PEMDAS Adventure Game: A Math Board Game Project
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PEMDAS Adventure Game: A Math Board Game Project

Grade 5Math5 days
★★★★★
5.0 (1 rating)
In this project, 5th-grade students design a board game that teaches players to solve multi-step math problems using the order of operations (PEMDAS). Students will apply their understanding of PEMDAS to create engaging game mechanics, develop challenging math problems, and incorporate real-world scenarios. Through collaborative design, playtesting, and feedback, students will refine their games to effectively reinforce PEMDAS rules and problem-solving strategies. The project culminates in a presentation of their games, where they explain the mathematical concepts and design choices behind their creations, demonstrating a deep understanding of PEMDAS and its applications.
PEMDASOrder Of OperationsGame DesignMath Board GameProblem-SolvingCollaborative LearningMathematical Expressions
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we design a fun and engaging board game that teaches players to solve multi-step math problems using PEMDAS in order to apply this skill to real-world scenarios?

Essential Questions

Supporting questions that break down major concepts.
  • How does the order of operations (PEMDAS) ensure consistent results in math?
  • In what real-life scenarios is it important to follow a specific order of steps to achieve the desired outcome?
  • How can a game be designed to effectively reinforce the rules of PEMDAS?
  • What strategies can be used to solve multi-step math problems efficiently and accurately?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Students will be able to apply the order of operations (PEMDAS) to solve multi-step math problems.
  • Students will be able to design a board game that reinforces the rules of PEMDAS.
  • Students will be able to explain how PEMDAS ensures consistent results in mathematics.
  • Students will be able to identify real-life scenarios where following a specific order of steps is crucial.
  • Students will be able to evaluate the effectiveness of their game in teaching PEMDAS to others and iterate based on feedback.
  • Students will be able to use game design principles to create a fun and engaging learning experience.
  • Students will be able to develop efficient and accurate strategies for solving multi-step math problems.
  • Students will be able to collaborate effectively with peers to develop and refine their board game design.
  • Students will be able to communicate mathematical ideas and game design concepts clearly through written and oral presentations.
  • Students will be able to reflect on their learning process and identify areas for improvement in their understanding of PEMDAS and game design principles.
  • Students will be able to demonstrate an understanding of PEMDAS by solving problems correctly within the game context.
  • Students will be able to create game mechanics that accurately reflect the rules of PEMDAS.
  • Students will be able to construct math problems of varying difficulty levels that require the application of PEMDAS.
  • Students will be able to test and refine their game based on playtesting feedback.
  • Students will be able to present their game to an audience and explain the mathematical concepts it teaches.
  • Students will be able to analyze and critique other students' games, providing constructive feedback.
  • Students will be able to connect the application of PEMDAS to real-world problem-solving scenarios.
  • Students will be able to understand the importance of precision and accuracy in mathematical calculations.
  • Students will be able to develop problem-solving skills through game design and mathematical challenges.
  • Students will be able to work collaboratively to design, develop, and present their board game.
  • Students will be able to plan the game's narrative, rules, and components in alignment with the PEMDAS concept.
  • Students will be able to implement PEMDAS rules accurately within the game mechanics.
  • Students will be able to create a scoring system that reflects the correct application of PEMDAS rules.
  • Students will be able to justify the design choices made during the creation of their game.
  • Students will be able to engage in peer review to improve the quality of their game design and PEMDAS content.
  • Students will be able to self-assess their game to reflect on its strengths and areas for improvement.
  • Students will be able to present their game and explain the math and design considerations involved.
  • Students will be able to use mathematical language to describe and explain the application of PEMDAS.
  • Students will be able to collaborate and communicate effectively within a group setting.
  • Students will be able to demonstrate critical thinking and problem-solving skills through game design.
  • Students will be able to engage in peer assessment to provide feedback and improve the design of their game.
  • Students will be able to reflect on their learning and evaluate their understanding of PEMDAS and game design principles.
  • Students will be able to identify and analyze real-world applications of PEMDAS and order of operations.
  • Students will be able to synthesize knowledge of mathematics and game design to create a unique learning experience.
  • Students will be able to design a visually appealing and engaging game board and related materials.
  • Students will be able to troubleshoot challenges during the design and development process.
  • Students will be able to use appropriate tools and resources to support the development of their game.
  • Students will be able to explain their design choices and the rationale behind their game mechanics.
  • Students will be able to apply PEMDAS to solve complex mathematical problems.
  • Students will be able to design a game that effectively teaches and reinforces the rules of PEMDAS.
  • Students will be able to communicate mathematical concepts and game design principles clearly and effectively.
  • Students will be able to collaborate effectively with peers to create a high-quality learning experience.
  • Students will be able to reflect on their learning and identify areas for improvement.
  • Students will be able to demonstrate an understanding of PEMDAS by solving problems correctly within the game context.
  • Students will be able to design game mechanics that accurately reflect the rules of PEMDAS.
  • Students will be able to develop and refine their game based on playtesting and feedback.
  • Students will be able to present their game to an audience and explain the mathematical concepts it teaches.
  • Students will be able to apply PEMDAS to solve complex mathematical problems presented in game form.
  • Students will be able to design a game that effectively teaches and reinforces the rules of PEMDAS in a fun and engaging way.
  • Students will be able to demonstrate creativity and innovation in their game design.
  • Students will be able to manage their time and resources effectively to complete the project within the given timeframe.
  • Students will be able to present their game to an audience and explain the mathematical concepts it teaches, as well as the design decisions behind the game mechanics.
  • Students will be able to analyze and critique other students' games, providing constructive feedback that is both helpful and encouraging.
  • Students will be able to reflect on their learning and identify areas for improvement in their understanding of PEMDAS and game design principles, and they will be able to articulate these insights in a clear and meaningful way.
  • Students will be able to design a game that effectively teaches and reinforces the rules of PEMDAS in a fun and engaging way, incorporating elements of storytelling, character development, and thematic design.
  • Students will be able to manage their time and resources effectively to complete the project within the given timeframe, adhering to a project plan and adapting to unexpected challenges or obstacles.
  • Students will be able to present their game to an audience and explain the mathematical concepts it teaches, as well as the design decisions behind the game mechanics, clearly and persuasively.
  • Students will be able to analyze and critique other students' games, providing constructive feedback that is both helpful and encouraging, while also demonstrating an understanding of the game design principles and mathematical concepts involved.
  • Students will be able to reflect on their learning and identify areas for improvement in their understanding of PEMDAS and game design principles, and they will be able to articulate these insights in a clear and meaningful way, using evidence from their own work and the feedback they received.
  • Students will be able to apply PEMDAS to solve multi-step mathematical problems in the context of a board game.
  • Students will be able to design an engaging board game that effectively teaches and reinforces the rules of PEMDAS.
  • Students will be able to communicate mathematical concepts and game design principles clearly and effectively to an audience.
  • Students will be able to collaborate effectively with peers to develop and refine their board game.
  • Students will be able to reflect on their learning and identify areas for improvement in their understanding of PEMDAS and game design.
  • Students will be able to create a visually appealing and user-friendly board game.
  • Students will be able to write clear and concise game rules.
  • Students will be able to test and refine their game based on feedback from others.
  • Students will be able to present their game to an audience and explain the mathematical concepts and design choices.
  • Students will be able to analyze and critique other students' games, providing constructive feedback.
  • Students will be able to connect the application of PEMDAS to real-world scenarios.
  • Students will be able to develop problem-solving skills through game design and mathematical challenges.
  • Students will be able to apply the order of operations (PEMDAS) to solve mathematical expressions.
  • Students will be able to design a game that requires players to use PEMDAS to advance.
  • Students will be able to explain the importance of following the correct order of operations.
  • Students will be able to work collaboratively to create a fun and engaging game.
  • Students will be able to test their game and make improvements based on feedback.
  • Students will be able to present their game to the class and explain how it teaches PEMDAS.
  • Students will be able to follow a design process to create a functional and aesthetically pleasing board game.
  • Students will be able to use mathematical language to describe the game and its rules.
  • Students will be able to self-assess their game and identify areas for improvement.
  • Students will be able to create a game that aligns with the principles of PEMDAS.
  • Students will be able to explain the math behind the game.
  • Students will be able to refine their game based on testing and feedback.
  • Students will be able to communicate effectively about their game.
  • Students will be able to work together to make a great game.
  • Students will apply PEMDAS to create a game.
  • Students will design the game.
  • Students will explain PEMDAS through the game.
  • Students will improve the game based on feedback.
  • Students will learn PEMDAS by creating a game.
  • Students will demonstrate their understanding of PEMDAS by designing a board game.
  • Students will apply problem-solving skills to create an engaging and educational game.
  • Students will collaborate with peers to develop a fun and interactive learning experience.
  • Students will improve their understanding of math concepts.
  • Students will use math to solve a game.
  • Students will use the game to show PEMDAS.
  • Students will make the game better by fixing it.
  • Students will understand PEMDAS through the game.
  • Students will know what PEMDAS is.
  • Students will know PEMDAS.
  • Students will develop a PEMDAS game.
  • Students will collaborate.
  • Students will improve their game.
  • Students will present.
  • Understand and apply the order of operations (PEMDAS/BODMAS).
  • Design a game that incorporates mathematical principles.
  • Collaborate with peers to create a shared project.
  • Develop problem-solving skills through game design.
  • Communicate mathematical ideas effectively.
  • Students will understand the purpose of PEMDAS.
  • Students will be able to create a math game.

Common Core Standards

CCSS.Math.Content.5.OA.A.1
Primary
Apply the order of operations (PEMDAS/BODMAS) to solve mathematical expressions.Reason: Directly addresses the core mathematical concept of the project.
CCSS.Math.Content.5.OA.A.2
Secondary
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.Reason: Supports the creation of mathematical problems for the game.
CCSS.Math.Practice.MP4
Supporting
Model with mathematics.Reason: Students are modeling mathematical concepts through game design.
CCSS.Math.Practice.MP5
Supporting
Use appropriate tools strategically.Reason: Students may use various tools (e.g., dice, cards, game pieces) in their game design.
CCSS.Math.Practice.MP6
Supporting
Attend to precision.Reason: Accurate application of PEMDAS is crucial for the game to function correctly.
CCSS.Math.Practice.MP7
Supporting
Look for and make use of structure.Reason: Students will be looking for the structure within the order of operations.

Entry Events

Events that will be used to introduce the project to students

The Mysterious Math Message

A famous mathematician

The Broken Game

The class receives a letter from a game developer
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

PEMDAS Prep Rally

Students review and practice the order of operations (PEMDAS) through worksheets and small group problem-solving, reinforcing the foundational skills needed for game design.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Complete individual PEMDAS practice problems.
2. Participate in a group discussion to review solutions and clarify any misunderstandings.
3. Summarize PEMDAS rules and create examples for each operation.

Final Product

What students will submit as the final product of the activityCompleted PEMDAS practice worksheets and a summary of key PEMDAS rules and examples.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.Math.Content.5.OA.A.1 (Apply the order of operations) - Focuses on understanding and applying PEMDAS rules.
Activity 2

Problem-Crafting Workshop

Students brainstorm and write a variety of multi-step math problems suitable for a 5th-grade level, focusing on different difficulty levels and real-world contexts.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Brainstorm real-world scenarios that involve multiple mathematical operations.
2. Write PEMDAS problems based on the scenarios, varying the complexity of each problem.
3. Categorize the problems by difficulty level and type (addition, subtraction, multiplication, division, exponents, parentheses).

Final Product

What students will submit as the final product of the activityA collection of diverse PEMDAS problems, categorized by difficulty and context.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.Math.Content.5.OA.A.2 (Write simple expressions) - Focuses on writing mathematical problems for the game.
Activity 3

Game Blueprint Bonanza

Students design the basic layout and mechanics of their board game, including the game board, player pieces, and action cards, ensuring that the game requires players to apply PEMDAS to advance.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Sketch the layout of the game board, including starting points, ending points, and spaces for PEMDAS challenges.
2. Develop game rules that require players to solve PEMDAS problems to move forward.
3. Design action cards or events that add an element of chance or strategy to the game.

Final Product

What students will submit as the final product of the activityA detailed game design document, including a sketch of the game board, rules of play, and examples of PEMDAS challenge cards.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.Math.Practice.MP4 (Model with mathematics) - Focuses on modeling mathematical concepts through game design.
Activity 4

Prototype Power-Up

Students create a prototype of their board game, using materials such as cardboard, markers, and dice. They test the game for playability and accuracy of PEMDAS problems.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Gather materials such as cardboard, markers, dice, and game pieces.
2. Construct the game board and player pieces based on the design document.
3. Create PEMDAS challenge cards and action cards.
4. Test the game to ensure it is playable and the PEMDAS problems are solvable.

Final Product

What students will submit as the final product of the activityA playable prototype of the PEMDAS board game, ready for testing and refinement.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.Math.Practice.MP5 (Use appropriate tools strategically) - Focuses on using tools in their game design.
Activity 5

Feedback Frenzy

Students playtest each other's games and provide feedback on the game's mechanics, clarity of rules, and effectiveness in teaching PEMDAS.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Playtest another group's game, following the rules carefully.
2. Provide written feedback on the game's design, rules, and PEMDAS problems.
3. Offer suggestions for improving the game's playability and educational value.

Final Product

What students will submit as the final product of the activityWritten feedback on at least two other groups' games, focusing on both the game design and the mathematical accuracy of the PEMDAS problems.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.Math.Practice.MP6 (Attend to precision) - Accurate application of PEMDAS is crucial for the game to function correctly.
Activity 6

Revise and Remix

Based on the feedback received, students revise their game design, rules, and PEMDAS problems to improve the game's overall quality and effectiveness.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Review the feedback received from playtesting and peer review.
2. Revise the game design, rules, and PEMDAS problems based on the feedback.
3. Test the revised game to ensure it is improved.

Final Product

What students will submit as the final product of the activityA final version of the PEMDAS board game, incorporating feedback from playtesting and peer review.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.Math.Practice.MP7 (Look for and make use of structure) - Students will be looking for the structure within the order of operations.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

PEMDAS Game Design Rubric

Category 1

PEMDAS Proficiency

Focuses on the accuracy and understanding of PEMDAS rules through practice problems and summaries.
Criterion 1

PEMDAS Application

Accuracy and application of PEMDAS rules in solving practice problems.

Exemplary
4 Points

Consistently and accurately applies PEMDAS rules to solve complex problems, demonstrating a deep understanding of the order of operations.

Proficient
3 Points

Accurately applies PEMDAS rules to solve most problems, demonstrating a good understanding of the order of operations.

Developing
2 Points

Applies PEMDAS rules inconsistently, with some errors in the order of operations.

Beginning
1 Points

Struggles to apply PEMDAS rules, with frequent errors and a lack of understanding of the order of operations.

Criterion 2

PEMDAS Summary

Clarity and correctness of the summary of PEMDAS rules and examples.

Exemplary
4 Points

Provides a comprehensive and clear summary of PEMDAS rules, with well-explained and accurate examples for each operation.

Proficient
3 Points

Provides a clear summary of PEMDAS rules, with accurate examples for most operations.

Developing
2 Points

Provides a basic summary of PEMDAS rules, but some examples may be unclear or inaccurate.

Beginning
1 Points

Provides an incomplete or unclear summary of PEMDAS rules, with few or inaccurate examples.

Category 2

Problem Creation

Focuses on the ability to create diverse and relevant PEMDAS problems from real-world contexts.
Criterion 1

Scenario Relevance

Relevance and creativity of the real-world scenarios presented.

Exemplary
4 Points

Presents highly relevant and creative real-world scenarios that effectively demonstrate the application of multi-step math problems.

Proficient
3 Points

Presents relevant real-world scenarios that demonstrate the application of multi-step math problems.

Developing
2 Points

Presents somewhat relevant real-world scenarios, but the connection to multi-step math problems may not be clear.

Beginning
1 Points

Presents irrelevant or unclear real-world scenarios, with little connection to multi-step math problems.

Criterion 2

Problem Variety

Variety and complexity of PEMDAS problems written.

Exemplary
4 Points

Writes a diverse range of complex PEMDAS problems, effectively varying the difficulty level and type of operations used.

Proficient
3 Points

Writes a variety of PEMDAS problems, varying the difficulty level and type of operations used.

Developing
2 Points

Writes some PEMDAS problems, but the variety and complexity are limited.

Beginning
1 Points

Writes few or simple PEMDAS problems, with little variety or complexity.

Criterion 3

Problem Organization

Organization and categorization of problems by difficulty and type.

Exemplary
4 Points

Categorizes problems meticulously by difficulty level and type, making it easy to differentiate and select appropriate problems.

Proficient
3 Points

Categorizes problems effectively by difficulty level and type.

Developing
2 Points

Attempts to categorize problems, but the organization may be inconsistent or unclear.

Beginning
1 Points

Does not categorize problems, or the categorization is disorganized and unhelpful.

Category 3

Game Design

Focuses on the design of the game, ensuring it effectively integrates PEMDAS into gameplay.
Criterion 1

Board Design

Clarity and detail of the game board layout.

Exemplary
4 Points

Sketches a highly detailed and clear game board layout, including well-defined starting and ending points, and engaging spaces for PEMDAS challenges.

Proficient
3 Points

Sketches a detailed and clear game board layout, including starting and ending points, and spaces for PEMDAS challenges.

Developing
2 Points

Sketches a basic game board layout, but some details may be unclear or missing.

Beginning
1 Points

Sketches a vague or incomplete game board layout, lacking essential details.

Criterion 2

Rule Effectiveness

Effectiveness of game rules in requiring PEMDAS application.

Exemplary
4 Points

Develops highly effective and engaging game rules that seamlessly require players to solve PEMDAS problems to advance, enhancing the learning experience.

Proficient
3 Points

Develops effective game rules that require players to solve PEMDAS problems to advance.

Developing
2 Points

Develops basic game rules that require players to solve PEMDAS problems, but the connection may be weak or inconsistent.

Beginning
1 Points

Develops unclear or ineffective game rules that do not consistently require players to solve PEMDAS problems.

Criterion 3

Action Card Design

Creativity and strategic value of action cards or events.

Exemplary
4 Points

Designs highly creative and strategically valuable action cards or events that add an element of chance and enhance the game's engagement.

Proficient
3 Points

Designs creative and strategically valuable action cards or events that add an element of chance to the game.

Developing
2 Points

Designs basic action cards or events, but their creativity and strategic value are limited.

Beginning
1 Points

Designs uninspired or ineffective action cards or events, with little impact on the game's engagement.

Category 4

Game Prototype

Focuses on the creation of a functional and engaging game prototype.
Criterion 1

Prototype Completeness

Completeness and functionality of the game prototype.

Exemplary
4 Points

Creates a fully functional and polished game prototype that demonstrates exceptional attention to detail and playability.

Proficient
3 Points

Creates a complete and functional game prototype that is ready for testing and refinement.

Developing
2 Points

Creates a partially complete game prototype, but some elements may be missing or non-functional.

Beginning
1 Points

Creates an incomplete or non-functional game prototype, with significant elements missing or broken.

Criterion 2

Problem Accuracy

Accuracy and solvability of PEMDAS problems within the game.

Exemplary
4 Points

Ensures that all PEMDAS problems within the game are accurate, solvable, and appropriately challenging for the target audience.

Proficient
3 Points

Ensures that most PEMDAS problems within the game are accurate and solvable.

Developing
2 Points

Includes some PEMDAS problems that may be inaccurate or difficult to solve.

Beginning
1 Points

Includes many PEMDAS problems that are inaccurate, unsolvable, or inappropriate for the target audience.

Criterion 3

Game Engagement

Playability and engagement of the game.

Exemplary
4 Points

Creates a highly playable and engaging game that captures the interest of players and effectively reinforces PEMDAS concepts.

Proficient
3 Points

Creates a playable and engaging game that reinforces PEMDAS concepts.

Developing
2 Points

Creates a game that is somewhat playable, but may lack engagement or clear PEMDAS reinforcement.

Beginning
1 Points

Creates a game that is difficult to play or lacks engagement, failing to effectively reinforce PEMDAS concepts.

Category 5

Peer Feedback

Focuses on the quality and constructiveness of feedback provided during playtesting.
Criterion 1

Feedback Quality

Thoroughness and insightfulness of feedback provided.

Exemplary
4 Points

Provides exceptionally thorough and insightful feedback on the game's design, rules, and PEMDAS problems, demonstrating a deep understanding of game design principles and mathematical concepts.

Proficient
3 Points

Provides thorough and insightful feedback on the game's design, rules, and PEMDAS problems.

Developing
2 Points

Provides basic feedback on the game's design, rules, and PEMDAS problems, but some areas may be overlooked.

Beginning
1 Points

Provides superficial or unhelpful feedback on the game, lacking depth and insight.

Criterion 2

Improvement Suggestions

Clarity and constructiveness of suggestions for improvement.

Exemplary
4 Points

Offers exceptionally clear and constructive suggestions for improving the game's playability and educational value, demonstrating a strong understanding of game design and pedagogical principles.

Proficient
3 Points

Offers clear and constructive suggestions for improving the game's playability and educational value.

Developing
2 Points

Offers some suggestions for improvement, but they may be vague or lack constructiveness.

Beginning
1 Points

Offers few or unhelpful suggestions for improvement.

Criterion 3

Playtesting Engagement

Engagement and respectfulness during playtesting.

Exemplary
4 Points

Actively engages in playtesting, demonstrating respect for the game designer and providing thoughtful feedback in a respectful manner.

Proficient
3 Points

Engages in playtesting and provides respectful feedback.

Developing
2 Points

Participates in playtesting, but may be disengaged or provide feedback that is not always respectful.

Beginning
1 Points

Is disengaged during playtesting or provides disrespectful feedback.

Category 6

Game Revision

Focuses on the ability to revise and improve the game based on feedback.
Criterion 1

Feedback Integration

Incorporation of feedback into revisions.

Exemplary
4 Points

Thoroughly incorporates feedback from playtesting and peer review, making significant improvements to the game's design, rules, and PEMDAS problems.

Proficient
3 Points

Incorporates most feedback from playtesting and peer review, improving the game's design, rules, and PEMDAS problems.

Developing
2 Points

Incorporates some feedback from playtesting and peer review, but some areas may be overlooked.

Beginning
1 Points

Fails to incorporate feedback from playtesting and peer review, or makes minimal changes to the game.

Criterion 2

Game Improvement

Overall improvement in game quality.

Exemplary
4 Points

Demonstrates a remarkable improvement in game quality, resulting in a highly polished and effective learning experience.

Proficient
3 Points

Demonstrates a noticeable improvement in game quality.

Developing
2 Points

Shows some improvement in game quality, but further revisions may be needed.

Beginning
1 Points

Shows little or no improvement in game quality.

Criterion 3

Revised Game Effectiveness

Effectiveness of the revised game.

Exemplary
4 Points

Creates a highly effective and engaging revised game that effectively reinforces PEMDAS concepts and provides a fun learning experience.

Proficient
3 Points

Creates an effective and engaging revised game that reinforces PEMDAS concepts.

Developing
2 Points

Creates a revised game that is somewhat effective, but may lack engagement or clear PEMDAS reinforcement.

Beginning
1 Points

Creates a revised game that is ineffective or lacks engagement, failing to reinforce PEMDAS concepts.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

How did creating this game deepen your understanding of PEMDAS?

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Question 2

What was the most challenging aspect of designing a game that effectively teaches PEMDAS?

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Question 3

How did the feedback you received from your peers influence the final design of your game?

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Question 4

In what real-life scenarios could you apply the problem-solving skills you used while designing this game?

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Question 5

To what extent do you agree with the following statement: 'My game is effective in teaching the rules of PEMDAS to someone who doesn't know them.'

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