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Problem Solving Wheel: Help Kids Solve Their Own Problems

Students who act out in aggressive behaviors often do so because they struggle with identifying solutions to their problems. A Problem-Solving Wheel can help teach your students to learn how to independently solve a problem.

A problem-solving wheel also known as the wheel of choice or solution wheel is a great way to give students a visual of choices to help them either calm down when they are upset or to help them solve a problem with a classmate.

It is best to use the problem-solving wheel when students are dealing with a “small” problem. “Small” problems include conflicts that cause “small” feelings of annoyance, embarrassment, boredom, etc. If the student has a BIG problem they should practice telling an adult. “BIG problems” are situations that are scary, dangerous, illegal, etc.

problem solving wheel lesson

Examples of Small Problems

  • A classmate broke your pencil
  • Someone cut in front of them in line
  • A classmate is using the color crayon they want to use
  • A friend keeps kicking their chair

Conflict Resolution

Children don’t always know what to do when they are experiencing conflicts with others. When students are stressed and in the moment of a conflict they can often forget how to solve the problem A problem-solving choice wheel can help them learn different ways to solve their problems. I’ve created a few free printable problem-solving choice wheels for you to choose from. Simply download and start using in your classroom today!

Problem Solving Wheel Freebie

Comes in 4 different versions:

  • Ready-Made: “What can I do?” choice wheel is ready to use right away. Simply download, print and start using this freebie!
  • Blank with Pictures: Have your students add their own words to the pictures.
  • Blank: Have your students draw their own pictures and write a short description.
  • Editable Version: Using the free version of Adobe Acrobat Reader edit all the blue boxes with your own words.

problem-solving-wheel

When you create a consistent pattern of how to solve problems students will eventually pick up on that pattern and begin to implement the pattern independently.

Send me the Problem Solving Choice Wheel!

Involve children in finding the solution..

Involving children in the problem-solving process can help give them buy-in into using the system that they take part in creating. Use the blank version or the editable version and have your students create their own ideas for how to solve “small” problems on their own. Your students might even surprise you and come up with some creative solutions.

Teach Feeling Words

In addition, for some of our students teaching feeling words can help them have the vocabulary necessary to express how they are feeling during a problem. We can start by naming students’ feelings for them and after some practice hopefully, the students will begin to use feeling words to describe how they are feeling during a conflict. For example, “Sam the way you yelled, “no” and stomped your feet tell me that you are angry.” Talking to our students this way can help bring their attention to their feelings so they can eventually identify their own feelings.

Help your students resolve a social conflict on their own with this – PROBLEM-SOLVING WHEEL .

 Where to Begin

  • Start by posting the PROBLEM-SOLVING WHEEL in a good spot in your classroom or office.
  • Start slowly and use 1-2 solutions and build up to using all 6 solutions.
  • Practice, practice, practice!

Helpful Tips

  • Start slowly: practice using 1-2 choices at a time and slowly build up to using all six. Be clear about what each choice looks like in practice.
  • Practice is critical: Even after introducing the Problem-Solving Wheel students will still depend on you to help them resolve their conflicts. Continue to modal and have your students practice.

Books on Problem Solving

For Younger Children: Recommended Ages 2-6

  • The Little Mouse, The Red Ripe Strawberry, and the Big Hungry Bear
  • Duncan the Story Dragon
  • The Whale in my Swimming Pool

For Older Children: Recommended Ages 8-12

  • Appleblossom the Possum
  • Dough Knights and Dragons
  • Rosie Revere, Engineer

Aggressive behaviors are often exhibited when a student struggles with identifying solutions to their problems. A problem-solving wheel can be a great way to give students a visual of choices to help them calm down and to solve a problem with a classmate or friend.

Grab your freebie printable today and get started helping your students independently solving their own problems!

Want More Problem Solving?

Be sure to check out my other problem-solving freebies:

  • 31 Wordless Videos to Teach Problem-Solving
  • 71+ Free Social Problem Solving Task Cards Scenarios

Get More Problem Solving Time Saving Materials

Next, be sure to check out the following time-saving materials to continue to teach your students how to solve their social problems in addition to this freebie.

Problem Size & Reaction Size

Problem Size and Reaction Size

  • Problem size and reaction size.   Teach your students to identify the size of a problem and to match the size of the problem with their reaction size.

Weekly Social Pragmatics Homework

Social Pragmatics Homework

  • Weekly problem-solving.   Send home a  weekly homework page  that includes a problem-solving scenario plus an idiom and a conversational practice scenario.

Weekly Social Pragmatics

Restorative Justice Problem Solving Flip Book

Restorative Justice

  • Restorative justice graphic visual.  Use this graphic visual to help your student  restore a social relationship  after a social problem.

restorative justice

Thursday 2nd of February 2023

Great idea!

71+ Free Social Problem-Solving Scenarios - Speech Therapy Store

Wednesday 23rd of October 2019

[…] with these small problems can be a great learning opportunity. Children can practice problem-solving with a small problem which can help them learn how to handle bigger problems in the […]

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The Wheel of Choice

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Wheel of Choice

Focusing on solutions is a primary theme of Positive Discipline, and kids are great at focusing on solutions when they are taught the skills and are allowed to practice them.

The wheel of choice provides a fun and exciting way to involve kids in learning and practicing problem-solving skills, especially when they are involved in creating it.

Make sure your child takes the primary lead in creating his or her wheel of choice. The less you do, the better. Your child can be creative and decide if he or she would like to draw pictures or symbols to represent solutions, or to find pictures on the Internet. Then let your child choose (within reason) where to hang his or her wheel of choice.

Older kids may not want to create a wheel, but could benefit from brainstorming ideas for focusing on solutions and writing them down on an easily accessible list. It is helpful when you have other options for finding solutions, such as family meetings. Then you can offer a choice: “What would help you the most right now—your wheel of choice or putting this problem on the family meeting agenda?”

Helping your child create a wheel of choice increases his or her sense of capability and self-regulation. From Mary’s story you will gain a sense of why it is best to have your kids make their own wheel of choice from scratch instead of using a template.

Success Story

The following Wheel of Choice was created by 3-year-old Jake with the help of his mom, Laura Beth. Jake chose the clip art he wanted to represent some choices. His Mom, shared the following success story.

Wheel of Choice

Jake used his Wheel of Choice today. Jake and his sister (17 months old) were sitting on the sofa sharing a book. His sister, took the book and Jake immediately flipped his lid. He yelled at her, grabbed the book, made her cry. She grabbed it back and I slowly walked in. I asked Jake if he’d like to use his Wheel Of Choice to help—and he actually said YES! He chose to “share his toys.” He got his sister her own book that was more appropriate for her and she gladly gave him his book back. They sat there for a while and then traded!

by Mary Tamborski , co-author of Positive Discipline Parenting Tools

It was such fun creating a wheel of choice with my son Reid when he was 7 years old. We purchased a few supplies in advance: poster board, stickers, scented markers, scissors, and colored paper. None of these materials are required, but I knew it would make it more fun.

It turned out to be even more of an advantage than I thought because his 3-year-old brother, Parker, wanted to be involved too. He had fun making his own wheel of choice (even though he didn’t really under- stand it). This was a great distraction for Reid’s little brother, who felt like he was involved in the process.

I started by asking Reid, “What are some of the things you do or can do when you are having a challenge?”

I was really impressed with how easy it was for Reid to come up with so many solutions. He had already been using many of these skills, so he created his list very quickly.

  • Walk away or go to a different room.
  • Take deep breaths.
  • Put it on the family meeting agenda.
  • Use a different tone.
  • Ask Mom or Dad for help.
  • Count to ten to cool off.
  • Hit the “reset button” and try again.

He had fun writing them all on his pie graph. The scented pens added to his enthusiasm. He wanted to “practice” writing them on a piece of scratch paper before he officially drew them on his poster board.

Wheel of Choice

I loved how he handled it when he misspelled a word or when his circle wasn’t even. He just crossed out the word and rewrote it. I was tempted to give my two cents and step in to fix it for him, but I remembered how important it was for him to do it by himself. I could see the pride in his grin and his little happy dance movement in his chair. I was relieved when Reid patiently allowed his little brother to be involved by adding stickers to his finished project.

Reid was so proud when he held up his wheel of choice. Even Parker was proud. They were both posing for a photo, and Reid even wanted me to take a video as he described it.

About two hours later he had his first challenge: his older brother, Greyson, was saying, “Reid smells like a fart.” Then he started mimicking everything Reid said.

Reid came to me and said, “Greyson keeps bugging me.”

I said, “You’re having a challenging moment. Would it help you to go to your wheel of choice to choose something you could do?”

He went to his wheel of choice, looked at it, and did his own little process of elimination. He said, “I’ve already walked away and he keeps following me.

I’m asking you for help.”

I asked, “What else could you try?”

Reid started taking deep breaths. Then he said, “I’m going to try asking him in a calm voice to please stop, and lie on the bed while you read us a book.”

Before I could even fully process this magical moment, all three boys were lying next to me while we read a book.

One of the most valuable lessons I learned was that he had the tools and skills to solve his problems on his own. Knowing that he had his wheel of choice reminded me to not get involved in solving the problem. After all, getting me involved wasn’t one of his “solutions.” (Yes, asking me for help was one of his solutions, and I used my judgment to know he could find something that didn’t involve me. If he had been in physical danger I would have helped.)

Click Here to view the Wheel of Choice from a program created by Lynn Lott and Jane Nelsen (illustrations by Paula Gray).

Click Here to get a more complete description and to order your own Wheel of Choice: A Problem Solving Program . It includes 14 lessons to teach the skills for using the Wheel of Choice.

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  • Kelso Recommends – The Digital Library

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What People Are Saying

Kelso’s Choices has impacted my school site tremendously. The program is engaging and easy to implement.

Lauren Link

I highly recommend this program for anyone who works with children.

Kerri Stritchfield

The students and their teachers love the problem solving skills Kelso teaches them.

King Avenue Elementary

We use a non threatening frog puppet to teach children how to solve problems in a peaceful way. Communities need to work together to promote a healthy, nonviolent environment for children from infancy through the teenage years. Teachers who participated in the Kelso’s Choice program during its first year reported a significant decrease in physical conflicts and tattling.

Kathy Trainer

About Kelso

Welcome to the home of Kelso’s Choice, the leading tool for teaching conflict management skills for children Pre-K through 5th grade. Home of the beloved choice wheel, this conflict resolution curriculum teaches children the difference between big problems and little problems. Kelso the frog is a fun and engaging way for children to learn conflict management.

Looking for our best-selling conflict resolution posters, counseling board games, award-winning conflict management curriculum and much more? Click here to see our Products page.

Looking to learn about the history of Kelso’s Choice? Click here . Want to download your free conflict resolution wheel? Click here for your free starter kit.

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problem solving wheel lesson

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Math Wheels for Note-taking?

Problem solving math wheels.

Help your students improve their problem solving skills using problem solving math wheels

Problem solving in math, or tackling word problems in math can be challenging for students, whether they’re in early elementary, upper elementary, middle school, or even high school! 

Especially if they don’t have any type of strategies to help them know where to start.

I’m not necessarily a fan of using ‘tricks’ or a specific approach every time students approach a problem.

But, there are times when students will feel very ‘stuck’ as to where to start, especially if they have trouble understanding or breaking down the actual text of the problem. They may also have difficulty in middle school if they don’t have a strong problem solving foundation.

We often see students in middle school who can understand what to do mathematically when presented with a problem situation. But some of those same students kind of freeze when that problem is presented in several sentences…. especially if there’s some extra information in there.

So, I created two different math wheels to help students with:

  • Deciphering word problems 
  • Problem solving strategies

Problem Solving Math Wheel #1

The first problem solving math wheel includes eight ideas students can use when breaking down a word problem and then solving:

1) Carefully read the problem

2) Identify the question, to be sure about what is being asked

Help students learn new word problem strategies with problem solving math wheels

3) Reread. Once students know what the problem is asking, they can reread to find pertinent information.

4) Circle key numbers. By circling key numbers students are taking the time to identify numbers they’ll use in their calculations.

This is helpful:

  • for identifying numbers that may be in word form
  • for identifying numbers that are NOT needed for the problem. These would not be circled and could even be crossed out.

5) Locate and box important words

  • These words don’t necessarily need to be ‘operation’ words, but rather any words that help students understand what is happening in the problem

6) Evaluate, or solve the problem

7) Interpret and label

  • The mathematical answer may not be the answer to the question (like when interpreting the quotient results in the answer being rounded up or down)
  • Adding the unit label to the answer

8) Take time to check

  • Is the answer reasonable? Does it make sense as an answer to the question?

This wheel has a  word problem that you can work through  with students when discussing these ideas.

Problem Solving Math Wheel #2

The second problem solving math wheel includes some of the well-known problem solving strategies and can be used as a simple reference to remind students that these strategies exist.

problem solving wheel lesson

These problem solving strategies include:

  • Organized List
  • Guess and Check
  • Work Backwards
  • Make a Table
  • Draw a Diagram
  • Write an Equation
  • Look for a Pattern
  • Use Logical Reasoning

This wheel would be great for a center or finished early activity, because it doesn’t require direct instruction.

  • Students can color this problem solving math wheel and then add it to their binders/notebooks and use as a reference throughout the year.
  • This wheel could also be used in conjunction with the  Problem Solving Doodle Notes , which can be used to teach each individual strategy, as explained in this problem solving strategies blog post .

I know your students will love this engaging way to talk about and reinforce math problem solving strategies.

The opportunity to color and add some of their own creative touches will help make the strategies more memorable. 

Keeping these finished notes in their math notebooks will give students a reference for the entire school year!

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CREATE Week: Using the Problem-Solving Wheel to Prioritize Solutions by Abby Woods

As a school leader for more than 15 years, having the ability to quickly problem solve while including my team has been a vital craft to develop. I’m Abby Woods , a longtime leader in schools working alongside teams to improve educational experiences for students. My current role, besides being a board member for CREATE , is as the Director of Internal Consulting for Charleston County School District .

Problem Solving Wheel

The problem-solving wheel graphic has been an essential tool for my school teams to attack educational issues related to student achievement and program evaluation. Many times teams gather to admire the problem and often get derailed with discussing the issues rather than prioritizing the solution through a process of performance measures and documentation .

Lessons Learned:

  • Ensure your team can stay focused on the issues at hand and encourage them to be specific with problem. For example, the literacy program is not working is vague; whereas gathering information and creating a ‘work flow’ of the literacy process will help identify the breakdown.
  • Providing stakeholders with an outline or steps helps the team feel successful in problem solving. Additionally, the cogs of the wheel can be assigned, then brought back to share for further examination. Teacher teams feel especially empowered through this level of responsibility and problem-solving for their students.
  • Guiding the team through this problem-solving wheel requires a systematic approach giving each member a role. Put differently, the ‘buy-in’ of the team will grow as the leader develops responsibility within the team.

Rad Resources:

  • American Evaluation Association is a great resource for leaders to evaluate how your team is growing. https://www.eval.org/page/competencies
  • The Flippen Group has a myriad of resources for growing, developing and stabilizing teams. These were practices that are most helpful when creating the appropriate culture for team growth and problem solving. https://flippengroup.com/capturing-kids-hearts/
  • The Racial Equity Institute provided an incredible insight and tools for evaluation as leaders work in a variety of organizations.

The American Evaluation Association is celebrating Consortium for Research on Educational Assessment and Teaching (CREATE) week. The contributions all this week to aea365 come from members of CREATE. Do you have questions, concerns, kudos, or content to extend this aea365 contribution? Please add them in the comments section for this post on the aea365 webpage so that we may enrich our community of practice. Would you like to submit an aea365 Tip? Please send a note of interest to [email protected] . aea365 is sponsored by the American Evaluation Association and provides a Tip-a-Day by and for evaluators.

1 thought on “CREATE Week: Using the Problem-Solving Wheel to Prioritize Solutions by Abby Woods”

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I am a student in the PME program at Queens University, in Kingston Ontario and am currently taking a course in Program Inquiry and Evaluation. I connected to your article as soon as I saw the “problem solving” wheel. As an instructional lead at my school, I can also see how this wheel would come in very handy to evaluate programs. I have led many PLC’s and we have taken on the Collaborative Inquiry model and follow the work of Jennifer Donohoo. This wheel and this model I have mentioned, have many similarities. Every stage of this wheel and the collaborative inquiry model are similar in that the contain the stages of problem solving (reflection), inquiry (awareness, gather information), collaboration (analyze information, vision and planning) and design (implement plan). Both of these models or processes allow stakeholders the ability to collaborate and through their inquires come up with a central idea or overall problem they need to try and solve by designing and implementing plans to meet their students learning needs. I appreciate that although the collaborative model is very systematic, it is not linear, and teams may need to go back and forth on the cycle. I would imagine this problem-solving wheel would be the same and participants would have the ability to go back and forth depending on any challenges the evaluation may pose. When I have facilitated inquiry teams, we brainstorm ideas, frame our problem and decide upon a common goal but after analyzing data we realize that we may need to take a step or two back and that the problem runs a little deeper than we thought. (i.e.: set a school goal of improving students reading fluency when after analyzing reading records realized that accuracy was the overall underlying issue and thus had to change our goal and focus.) I appreciate the three points you made as I also agree that participants need a systematic approach, with every member serving a specific purpose, clearly defined goals, which everyone agrees upon and are working towards and a clearly defined process to keep everyone motivated and on track. I wonder about any challenges you may face when evaluating programs and working collaboratively with a team. I wonder how you have overcome these challenges. I also have found that if success is not found after a certain amount of time, participants may lose interest in the end goal. Do you have any advice for keeping members motivated to continue and complete the program evaluation using this problem-solving wheel? I appreciated the link provided to the “performance measures and documentation” and look forward to sharing this with my team at work as I think it will help guide our evaluation questions.

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  • the wheel shop

The Wheel Shop

In the problem The Wheel Shop , students use algebraic thinking to solve problems involving unknowns, equations, and simultaneous constraints. The mathematical topics that underlie this problem are variables, inverse operations, equations, equalities, inequalities, and simultaneous systems. In each level, students must make sense of the problem and persevere in solving it ( MP.1 ). Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity.

PRE-K In this task, students will count the number of wheels on a tricycle. They will use counters to represent the wheels and solve for how many wheels would be on 3 and 10 tricycles.

LEVEL A      In this level, students are presented with the task of considering a tricycle shop with 18 wheels and determining how many tricycles there are. Their task involves finding an unknown and “undoing” the straightforward question of how many wheels 6 tricycles have in all.    

This level supports Common Core standards 3.OA.A.1 and 3.OA.A.2 . Students can approach solving this problem using either multiplication with an unknown number of groups or division to find the number of tricycles there are if the shop has 18 wheels.          LEVEL B      In this level, students are presented with a new situation that involves components of bicycles and go-carts.    

Students at an elementary level can use skills and strategies related to Common Core standard 4.OA.A.3 to solve this problem. They will use their understanding of the four operations to work through the problem in multiple steps—an important precursor to equations work in middle school. At a secondary level, this problem addresses standards 8.EE.C.8b and  8.EE.C.8c , where students write and solve two linear equations with two variables. 

LEVEL C      In this level, students are presented with a situation that involves components of bicycles, adult tricycles, and tandem bicycles. The situation can be translated into systems of linear equations with three unknowns.    

This level supports Common Core standard A-REI.C.6 . Students write and solve a system of three linear equations with three unknowns.           LEVEL D      In this level, students are given a situation that can be translated into a system of three equations with four unknowns. Students are asked to define the relationship between two unknowns.    

This level extends the work of Common Core standard A-REI.C.6 . Students build on algebraic and symbolic methods for solving systems of equations, including substitution and balance. They reason to find the relationship between two of the unknowns. Students will look for and make use of the structure ( MP.7 ) within the equations to help them find the relationship between the two unknowns.          LEVEL E      In this level, students are presented with a logic situation that involves using rational numbers, inequalities, and a set of constraints. Students are asked to find the number of bikes in the shop and the range of repairs that need to be made.    

This problem supports Common Core standard S-CP.A.1 as students must interpret the number and types of repairs represented in the problem as a sample space. They must also think about the complement of what is known. In the last part of the problem, students must solve a system consisting of an inequality and an equation. Students can use algebraic techniques or graphing, as described in Common Core standard A-REI.D.12 . Students must reason abstractly and quantitatively ( MP.2 ) as they make sense of the problem and potential solutions. Students may choose to organize their thinking using a diagram or table.      PROBLEM OF THE MONTH  Download the complete packet of The Wheel Shop Levels A-E here . 

You can learn more about how to implement these problems in a school-wide Problem of the Month initiative in “Jumpstarting a Schoolwide Culture of Mathematical Thinking: Problems of the Month,” a practitioner’s guide.   Download the guide as iBook with embedded videos or Download as PDF without embedded videos .

SOLUTIONS To request the Inside Problem Solving Solutions Guide, please get in touch with us via the feedback form .

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Problem wheel

Examples from our community, 10000+ results for 'problem wheel'.

Organizational Problem Wheel

Heart-Mind Online

Lesson plan: the emotion wheel.

  • Secure and Calm
  • Gets Along with Others
  • Alert and Engaged
  • Compassionate and Kind
  • Solves Problems Peacefully

problem solving wheel lesson

While scientists have, for centuries, attempted to come up with a list of the most core and universal emotions, there is no agreement among scholars.  Some argue that reducing a list of emotions to a handful of basic ones is too simplistic and doesn't reflect human complexity. 

Identifying emotions in ourselves and in other people plays a crucial role in the development of emotional regulation [ 1 ] .  This lesson plan [ 2 ]  allows students to explore emotions that are personally relevant.  The emotion wheel will help students see and identify possible interconnections, subtle differences and levels of emotional intensity.

Teaching and Learning Activities:

1.  ACTIVATE LEARNING: Think about where emotions come from. Are there basic emotions that all humans share no matter what culture? Brainstorm a list (or add an internet search).

2.  Choose one of the following:

  • From the student generated list, identify 8 emotions the class would like to examine more fully.
  • Align the choice with  American psychologist Paul Ekman  who identified basic emotions [ 3 ] including happiness, fear, surprise, sadness, disgust, anger, contempt and interest.
  • Choose emotions that support other related learning. Keep your choice of 8 emotions secret from the class until after the following step.

3. Divide the class into eight small groups. Secretly assign one emotion to each group and ask them to create a skit or mime to act out the emotion. The other groups can guess the emotion based on facial expressions, body language, or scenario if the actors are using words.

4. Individually, have students draw a wheel with 8 segments. Have them place each of the 8 chosen emotions on the wheel, arranging them so that they are next to emotions that they are related to, or closely connected with.

5. Invite students to add other emotion descriptors to the 8 categories of the wheel. Have them arrange the emotion words from mild to intense, with the most intense at the centre of the wheel. Utilize colours to reflect the levels of intensity. Encourage students to expand their emotional vocabulary by searching the internet, thesaurus and using personal experiences.

6. In pairs, have students compare their emotion wheels and brainstorm ways that the wheel could be used in the school setting or at home. Report out ideas.

Adaptations:

  • Use the wheel as a classroom tool to help solve disputes. Begin conflict resolution with the statement “I feel….”
  • Use the wheel to spark creative writing. Invite students to describe a time when they felt a particular emotion. Alternatively students can create a fictional story in which the main character experiences the emotion.
  • Use paint chips (with 3-5 colour gradations) to sort the intensity degrees of emotions.
  • Complete an internet search and compare wheels to American Psychologist Robert Plutchik’s Gradations. Discuss any emotions on the wheel that student’s have never experienced? Ask: can you experience more than one emotion at the same time?

problem solving wheel lesson

  • Conflict Resolution
  • Self-Regulation
  • Middle Years

B asic emotion awareness is a foundational competency in the development of emotion regulation. Research links the skills of emotional identification (starting in 3 year olds) with stimulation of the brain for awareness, arousal and, ultimately, regulation.

This lesson plan is adapted from activity descriptions found in the following resources:

Shanker, Stuart. (2013) Calm, Alert, and Learning: Classroom Strategies for Self-Regulation, Pearson: Toronto.

Carney, Patrick. (2015) Well Aware: Developing Resilient, Active and Flourishing Students, Pearson: Toronto.

Paul Ekman, known for his research on  facial expressions and scientific advise on the popular tv show Lie to Me, identified  basic emotions including anger, disgust, contempt, sadness, happiness, fear and surprise. He argued that these emotions are marked by distinctive changes in the face, voice and physiological processes such as heart rate.

Brought to you by CU Engineering (University of Colorado Boulder)

FREE K-12 standards-aligned STEM

curriculum for educators everywhere!

Find more at TeachEngineering.org .

  • TeachEngineering
  • Let's Move It!

Lesson Let's Move It!

Grade Level: 4 (3-5)

Time Required: 45 minutes

Lesson Dependency: None

Subject Areas: Geometry, Physical Science, Problem Solving, Reasoning and Proof, Science and Technology

NGSS Performance Expectations:

NGSS Three Dimensional Triangle

  • Print lesson and its associated curriculum

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.

  • Stack It Up!
  • Choosing a Pyramid Site
  • Solid Rock to Building Block
  • Wheeling It In!
  • Watch It Slide!
  • Pulley'ing Your Own Weight
  • Modern Day Pyramids

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Engineering connection, learning objectives, worksheets and attachments, more curriculum like this, pre-req knowledge, introduction/motivation, associated activities, lesson closure, vocabulary/definitions, additional multimedia support, user comments & tips.

Engineering… designed to work wonders

The simple machines explored in this lesson — wheel and axle, and lever — are relevant to modern-day, real-world methods of material transportation. Just as ancient engineers used simple machines in the transportation of stone for pyramid building, today's construction engineers continue to use simple machines to gain mechanical advantage in the transport of large and heavy materials. Think of all the big trucks that are used to transport materials. Some of these trucks have lifts — like garbage trucks — that work like levers to unload materials. Ancient and modern day engineers use the concept of balanced and unbalanced forces to move large and heavy materials.

After this lesson, students should be able to:

  • Explain the evolution and re-engineered uses of the wheel and axle.
  • Explain the evolution and re-engineered uses of a lever.
  • Understand how a wheel can be described as a lever.
  • Understand the many ways that engineers use the wheel and axle, and lever (as well as other simple machines) on a daily basis.

Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .

Ngss: next generation science standards - science, international technology and engineering educators association - technology.

View aligned curriculum

Do you agree with this alignment? Thanks for your feedback!

General knowledge of pyramids and geometric angles. Familiarity with the six simple machines introduced in Lesson 1 of this unit.

Have any of you seen images of the pyramids in Egypt or Mesoamerica ? Most of you should be raising your hand, because through our imagination we have all visited the pyramids. Historians estimate that it took ancient engineers 20 years to build some of the great pyramids. What do you think were some of the most difficult things people had to do in order to build them? (Possible answer: Move the huge stones, weighing up to 9,000-kilograms [~10-tons], and put them in position.) Can you imagine how strong you would have to be to move those stones? Or was there an easier way than using your hands to move them?

To build the Egyptian pyramids, engineers had to develop methods of transporting rock a great distance , perhaps hundreds of kilometers! Often, these stones also had to be transported across rivers. Have any of you ever tried crossing a river or creek with a fast-moving water? Maybe some of you have been tubing before? Do you remember anything about the speed at which the water pulled you? To build the Mesoamerican pyramids, the stone blocks were much smaller. Do you think they used the same methods for stone transportation that the Egyptians used? Mesoamerican engineers had no need for transporting stone a long distance because they used nearby stone.

It is incredible! While the Egyptian and Mesoamerican cultures existed millennia apart, and we believe there was no formal communication between them, both built incredible structures that have survived to this day. Each stone was cut with such accuracy, delicacy and artistry, that the pyramids are visited in wonder by millions of people each year! In fact, the Great Pyramids in Egypt, are considered to be one of the seven wonders of the world. Today, we are going to learn about the very clever ways that engineers of those times devised to transport heavy stones to their pyramid construction sites.

Optional introductory activity : Using images embedded in the attached Wheeling It In! Presentation (PowerPoint), print out many illustrations, hand them out, and ask students to classify them as "wheel and axle" or "lever."

Lesson Background and Concepts for Teachers

Use the attached Wheeling It In! PowerPoint presentation as a helpful classroom tool. (Show the PowerPoint presentation, or print out the slides to use with an overhead projector. The presentation is animated to promote an inquiry-based style; each click reveals a new point about each machine; have students suggest characteristics and examples before you reveal them.)

A lever is a simple machine that provides a mechanical advantage when used. Specifically, it is a bar pivoted on a fixed point (called the fulcrum) that is used to lift an object by applying force to one end. The idea, usually, is that you apply force to one end of a bar, in order to lift the other end. In Figure 1, force would be applied on the right side of the lever, while an object sitting on the left side would exert a resistance on the bar.

Diagram showing the location of the fulcrum in a lever, and a wheel and axle, and the location of the applied force and resistance.

Although the type of lever in Figure 1 is the one most commonly referenced (fulcrum between force and resistance), there are two other types of levers. One, such as a bottle opener, has the fulcrum on one end of the bar and the resistance is between the fulcrum and the force. The second, such as a broom (see Figure 2), has the fulcrum on one end, and the force is between the resistance and the fulcrum.

Photograph from above, showing a person sweeping with a broom.

It is believed by many historians that ancient engineers used levers extensively to lift or hoist large blocks and stones into place. As the ancient Greek historian Herodotus wrote:

"After laying the stones for the base, they raised the remaining stones to their places by means of machines formed of short wooden planks. The first machine raised them from the ground to the top of the first step. On this there was another machine, which received the stone upon its arrival, and conveyed it to the second step, whence a third machine advanced it still higher." Source: World Mysteries, Mystic Places, Construction of the Great Pyramid: www.world-mysteries.com/mpl_2_1.htm#Machines

In this manner, ancient engineers were able to methodically iterate "hoists" that lifted the heavy stone with a relatively small force.

(Herodotus, the "father of history," [425-485 BC] is an ancient Greek historian whose accounts, chiefly concerning the wars between the Greeks and Persians, are the earliest known examples of narrative historical writing.)

Show students an excellent animation at a Polish website about transportation methods that do not use a wheel and axle: www.swbochnacki.com (click on Site Map, then click on Transport within Pyramid's Benches). The animation shows use of levers and inclined planes to move objects up the steps of a pyramid.

Mechanical Advantage

Simple machines provide an easier way to do work due to a tradeoff between force and distance. This is called mechanical advantage . A lever allows an object to be lifted by exerting minimal downward force.

Wheel and Axle

With the popularity of vehicles today, we can see that the wheel and axle are main components in a very effective mode of transportation. Refer to the open-ended design associated activity Wheeling It In! to challenge students to design their own wheel and axle carts. Whether transporting people on long road trips, hauling cement or gravel, or moving furniture, cars, dump trucks, moving trucks and buses are successful modes of transportation. In fact, virtually all methods of transportation use the wheel and axle in some way. Although these types of vehicles did not exist in the early days of pyramid building, the wheel and axle, a simple machine, did exist.

Drawing of giant stones on logs being pulled and pushed by many people.

Many archeologists believe that Egyptian engineers transported stone blocks long distances by placing logs under the stones, with large numbers of people manually pulling on a rope attached to the front end of the stone, and continually adding new logs under the leading edge of the stone as the block was rolled forward (see Figure 3). This transportation method can be thought of as a simple wheel and axle, with the logs serving as rudimentary wheels. This method facilitated the transportation of stone that would otherwise have been much too heavy to move from a rock quarry to a construction site.

Other Transport Methods

Other stone transportation methods included two- to four-wheeled carts. The stone could have been hoisted onto the cart by the same method that is believed to have been used by the Egyptians. However, in the case of Mesoamerican pyramids, where the block size was not as huge, simpler levers could have been used.

Photograph of dump truck carrying rocks.

If we were to transport large blocks of stone today, we would probably use a dump truck (see Figure 4). Many present day construction materials are transported from a quarry to a foundation site using dump trucks. These trucks employ hydraulic cylinders that lift and tilt the truck bed to release its contents. The bed of the truck is essentially a lever; the fulcrum is created at the point at which the bed tilts. This transportation method demonstrates an effective combination of two simple machines — the wheel and axle, and the lever — to transport large and heavy loads. The wheel and axle allow for long distances to be traveled at a faster pace — providing a mechanical advantage. But, because a wheel is used, many revolutions are needed to travel this distance.

Engineering Design Process

As the students design and build their own version of an ancient transport system, consider introducing them to the engineering design process   — a series of steps that engineering teams use to guide them as they solve problems.

  • Ask: Identify the Needs and Constraints: What is the problem? What do I want to do? What are the project requirements? What are the limitations? Who is the customer? What is the goal? 
  • Research the Problem:  Gather information and research what others have done. Talk to people from many different backgrounds and specialties to assist with researching what products or solutions already exist, or what technologies might be adaptable to your needs.
  • Imagine: Develop Possible Solutions: You work with a team to brainstorm ideas and develop as many solutions as possible. This is the time to encourage wild ideas and defer judgment! Build on the ideas of others! Stay focused on topic, and have one conversation at a time! Remember: good design is all about teamwork!
  • Plan: Select a Promising Idea: Revisit the needs, constraints and research from the earlier steps, compare your best ideas, select one solution and make a plan to move forward with it.
  • Create: Build a Prototype: Building a prototype makes your ideas real! These early versions of the design solution help your team verify whether the design meets the original challenge objectives. Push yourself for creativity, imagination and excellence in design.
  • Test and Evaluate Prototype:  Does it work? Does it solve the need? Communicate the results and get feedback. Analyze and talk about what works, what doesn't and what could be improved.
  • Improve: Redesign as Needed:  Discuss how you could improve your solution. Make revisions. Draw new designs. Iterate your design to make your product the best it can be. And now, REPEAT!

Engineers explore all possible options and compare many design ideas. This is called open-ended design because when you start to solve a problem, you don't know what the best solution will be. Engineers use prototypes, or early versions of the design to improve their understanding of the problem, identify missing requirements, evaluate design objectives and product features, and get feedback from others. Engineers select the solution that best uses the available resources and best meets the project's requirements.

Watch this activity on YouTube

Let's discuss the pyramid building processes that may have been employed by engineers from ancient cultures. How might these processes have differed based on the kinds of pyramids they built or where they built them? (Answer: Different methods were used to move smaller rocks than larger rocks; used simple machines like the lever, and wheel and axle.)

How might a wheel and axle, a lever, or a combination of both, facilitate the transportation of materials? (Answer: These simple machines provide a mechanical advantage, which allows for the transportation of objects that would be otherwise too large or heavy for the average person to transport by hand. It also allows for faster and longer distance transportation.)

Conduct summary assessment activities as described in the Assessment section.

In other lessons of this unit, students study each simple machine in more detail and see how each could be used as a tool to build a pyramid or a modern building.

design: (verb) To plan out in systematic, often graphic form. To create for a particular purpose or effect. Design a building. (noun) A well thought-out plan.

distance: A measure of space between two objects.

engineering: Applying scientific and mathematical principles to practical ends such as the design, manufacture and operation of efficient and economical structures, machines, processes and systems.

force: A push or pull on an object.

fulcrum: The point at which a lever pivots.

lever: A simple machine that increases or decreases the force to lift something. Usually a bar pivoted on a fixed point (fulcrum) to which force is applied to do work.

mechanical advantage : An advantage gained by using simple machines to accomplish work with less effort. Making the task easier (which means it requires less force), but may require more time or room to work (more distance, rope, etc.). For example, applying a smaller force over a longer distance to achieve the same effect as applying a large force over a small distance. The ratio of the output force exerted by a machine to the input force applied to it.

mesoamerica: A region extending south and east from central Mexico to include parts of Guatemala, Belize, Honduras and Nicaragua. In pre-Columbian times it was inhabited by diverse civilizations, such as the Mayan and the Olmec.

quarry: A pit from which rock or stone is removed from the ground.

simple machine: A machine with few or no moving parts that is used to make work easier (provides a mechanical advantage). For example, a wedge, wheel and axle, lever, inclined plane, screw, or pulley.

speed: A measure of how fast an object is traveling.

transport: To carry from one place to another; to convey.

weight: A measure of how heavy or light something is. The weight of an object is the mass of the object times the force of gravity pulling on the object.

wheel and axle: A simple machine that reduces the friction of moving by rolling. A wheel is a disk designed to turn around an axle passed through the center of the wheel. An axle is a supporting cylinder on which a wheel or a set of wheels revolves.

wonder: Something that arouses awe, astonishment, surprise or admiration; a marvel.

work: Force on an object multiplied by the distance it moves. W = F x d (force multiplied by distance).

Pre-Lesson Assessment

Brainstorming: As a class, have the students engage in open discussion to generate a number of possible ideas about transportation for pyramid design. Remind students that in brainstorming, no idea or suggestion is "silly." All ideas should be respectfully heard. Take an uncritical position, encourage wild ideas and discourage criticism of ideas. Have them raise their hands to respond. Write their ideas on the board. Encourage discussions that involve the use of any simple machines as you ask the students:

  • How did ancient engineers build pyramids? What tools did they use?

Post-Introduction Assessment

Question/Answer: Ask the students and discuss as a class:

  • For what reason do engineers use a combination of wheel and axle, and levers to transport materials today? (Answer: Using a wheel and axle, or lever system creates a mechanical advantage, making easier the transportation of materials that would otherwise be too large or heavy to transport.)
  • Why is the wheel referred to as a type of lever? (Answer: A wheel is a lever that is able to rotate 360 degrees about its focal point [axle].)
  • How might you use a wheel and axle, or lever, if you were constructing your own house? (Possible Answers: Use a dump truck to transport materials such as rock, sand and gravel. Use a flat-bed truck to transport materials such as beams, wood and appliances. Use a wheel barrow or dolly to move items around once off the truck.)

Lesson Summary Assessment

Engineering Report: Assign the students to write a short entry in their "ancient time capsule journal" that describes the relevance of the wheel and axle, and the lever in the building of pyramids, and addresses the following issues:

  • How might Egyptian and Mesoamerican engineers have used the wheel and axle?
  • How might Egyptian and Mesoamerican engineers have used the lever?
  • Why was the use of these simple machines so important?
  • Draw and label the parts of a wheel and axle.
  • Draw and label the parts of a lever.
  • List five items with which you are familiar that use either a wheel and axle, or a lever.
  • Describe the steps of the engineering design process.

Pass the Buck: Engineering Design- In groups of four, have students brainstorm ideas to define an engineering design problem related to the above lesson (i.e. some sort of transportation problem). What is the need or want of your problem? First, assign one student in the group to be the recorder. Then, have someone toss out an idea. Next, another person in the group provides an idea that builds on the first. Go around the group in this fashion until all students have put in enough ideas to define an engineering design problem. Next, have students define a short list of criteria that the design must meet. For instance, the design must move lift the object 50 feet. Help the students understand what a design criteria is. Lastly, have students come up with a short list of constraints for their problem (e.g.. material constraints such as they only have materials that were available in ancient times; or they only have a budget of one hundred dollars). Help students understand the idea of engineering constraints (materials, time, costs, etc). When they are done, have them share their idea(s) with the class. Encourage the incorporation of any simple machines they have learned about. This can also be a fun exercise as an entire class- especially if students are new to the engineering design process!

Lesson Extension Activities

Take a "field trip" to the playground and have students draw and list objects containing a lever, or wheel and axle (or any other simple machines).

Ancient engineers had to transport large, heavy rock across water. Have students brainstorm ways in which they would transport pyramid stones across water.

Have students play the BBC's Pyramid Challenge online educational game at http://www.bbc.co.uk/history/ancient/egyptians/launch_gms_pyramid_builder.shtml .

Show students a six-minute online video about a Michigan man who is building a Stonehenge replica to show people how its huge blocks could have been placed without modern heavy equipment. See "Building Stonehenge: This Man Can Move Anything" at: https://www.youtube.com/watch?v=lRRDzFROMx0

problem solving wheel lesson

Students are introduced to the six types of simple machines — the wedge, wheel and axle, lever, inclined plane, screw, and pulley — in the context of the construction of a pyramid, gaining high-level insights into tools that have been used since ancient times and are still in use today.

preview of 'Engineering: Simple Machines' Lesson

In this open-ended design activity, students use everyday materials—milk cartons, water bottles, pencils, straws, candy—to build small-scale transportation devices. They incorporate the use of two simple machines—a wheel and axle, and a lever—into their designs.

preview of 'Wheeling It In!' Activity

Students are introduced to three of the six simple machines used by many engineers: lever, pulley, and wheel-and-axle. In general, engineers use the lever to magnify the force applied to an object, the pulley to lift heavy loads over a vertical path, and the wheel-and-axle to magnify the torque appl...

preview of 'Levers That Lift' Lesson

Students apply the mechanical advantages and problem-solving capabilities of six types of simple machines (wedge, wheel and axle, lever, inclined plane, screw, pulley) as they discuss modern structures in the spirit of the engineers and builders of the great pyramids.

preview of 'Simple Machines and Modern Day Engineering Analogies' Lesson

Bochnacki, Andrzeh. 2005. O Piramidach Inaczeh. Andrzej Bochnacki (Polish engineer). www.swbochnacki.com. Accessed January 18, 2006. (An excellent animation shows use of levers to move objects up the steps of a pyramid, Click on Site Map, then click on Transport within Pyramid's Benches.)

Construction of the Great Pyramid, Construction Theories. www.World-Mysteries.com. Accessed January 18, 2006. (Includes translated quotations from the ancient Greek historian Herodotus, and an excellent animation of the method of raising pyramid stone blocks, as described by Herodotus.)

Dictionary.com. Lexico Publishing Group, LLC. www.dictionary.com. Accessed January 18, 2006. (Source of some vocabulary definitions, with some adaptation)

Dollinger, André, "An Introduction to the History and Culture of Pharaonic Egypt" and "Building in Stone: The Tools." André Dollinger, Reshafim, Israel. nefertiti.iwebland.com. Accessed January 18, 2006.

Dollinger, André, Building in Stone: The Tools, André Dollinger, Reshafim, Israel. Accessed January 18, 2006.

Loethen, Chris. Pyramids Schmeramids: Why the Pyramids of Egypt and Mesoamerica Do Not Share a Common Source. anth507.tripod.com. Accessed January 18, 2006.

Pyramid Challenge. BBC-History, British Broadcasting Corporation, London, UK. www.bbc.co.uk/history/ancient/egyptians. Accessed January 18, 2006.

Westbroek, Glen. Wheel and Axle. Updated August 7, 2000. Utah State Office of Education. www.usoe.k12.ut.us. (Excellent animation of wheel and axle) Accessed January 18, 2006.

Contributors

Supporting program, acknowledgements.

The contents of these digital library curricula were developed by the Integrated Teaching and Learning Program under National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: October 30, 2020

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    Lessons Learned: Ensure your team can stay focused on the issues at hand and encourage them to be specific with problem. For example, the literacy program is not working is vague; whereas gathering information and creating a 'work flow' of the literacy process will help identify the breakdown.

  14. The Wheel Shop

    In the problem The Wheel Shop, students use algebraic thinking to solve problems involving unknowns, equations, and simultaneous constraints. The mathematical topics that underlie this problem are variables, inverse operations, equations, equalities, inequalities, and simultaneous systems. In each level, students must make sense of the problem and persevere in solving it (MP.1).

  15. Problem Solving Wheel

    Units & Lesson Plans. Take your class on an educational adventure over multiple lessons. Widgets. Use simple apps that help you do all kinds of useful things. ... Results for ‛Problem Solving Wheel' 269 teaching resources Problem Solving Wheel Sort: Relevance . Grades Grade 1 73. Grade 2 102. Grade 3 133. Grade 4 100. Grade 5 99. Grade 6 79.

  16. Problem Solving

    1 hours 15 minutes (two 40-minute class periods) Subject Areas: Print this lesson Everyday, teams problem solve to figure out the best solutions to various challenges. copyright Summary Students are introduced to a systematic procedure for solving problems through a demonstration and then the application of the method to an everyday activity.

  17. Problem Solving Lessons

    1. 2. 3. TED-Ed lessons on the subject Problem Solving. TED-Ed celebrates the ideas of teachers and students around the world. Discover hundreds of animated lessons, create customized lessons, and share your big ideas.

  18. Problem wheel

    10000+ results for 'problem wheel'. Movement cool down wheel. Random wheel. Number wheel by 10s to 1,000 (Part 2) 360-650! Random wheel. Wheel Of Names! Random wheel. Organizational Problem Wheel - Problem Solving Situations - emoji spinning wheel - Movement cool down wheel. - Random but fun questions.

  19. Engineering: Simple Machines

    Summary Simple machines are devices with few or no moving parts that make work easier. Students are introduced to the six types of simple machines — the wedge, wheel and axle, lever, inclined plane, screw, and pulley — in the context of the construction of a pyramid, gaining high-level insights into tools that have been used since ancient times and are still in use today.

  20. Lesson Plan: The Emotion Wheel

    4. Individually, have students draw a wheel with 8 segments. Have them place each of the 8 chosen emotions on the wheel, arranging them so that they are next to emotions that they are related to, or closely connected with. 5. Invite students to add other emotion descriptors to the 8 categories of the wheel. Have them arrange the emotion words ...

  21. In last week's PBL lesson, we...

    Punchbowl Public School. · November 6, 2022 ·. In last week's PBL lesson, we launched our new and improved Problem Solving Wheel. This week we will be discussing one of the strategies that students can use to solve problems.

  22. Let's Move It!

    The simple machines explored in this lesson — wheel and axle, and lever — are relevant to modern-day, real-world methods of material transportation. ... Students apply the mechanical advantages and problem-solving capabilities of six types of simple machines (wedge, wheel and axle, lever, inclined plane, screw, pulley) as they discuss ...