearned concepts he had missed along the way, and then returned to school in his early 30s to earn a PhD in math at the University of Toronto.

“Math is actually accessible, very accessible,” he said.

He explained that the current method – investigating ideas through problem solving, pattern discovery and open-ended exploration – rushes children past learning math facts in the hopes of making the subject more engaging. It has the opposite effect, he said, because children actually just become confused and disengaged.

His program provides lesson plans for teachers that allows for an incremental approach to problem solving. There’s a workbook for students, but Mr. Mighton said that should only be used after the lessons. “You want to get to those problems, but that’s not where you start. That’s the mistake we’re making,” he said. “We always think kids are experts. And we give them problems that are designed for experts when they’re novice learners.”

Math professor Anna Stokke feels that methods of teaching introduced in the 1980s have done a 'disservice to children' in the decades since. John Woods/the Globe and Mail

Anna Stokke, a mathematics professor at the University of Winnipeg and a vocal proponent for schools to once again focus on fundamentals, said the change in how math was taught began in the late 1980s under the school of thought called constructivism. The theory suggests students should not passively acquire knowledge through direct instruction but rather learn through experiences and interactions. At the time, the National Council of Teachers of Mathematics in the U.S. released a set of standards where problem solving became the focus of instruction, she said. The movement then spread to Canada.

Prof. Stokke said the change in instruction has been a “disservice to children” because students should be practising math procedures and memorizing facts before they can grasp more complex problems. “I’m a mathematician and, believe me, I know how to solve complex problems. And you can’t do complex problems without having a web of knowledge in your brain.”

The result of this change has been a widening equity gap, she said, where families who have the means provide tutoring for their children, while others continue to struggle in the subject.

However, Jason To, a math co-ordinator at the Toronto District School Board, said the argument that schools are teaching one way over another is misplaced. He worries that some experts are latching onto international test scores and insinuating that inquiry-based instruction is dominating the education space. But teachers, he said, are doing both: instructing their students on math fluency and immersing them in complex problems.

“This debate to me is you got to do one versus the other, and it’s not productive. It’s more like, how do these co-exist?”

Math fluency, and the way it is measured in standardized test, can be polarizing subjects in the world of education. Justin Tang/The Globe and Mail

Janelle Feenan, a teacher and peer support co-ordinator at the Delta school division, echoed the sentiment. For years, she and her Grade 3 teacher colleague would spend an evening a week researching and pulling resources to help their students with math fluency and to develop a more comprehensive understanding for concepts.

“We were struggling a little bit to make sure our students were understanding what we were doing. We’re going through the motions, but we just didn’t feel that they were where they needed to be,” she said.

They raised their hands to participate in the pilot that introduced JUMP Math to students.

Having worked with the program, Ms. Feenan found that there’s a place for both the structural approach that JUMP provides as well as allowing for problem solving and conceptual understanding. She uses JUMP as her main lesson plan, and then supports that with games and visual aids to deepen understanding.

“Neither of those approaches alone would be adequate to prepare kids for success in math,” she said. “I think you have to supplement lessons with activities and resources that are fun and engaging to build their understanding and enrich their learning experience.”

Pop quiz: Test your math skills, JUMP-style

These are Grade 6-level problems from JUMP Math assessment and practice books. Get out your calculator app and give them a try!

c. If the pitcher pitches on the first game (or on the second, or on the third), she will pitch a total of 10 games, ending on the 46th game (or 47th, or 48th, respectively).

Photo: Jon Blacker/The Canadian Press

d. The lake with the longest shoreline is Huron, at 6,164 km. The shortest is Lake Ontario, 1,146 km. The difference is 6,164 – 1,146 = 5,018 km.

a. Avril’s grade sold 10 + 15 + 25 + 10 = 60 tickets in total. Of those 60 tickets, 30 (half) are adult tickets and sell for $5 each, and the other 30 sell for $3 each. So Avril’s grade raises (30 × $5) + (30 × $3) = $150 + $90 = $240. Since the bus costs $320, there is still $320 – $240 = $80 needed.

c. Round 3,128 to 3,000, and 4,956 to 5,000. So 3,128 × 4,956 is approximately equal to 3,000 × 5,000 = 15,000,000, i.e., 15 million.

b. 821 × 4 = 3,284. To calculate mentally, multiply the digits separately.

c. The perimeter of the field is 921 × 5 = 4,605 m. The farmer needs 4,605 – 4,500 = 105 more metres of fence to surround the field.

Photo illustration (source: Ina Fassbender/AFP/Getty Images, JUMP Math

b. Add the digits and check if the sum makes a multiple of nine.

c. 40 per cent of 20 = 8, and 25 per cent of 20 = 5. Since 8 + 5 = 13, there are 20 – 13 = 7 green fish.

a. $7.21 × 3 = $21.63. To multiply mentally, multiply the digits separately.

Photo: Kham/Reuters

d. 84.8 mm ÷ 4 = 21.2 mm. To divide mentally, divide the digits separately.

b. 220 kg ÷ 4 = 55 kg.

c. 15 × 8 = 120, 120 ÷ 100 = 1.20. They will pay $1.20 in taxes.

d. Three quarters of 12 is nine, so nine green balloons have writing on them. Sixty per cent of 15 is nine, so nine blue balloons have writing on them. So, 9 + 9 = 18 balloons in total have writing on them.

Photo: Vadim Ghirda/AP

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Synonyms for Solve problems

386 other terms for solve problems - words and phrases with similar meaning.

Where Is the Line with Gossiping?

No matter how you spell it, gossip is a three-letter word — sin. Talk is talk, but when a conversation’s motive moves toward disparaging or denigrating another’s character, it becomes the sin the Bible calls gossip. The Bible takes gossip very seriously, for it (and its synonyms) is included in passages of evil behaviors (e.g., Proverbs 25:23 ; Ezekiel 36:3 ). Whether for exalting oneself or for the defamation of another, gossip is a result of pride, and pride drove Lucifer out of heaven to become the devil ( Isaiah 14:12-14 ). Pride is at the top of the list of things God hates ( Proverbs 6:16-19 ), and one of the ways Satan tries to devour us is by tickling our pride and inciting gossip.

The line drawn regarding gossip is clear; the Bible tells us to stay clear of it ( Proverbs 20:19 ). We’ll see what God’s Word says about gossip and respect how we are to respond to it and how to use our speech in a godly way.

Where Does the Bible Mention Gossip?

Direct references to gossip, gossips, and gossiping are mentioned in the ESV in Proverbs 25:23 , Ezekiel 36:3 , 2 Corinthians 12:20 , Romans 1:29 , and 1 Timothy 5:13 . But the cross -references and allusions equating gossip to evil behavior are numerous. Looking through a concordance will give you days’ worth of cross-references to study what the Scriptures say about gossip.

The first mention of the idea of gossip, however, is in Leviticus 19:16 , in which the Bible uses a pointed synonym. “You shall not go about as a slanderer among your people; and you are not to jeopardize the life of your neighbor. I am the LORD” (emphasis added). Here, we see gossip as slander, and for it to be mentioned in the list of laws lets us know how important proper and holy speech is to the Lord. Gossip is forbidden. Period.

How Does the Bible Define Gossip?

God’s Word uses a number of terms and phrases that leave no doubt how God defines gossip. Gossip is defined in the Bible by the actions and character of those who partake in the sin. Pastor Matt Mitchell says this about the biblical view of gossip, “The Bible often uses the word gossip to describe a kind of person more than just a pattern of communication. My way of summarizing the Bible’s teaching on this topic is to say that the sin of gossip is bearing bad news behind someone’s back out of a bad heart . This functional definition considers the action itself, the content of the corrupt communication, the situation in which it occurs, and perhaps most importantly, the motivations of the people involved.”

Gossip’s counterpart is slander, and the Holman Illustrated Bible Dictionary defines slander as, “To speak critically of another person with the intent to hurt.” Gossip is never given mention in the Bible as a good thing; it’s always evil. In fact, it, along with slander are among the most condemned sins in the Bible.

A few ways gossip is defined in the Bible: 

Ezekiel 36:3 describes gossip as evil.

In 2 Corinthians 12:20 , gossip is included in a list of unrepentant sins committed by the warring factions of the Corinthian church.

In Romans 1:30 , gossip is akin to a “backbiter.”

Ecclesiastes 10:11 equates gossiping with the imagery of a snake charmer who seeks to sway a person’s opinion with “a murmured enchantment.”

Vines Expository Dictionary marries gossip with “open slander.” 

A gossiper is called a “simple babbler,” which can also be written, a foolish gossip ( See also Proverbs 10:18 ) .

In Ephesians 4:29 uses “corrupting talk.” Not only is the subject of the gossip being slandered, so too is the audience corrupted by the malevolent talk.

Gossip is also called secret whisperings (or secret slander).

The Apostle Paul, in Romans 1:29 , says, “They were filled with all manner of unrighteousness, evil, covetousness, malice. They are full of envy, murder, strife, deceit, maliciousness. They are gossips.” We can plainly see gossips live in the company of ungodly people, sharing their sins.

Sadly, studies show women are the most likely to gossip, but men don’t fall too far behind (67% of women gossip vs 55% of men). In their book, The Quick-Reference Guide to Counseling Women, Doctors Tim Clinton and Diane Langberg state, “Gossip exploits the personal issues or matters of another person. Someone who gossips habitually reveals personal or sensational facts about others. Such conversations typically involve rumors, opinions, or inside information… [Gossip] is not an innocent pastime. It is sin.”

How Can Christians Use Their Speech to Honor God?

Knowing what gossip is and how the Lord regards it as evil, we can now look to the Word to learn how we are to communicate with others.

As many times as the Bible tells us how to act with righteousness ( Ephesians 6:14 b), it also encourages (commands) us to honor the Lord with our speech ( Psalm 141 ). We need to remember God’s standards are not man’s standards. In Matthew 12:36 , Jesus said, “I tell you, on the day of judgment people will give account for every careless word they speak,” God is not stingy with commands for holy living, which includes speaking from a righteous heart and mind. We gain them by virtue of His Word and His Spirit dwelling in us.

Following are a few passages which help us to know how to guard our hearts and tongues:

“For whoever desires to love life and see good days, let him keep his tongue from evil and his lips from speaking deceit” ( 1 Peter 3:10 ).

“So put away all malice and all deceit and hypocrisy and envy and all slander” ( 1 Peter 2:1 ).

“Let no corrupting talk come out of your mouths, but only such as is good for building up, as fits the occasion, that it may give grace to those who hear” ( Ephesians 4:29 ).

“Do not speak evil against one another, brothers. The one who speaks against a brother or judges his brother, speaks evil against the law and judges the law. But if you judge the law, you are not a doer of the law but a judge” ( James 4:11 ).

How Can Christians Respond to Gossip Among Friends and in the Workplace?

You may have been privy to these conversation starters (aka gossip):

“Let’s pray for Susan. She’s caught up in an affair.”

“Can you believe what Tom did? He has no business…”

“I don’t like Karen, she doesn’t believe the way we do.”

“John really hurt Simone, he…”

“Did you hear what nonsense they are studying in that group?”

“Pastor really blew that sermon!”

Oftentimes gossip begins with what seems to be a sincere desire to explain and/or solve a problem or concern for another, but if the information is inflammatory, denigrates or slanders a person or group, is unsubstantiated or otherwise puts a person in a bad light, it’s gossip.

Many times, a person may be drawn into gossip while in the midst of a casual and innocent conversation. Another person’s name will come up and the participants are unwittingly pulled in a direction they did not envision or intend. Often a name will be brought up with the proviso, “let’s pray for so and so, because he/she is…” It’s time to, in either case, turn the conversation toward godly talk or, if no one follows suit, leave the conversation all together.

A number of biblical responses and actions may be taken when a Christian is subjected to gossip. So many passages in the Bible give us counsel on righteous speech and behavior, but two should come immediately to mind:

1. Luke 6:31 gives us Jesus’ words as He recited the beatitudes to His disciples. He said, “And as you wish that others would do to you, do so to them.” We know this admonition as the golden rule, and, as Jennifer Heeren states, “In Mark 12:30-31 , Jesus said, ‘You must love the Lord your God with all your heart, all your soul, all your mind, and all your strength. The second is equally important: Love your neighbor as yourself. No other commandment is greater than these.’ Without doing the first part, you really don’t have the ability to even try the second part. When you strive to love the Lord your God with all your heart, soul, mind, and strength, you gain the help of the Holy Spirit which helps you to love other people.”

Loving the Lord God first and then other people will guide our defenses and offenses as we engage in conversation with them.

2. “Finally, brothers, whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is lovely, whatever is commendable, if there is any excellence, if there is anything worthy of praise, think about these things. What you have learned and received and heard and seen in me — practice these things, and the God of peace will be with you” ( Philippians 4:8-9 ).

What proceeds from our lips has been formed in our hearts ( Luke 6:45 ). If we think as the Apostle Paul commands in Philippians 4:8-9 , our responsive speech to the gossipers will reflect all those Christlike characteristics.

Pursue Righteousness

In both of these passages, we are reminded of who we are and Whom we represent. When gossip strikes a conversation, pray for the wisdom the Lord always gives when we ask in faith ( James 1:5 ). Also, the Holy Spirit will bring to mind Scripture to help you counsel those involved ( Ephesians 6:17-18 ). If you can, calmly stop the conversation or steer it in another direction. If the others refuse to cease, walk away. If possible, speak to each individual later and explain why you walked away. Don’t fall for self-defensiveness or justifications. Remain steadfast in your faith and obedience to the Lord to “not associate with a simple babbler” ( Proverbs 20:19 ). A babbler is another term for a gossip.

Even though we will be confronted at times with negative thoughts and comments (even our own), we must strive to intercept what might flow from negativity with godly wisdom. Problems exist within the church, too, and by their very nature they are negative (e.g., a believer may be angry with how a Christian brother or sister is being persecuted for their faith, or they might take issue with a new law being passed that rewards ungodly actions). Our role is to remain self-controlled and give counsel as we are filled and led by the Holy Spirit.

Some issues may come up which have negative ramifications if left unsolved. The purpose, once again, is to seek restitution and godly restoration.

When the sin of a brother or sister is revealed, God calls us to lovingly confront and rebuke them Galatians 6:1 ; Matthew 18:5 ; 2 Timothy 3:16 ). It’s important to remember that as we lovingly rebuke and correct, our goal is to restore them (as Galatians 6:1 says).

We’ve learned the Bible is clear about gossip being a sin. We’ve also learned God has given us many remedies for both dealing with gossip and its ramifications as well as commands for and examples of righteous speech. If you have been involved with gossip, remember to go first to the Lord ( 1 John 1:9 ) and then go with humility and compassion to others against and/or with whom you have sinned ( Matthew 5:23-24 ).

Let’s pray.

As we consider Your words about gossip, what it is and who takes part in it, we are reminded of the serious nature of how we live in this world. We are to be in but not of it, and gossip, while not confined to the world, reflects the world’s hold on us as Christians — if we let it. Help us as only You can, to keep our speech gracious and seasoned with salt for the edification and encouragement of the saints and for the watching world, that people may see Your goodness through us. May You be glorified in us.

In Jesus’ name and for His glory we pray,

Photo credit: ©Getty Images/Paul Bradbury

Word of the Day

What it means.

Dearth refers to a lack or inadequate supply. It is usually followed by of .

// There is no dearth of opportunities for volunteers at the fair.

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dearth in Context

“Of course, it’s one thing to survey the marketplace and acknowledge the dearth of female voices in genres like history and biography. It’s another entirely to understand in practical terms how the absence of female perspectives affects the way history is told, to recognize the threads that go unexplored or are never thought of in the first place.” — Katie Gee Salisbury, LitHub.com , 13 Mar. 2024

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Dearth has, in one form or another, been used to refer to scarcity since at least the 13th century, when it often referred specifically to the plague of famine (as in “a time of dearth”), whether brought on by an insidious crop disease or by invaders. The word traces back to the Old English adjective dēore , meaning “dear” ( dēore is also the ancestor of dear , which also once meant “scarce,” though that sense is now obsolete). That notion of dearness or importance endures in dearth , which implies the absence or scarcity of not just any old thing, but of something one wants or needs. A dearth of mauls , for example, would be the bane of a woodcutter’s existence.

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John McWhorter

‘joy’ is a euphemism for a word no one wants to say out loud.

By John McWhorter

Opinion Writer

I hate to rain on the parade, but there is something fake about this business of the joy — and not just joy but JOY as Oprah told us last week — surrounding the elevation of Kamala Harris. The problem is that no one is talking about what the joy is really based on and how it could let us down in the end.

Certainly, part of the joy comes from Democrats’ relief at having a candidate who is mentally alert and has at least a chance of winning the election. But that isn’t all of it, and some thought experiments show why.

Imagine if after President Biden stepped down, the party had united around a white male candidate. If the person accepting the nomination last week had been Gavin Newsom, Beto O’Rourke or even Tim Walz, there would have been some joy, sure. But not of the theatrical degree we saw in Chicago. Not too many people in the audience would be crying with joy as they did for Harris.

Let’s take it further. Suppose the nominee were a white woman. There would surely be some joy, of the Hillary vintage. Some, but not like in Chicago. Tearful beaming elation for Amy Klobuchar? Gretchen Whitmer? Kirsten Gillibrand? I really doubt it.

That’s because a good deal of the joy people keep talking about is a result of one fact: that Harris is Black.

Yes, she’s got a big laugh and a casual affect and she seems to be having a good time. But this isn’t anything close to the whole story. Don’t believe me? Run the thought experiment again, but this time picture Stacey Abrams or Michelle Obama accepting the party’s nomination. It’s a lot easier to picture those same joyful tears, isn’t it.

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