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Math word Problems With Answers for Grade 6

Grade 6 maths word problems with answers are presented. Some of these problems are challenging and need more time to solve. Also detailed solutions and full explanations are included.

Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
If the area of a circle is 81pi square feet, find its circumference.
Find the greatest common factor of 24, 40 and 60.
In a given school, there are 240 boys and 260 girls. a) What is the ratio of the number of girls to the number of boys? b) What is the ratio of the number of boys to the total number of pupils in the school?
If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?
Find k if 64 ÷ k = 4.
Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?
What is x if x + 2y = 10 and y = 3?
A telephone company charges initially $0.50 and then $0.11 for every minute. Write an expression that gives the cost of a call that lasts N minutes.
A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours?
A small square of side 2x is cut from the corner of a rectangle with a width of 10 centimeters and length of 20 centimeters. Write an expression in terms of x for the area of the remaining shape.
A rectangle A with length 10 centimeters and width 5 centimeters is similar to another rectangle B whose length is 30 centimeters. Find the area of rectangle B.
A school has 10 classes with the same number of students in each class. One day, the weather was bad and many students were absent. 5 classes were half full, 3 classes were 3/4 full and 2 classes were 1/8 empty. A total of 70 students were absent. How many students are in this school when no students are absent?
The perimeter of square A is 3 times the perimeter of square B. What is the ratio of the area of square A to the area of square B.
John gave half of his stamps to Jim. Jim gave gave half of his stamps to Carla. Carla gave 1/4 of the stamps given to her to Thomas and kept the remaining 12. How many stamps did John start with?
Two balls A and B rotate along a circular track. Ball A makes 4 full rotations in 120 seconds. Ball B makes 3 full rotation in 60 seconds. If they start rotating now from the same point, when will they be at the same starting point again?
A segment is 3 units long. It is divided into 9 parts. What fraction of a unit are 2 parts of the segment?

A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter's age was twice the sum of Carla's & Jim's age. Find the present age of each one of them.
Linda spent 3/4 of her savings on furniture. She then spent 1/2 of her remaining savings on a fridge. If the fridge cost her $150, what were her original savings?
The distance bewteen Harry and Kate is 2500 meters. Kate and Harry start walking toward one another and Kate' dog start running back and forth between Harry and Kate at a speed of 120 meters per minute. Harry walks at the speed of 40 meters per minute while Kate walks at the speed of 60 meters per minute. What distance will the dog have travelled when Harry and Kate meet each other?

Answers to the Above Questions

a) 13:12 b)12:25
0.50 + N * 0.11
4.5 gallons
450 centimeters squared
108 cubic centimeters
1250 meters/minute
Carla:5 years, Jim: 6 years, Peter: 19 years.
3000 meters

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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."

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

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.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

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."

Sandeep Kashyap

7 Easy problem-solving activities & how your team benefits from them

Introduction

“Problems are not stop signs, they are guidelines.” – Robert Schuller

Problem-solving activities are a great way to know how team members identify problems, the way they react to them, how quickly they can find potential solutions, and then implement the best one.

When working with a team, there are not one but several types of problems that might occur and as a leader, your mindset should be to guide your team to solve those problems.

You have to take the initiative to make your team better at generating creative solutions when things go wrong.

In this article, you will find 7 easy problem-solving activities designed to encourage teamwork and unlock your team’s creativity.

7 of the easiest problem-solving activities for teams of all sizes

There are some amazing creative activities out there that can work well for team building. These will help you put your team’s problem-solving abilities to the test while they learn how to bring their best qualities forward for effective collaboration.

These creative problem-solving games will break the monotony at the workplace and help you build a more inclusive and welcoming environment for the whole team for effective team building. Here are some of the easiest activities that will help bring substantial change to your team culture and the workplace as a whole.

1. Human knots

Helps with: Collaboration & communication skills

Estimated time: 15-20 minutes

Things you’ll need: Nothing

How to do it:

Make your team stand in a small circle. If your team is large, then you can divide it into smaller groups and make them stand in multiple circles. Each person should hold the hands of two other people standing in the circle, but not of those who are standing directly beside them.

This should result in creating a “human knot.” The fun part (also the challenging) begins now. Ask each member of the group to untangle themselves without letting go of each other’s hands. You can set a time limit if you want. You can watch your team members as they work out moves to untangle their bodies.

This activity gives them a chance to communicate and collaborate to solve the problem quickly. They may or may not fully entangle themselves but would have started to work together to solve the problem.

Why communication is essential to problem-solving

When working as a team, no problem is big enough. A bunch of committed individuals can collaborate to overcome even the most difficult of hurdles. When all team members come together and put in a joint effort as per strategy, the problem will likely be resolved sooner.

Having problems communicating your ideas to the team? Use ProofHub discussions to keep track of ideas and important pitches.

2. A shrinking vessel

Helps with : Adaptability & Quick Thinking

Estimated time: 10-15 Minutes

Things you’ll need: A rope and a ball of yarn

Take a rope and place it on the floor in a particular shape such that all your team members can stand inside it. If your team is large, you can use multiple ropes and divide your team into smaller groups.

The challenging part starts when all team members are made to stand inside the rope, and you start to shrink the rope slowly. As space reduces, team members will have to make subtle adjustments to maintain their position as well as balance inside the shrinking circle.

No one should step outside the circle. The challenge before your team is to quickly think together about how to keep everyone inside the circle.

Why adaptability is essential to problem-solving

This amazingly effective problem-solving activity is for teams who are facing adaptability issues. Adaptability and cognitive diversity go hand in hand, which enables your team to work out things faster. People and organizations that can adapt quickly usually come out on top because they can condition themselves to change circumstances and environments and take on board new ideas and concepts.

3. Marshmallow spaghetti tower

Helps with: Collaboration

Estimated time: 20-30 Minutes

Things you’ll need (per team):

20 sticks of uncooked spaghetti
1 marshmallow
A yard of string
A single roll of masking tape

Ask your team to utilize all the available materials to construct the tallest tower within a specific period. The tower must stand on its own and be able to support a marshmallow.

The point behind this problem-solving activity is to train the team to think on their feet while encouraging prototyping and iteration. This activity also helps to promote and build strong camaraderie and leadership.

Why collaboration is essential to problem-solving –

Peter Singe, in the Fifth Discipline , writes, “ Collectively, we can be more insightful, more intelligent than we can be individual .” This means we can solve problems better when working as a team than we can alone.

This problem-solving activity emphasizes team collaboration, which is crucial for the success of any group, irrespective of its size. It also shows that success is dependent upon close collaboration between team members.

4. Frostbite

Helps with: Decision Making, Trust, Leadership

Things you’ll need:

An electric fan
Construction materials (toothpicks, cardstock, rubber bands, sticky notes, etc.)

Divide your team into groups of 4-5 people each (applicable for large teams). Each team should have its leader to guide them. Remember, team leaders, are not allowed to use their hands in any way to help their respective groups. Now, the fun part of this problem-solving activity is that team members are blindfolded, so they can’t use their hands!

Every team is given 30 minutes to build a tent. The time is set to create a sense of urgency within the team. For example, give your team a scenario where they have to make a tent to save themselves from approaching thunderstorms. The tent should be able to withstand high winds from the storm.

After the game is over, you can turn on the fan to see which tent can stand on its own even after withstanding winds blowing at high speed.

This problem-solving activity aims to improve the listening skills of team members to execute the task as per the leader’s instructions.

Why decision-making is essential to problem-solving

When managing teams and projects , team managers are burdened with the responsibility of making decisions that concern all. Decision-making is essential to problem-solving because if the right decision is taken at the right time, it could resolve the problem, eventually benefiting the entire team and the organization.

5. Egg drop

Helps with: Decision Making & Collaboration

A carton of eggs
Construction materials (balloons, rubber bands, straws, tape, plastic wrap, etc.)
A place where you can let things get messy!

Give a single egg to each team and let it choose randomly from different construction materials. The task that is to be assigned to each team is that it has to create a carrier for an egg that prevents it from breaking.

Once teams are done with creating carriers, place an egg in them and drop them (from over a ledge or a balcony), one by one. The purpose is to find which team’s carrier (s) can save an egg from breaking.

If multiple eggs remain unbroken, you can keep increasing the height of the fall to find out the last egg that survives even after falling from a higher height. The winning team is the one that created the most durable carrier that survived until the last.

The idea behind this problem-solving activity is to encourage all members of the team to work together towards achieving the common goal.

Why teamwork is essential to problem-solving

Joint efforts by a group of individuals to achieve the set target by utilizing limited resources can save the organization valuable time, money, and resources.

6. Dumbest idea first

How it helps: Critical Thinking & Creative Problem Solving

Estimated time: 15-20 minutes

Things you’ll need: A piece of paper, pen, and pencil

As the name of this problem-solving activity suggests, the idea is to present a problem to your team and ask them to quickly come up with the dumbest ideas for the problem at hand. This could be a real-world problem that your team is facing, or it could be an imagined scenario.

Once all team members have written down the dumbest ideas, they could think of, evaluate every idea to determine which ones are most likely to work and which ones are least likely to be seen as a viable solution that can work.

How critical thinking is essential to problem-solving

Some problems need to be solved by out-of-the-box thinking. Creative problem-solving ideas might sound unorthodox to work, but these give you additional options to consider. You can discover some solutions that might not be obvious to start with but can be incredibly effective in delivering expected results.

Brainstorm these dumb (or not so dumb) ideas in ProofHub through online chat. And start your uninterrupted collaborative journey for FREE today.

How it helps: Communication, Problem-solving, & Management

A lockable room
5-10 puzzles or clue

Hike the key and a list of clues around the room. Ask team members to solve all the clues to find the key and unlock the room to escape within the allotted time. Hide the clues and, most importantly, the key around the room.

Ask all team members to enter the room and lock the door. Give them 30 minutes or 1 hour to find the key using the clues hidden in the room. This problem-solving activity can get your team going up and running as they race against the time to find a solution to the problem at hand.

How putting intensive efforts is essential to problem-solving

Complex problems require an intensive team effort. Your team can achieve specific, time-bound goals by collaborating closely and thinking quickly under pressure.

What team problems are these activities going to solve?

1. lack of mutual trust.

Trust is the basis of strong relationships. No team can hope to achieve success if members do not want to engage with each other and make that human connection that is so vital for them for better collaboration.

Team members should first know each other well, both professionally and personally, primarily before they are assigned a large, complex project where tensions will run high at some point.

2. Not having a central location for information sharing

When some team members do not get easy access to crucial information related to a project, it can lead to a dreaded information gap within the team. Scattered information makes matters worse for managers and team members.

Having all the information stored and organized in a single location, in the form of files and folders, makes information accessibility easy for all team members. Team members can collaborate on them effectively , review, proof, and share feedback in one place , which saves a whole lot of time.

3. Lack of transparency

“According to an American Psychological Association survey that spoke to more than 1,500 workers , it was found that 50% didn’t feel that their employers shared the information they required to be successful within their jobs.”

For any project to be a success, teams, managers, and clients must be on the same page. Without transparency, trust will take a backseat within the team, and it can lead to a plethora of problems that can spell doomsday for the company.

The task of establishing transparency starts at the top. Project managers are responsible for setting a prime example for their team members in terms of the way they conduct themselves. Employees are likely to follow their leader’s behaviors, positive or negative, and it becomes your responsibility to inspire them through positive actions.

4. Poor communication

“David Grossman reported in “The Cost of Poor Communications” that a survey of 400 companies with 100,000 employees each cited an average loss per company of $62.4 million per year because of inadequate communication to and between employees.”

Poor communication happens when it doesn’t happen regularly across the team, and not all members participate in it. It can also occur when team members interrupt one another, maintain silence, and indicate problems but fail to address them formally. Some members may nod in agreement but may not agree in reality.

Using different communication modes can bridge the gap between team members. At the same time, encouraging members to share their ideas and concerns openly can also help clear any misunderstandings, doubts, and confusion.

5. Lack of purpose

“ One in two employees report that their jobs lack purpose, and an equal number feel disconnected from their company’s mission.”

If I think about the teams I least enjoyed working with, they were the ones that had a vague understanding of what exactly their purpose was and how they planned to achieve that goal. It’s hard to put in your best efforts when you don’t know the purpose behind the work you’re doing. The most satisfying teamwork occurs when the purpose is well-defined and team members are aligned with each other.

6. Conflict and tension

“ $359 billion in paid hours or the equivalent of 385 million working days are lost each year due to workplace conflict.”

Conflicts and tension can be healthy and trigger useful debates if managed carefully. However, team members can cross the line often. The negative effects of workplace conflict include but are not limited to, poor productivity, absenteeism, work disruptions, project failure , lower retention rates, and termination. Different opinions in the workplace are common, but it’s their mishandling that can spell troubles for an organization.

Team leaders can practice constructive criticism to make employees realize their shortcomings without making them feel humiliated. You can appreciate their strong points but should not hesitate to point out their weaknesses (in performance or conduct) in an affirmative tone.

7. Uncertainty of roles

This is a common problem, especially among large teams. Some team members are not clear about their roles; what are they supposed to do, and when. At the end of the day, the blame game happens. Team members blame their managers and vice versa, and it’s all due to poor task management.

By creating and assigning custom roles , managers can allow team members or clients to do things that fall under their work domain and job responsibilities.

8. Lack of motivation

“When managers recognize employees’ contribution, their engagement increases by 60%”.

Having demotivated employees working for you is probably the biggest misfortune of your organization. However, have you ever tried to find out the reason for some of your employees losing motivation? It can be due to not being appreciated at work , not feeling like a part of the team, personal reasons, etc.

Whatever the reason may be, a team manager should quickly confront the situation to solve it for good. Having one-on-one discussions with team members can go a long way in helping you to know about the exact reasons behind their below-par performance and come up with effective solutions.

What are the benefits of these problem-solving activities ?

“ But how problem-solving activities are going to help me, my team members, and the organization?” Many readers, especially team managers, must have this question in mind while reading this article.

I understand that readers want to know how problem-solving activities can benefit them. So, I have prepared a list of the pros of such activities to develop positivity in the workplace. Read on to know more about it.

1. Better thinking

Problem-solving activities help in bringing about the best in every member of the team. Every member enthusiastically puts forth his unique idea of solving the problem. This helps team managers to weigh in different solutions for resolving a problem and then choose the most suitable one. In other words, this process stimulates better thinking.

For example – A remote team with widely dispersed members was struggling with a lack of communication . Emails and texting were just not good enough. Mike was leading the team, and he asked all members to suggest ways to improve communication within the remote team.

John suggested using online chat software for instant group or individual chat, Sid suggested using video conferencing software for daily team meetings, and Shane suggested using telephonic calls, texting, and emails for official communication.

As a result of quick thinking and sharing of ideas, Mike and his team benefited greatly by using different communication modes to share information and feedback easily.

2. Better risk handling

Some people can handle a higher amount of risk. It’s because they have successfully dealt with difficult situations before. Team problem-solving activities help in conditioning the minds of individuals so they can respond to stressful situations better.

3. Better communication

Regular communication between team members can help to solve problems efficiently. Problem-solving activities within teams foster cooperation and intra-team communication, which eventually creates a better understanding between team members.

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4. Improved productivity output

When a team works as a strong unit, the company or organization experiences improved productivity, which eventually leads to improved profit margins. The involvement of managers and team members in problem-solving activities can have a positive result for the company in terms of overall growth and profitability.

How management tools can help you sort out your team collaboration problems

Even though the aforementioned problem-solving activities can be amazingly effective in enhancing collaboration and communication within your team, there’s no denying the fact that using a top-rated team collaboration and project management software like ProofHub can help team managers solve quite a few problems efficiently.

Whether you’re having trouble with delayed communication, poor organization of files and folders, poor time management, inadequate task management , or low control over teams and projects, ProofHub is your all-in-one solution to put an end to your managerial woes and help you and your team achieve more in less.

Some powerful features of ProofHub include:

Workflows and Kanban Boards
Online Proofing
Gantt Charts
Online Discussions
Custom Reports
Timer and Timesheets
Third-party Integrations
Announcements
IP Restrictions

Pricing – Simple pricing for all team sizes. For information on our pricing plans, kindly visit our pricing page .

The final thought

Many organizations face a plethora of problems that haunt their teams consistently. These problems have a rippling effect on the team’s performance, hamper its productivity, and cause delays in the organizational goals.

However, problem-solving activities can bring all members closer as a team and encourage them to contribute to resolving problems effectively while having fun. These easy problem-solving activities can improve your team’s solutions-generating capabilities, eventually benefiting everyone.