Created byJacob Shoesmith-Fox

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Law of Sines: Create a Board Game

Grade 11Math2 days

In this project, 11th-grade math students design a board game that applies the Law of Sines to real-world challenges. Students will research applications like surveying and navigation, then create a game incorporating the Law of Sines formula and its relationship to triangle properties. The game design will require students to understand and apply different cases of the Law of Sines (ASA, SSA, AAS) while creating a fun and educational experience.

Law of SinesTriangle PropertiesGame DesignReal-World ApplicationsProblem SolvingASASSA

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we design a game that uses the Law of Sines to navigate real-world challenges and demonstrate its relationship to triangle properties?

Essential Questions

Supporting questions that break down major concepts.

How can the Law of Sines be used to solve real-world problems involving triangles?
What are the different cases when the Law of Sines can be applied (e.g., ASA, SSA, AAS)?
How does the Law of Sines relate to the properties of triangles (e.g., angles, side lengths)?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:

Apply the Law of Sines to solve real-world problems.
Understand the relationship between the Law of Sines and triangle properties.
Identify and apply different cases of the Law of Sines (ASA, SSA, AAS).
Design a board game that incorporates the Law of Sines.

Entry Events

Events that will be used to introduce the project to students

Missing Persons Mystery

**Missing Persons Mystery:** Present students with a fictional missing person case where the last known location can only be determined using the Law of Sines. Students must use the Law of Sines to calculate distances and potential search areas, sparking their interest in how the Law of Sines can be applied to real-world scenarios. This creates immediate relevance and a sense of purpose for their board game creation.

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Portfolio Activities

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

Activity 1

Law of Sines in the Real World

Students will begin by researching real-world applications of the Law of Sines, such as surveying, navigation, or astronomy. They will then select one application to focus on for their board game.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Research real-world applications of the Law of Sines (e.g., surveying, navigation, astronomy).

2. Select one application to focus on for the board game.

3. Write a brief report (1-2 pages) outlining the chosen application and how it will be integrated into the game. Include diagrams or examples.

Final Product

What students will submit as the final product of the activityA brief report outlining the chosen real-world application of the Law of Sines and how it will be incorporated into the game.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Apply the Law of Sines to solve real-world problems.

Activity 2

Decoding the Law of Sines Formula

Students will explore the mathematical foundation of the Law of Sines and its connection to triangle properties (angles and side lengths). This activity reinforces their understanding of the formula and its applicability.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Review the Law of Sines formula and its components (angles, side lengths).

2. Create a diagram that visually represents the relationship between the Law of Sines and triangle properties.

3. Write a detailed explanation of the formula, referencing the diagram and explaining how it relates to triangle properties.

Final Product

What students will submit as the final product of the activityA detailed explanation of the Law of Sines formula, including a diagram illustrating its relationship to triangle properties.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Understand the relationship between the Law of Sines and triangle properties.

Activity 3

Mastering the Cases: ASA, SSA, AAS

Students will practice applying the Law of Sines in different scenarios (ASA, SSA, AAS) through a series of problem-solving exercises. This ensures they can accurately use the law in various contexts within their game.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Review the different cases of the Law of Sines (ASA, SSA, AAS).

2. Create a problem set with 2-3 problems for each case, including diagrams.

3. Solve each problem, showing all steps and calculations.

Final Product

What students will submit as the final product of the activityA problem set with solutions demonstrating the application of the Law of Sines in ASA, SSA, and AAS cases.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Identify and apply different cases of the Law of Sines (ASA, SSA, AAS).

Activity 4

Game Design Challenge: Law of Sines Adventure

Students will design their board game, incorporating the Law of Sines to solve challenges and navigate the game. They will create game rules, a game board, and playing pieces.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Brainstorm game ideas and mechanics that incorporate the Law of Sines.

2. Design the game board, including locations or scenarios where the Law of Sines is needed.

3. Create game rules and instructions, ensuring they are clear and easy to follow.

4. Develop playing pieces or components for the game.

5. Test the game to ensure it is playable and effectively demonstrates the Law of Sines.

Final Product

What students will submit as the final product of the activityA fully designed board game, including game rules, a game board, playing pieces, and instructions on how to play. The game should clearly demonstrate the application of the Law of Sines.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goals: Design a board game that incorporates the Law of Sines; Apply the Law of Sines to solve real-world problems; Understand the relationship between the Law of Sines and triangle properties; Identify and apply different cases of the Law of Sines (ASA, SSA, AAS).

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Law of Sines Portfolio Rubric

Category 1

Real-World Application

Assesses the student's ability to research and apply the Law of Sines in real-world contexts.

Criterion 1

Real-World Application

Depth of research into real-world applications and clarity of connection to the game concept.

Exemplary

4 Points

Demonstrates exceptional research into real-world applications of the Law of Sines, providing innovative and insightful connections to the game concept.

Proficient

3 Points

Demonstrates thorough research into real-world applications of the Law of Sines, providing clear connections to the game concept.

Developing

2 Points

Shows emerging research into real-world applications of the Law of Sines, with some connections to the game concept.

Beginning

1 Points

Shows minimal research into real-world applications of the Law of Sines, with weak or unclear connections to the game concept.

Criterion 2

Report Clarity

Clarity and coherence of the report, including effective use of diagrams and examples.

Exemplary

4 Points

The report is exceptionally clear, concise, and well-organized, with highly effective use of diagrams and examples to illustrate the real-world application.

Proficient

3 Points

The report is clear, concise, and well-organized, with effective use of diagrams and examples to illustrate the real-world application.

Developing

2 Points

The report is generally understandable but may lack clarity or organization in some areas. Diagrams and examples may be present but not fully effective.

Beginning

1 Points

The report is difficult to understand due to lack of clarity, organization, or relevant diagrams and examples.

Category 2

Formula Comprehension

Evaluates the student's comprehension of the Law of Sines formula and its connection to triangle properties.

Criterion 1

Formula Explanation

Accuracy and depth of explanation of the Law of Sines formula, including connection to triangle properties.

Exemplary

4 Points

Provides an exceptionally clear and insightful explanation of the Law of Sines formula, demonstrating a deep understanding of its connection to triangle properties with novel insights.

Proficient

3 Points

Provides a clear and thorough explanation of the Law of Sines formula, demonstrating a solid understanding of its connection to triangle properties.

Developing

2 Points

Provides a basic explanation of the Law of Sines formula, but the connection to triangle properties may be superficial or incomplete.

Beginning

1 Points

Provides a limited or inaccurate explanation of the Law of Sines formula, with a weak or missing connection to triangle properties.

Criterion 2

Diagram Effectiveness

Effectiveness and clarity of the diagram illustrating the relationship between the Law of Sines and triangle properties.

Exemplary

4 Points

The diagram is exceptionally clear, accurate, and insightful, providing a novel visual representation of the relationship between the Law of Sines and triangle properties.

Proficient

3 Points

The diagram is clear, accurate, and effectively illustrates the relationship between the Law of Sines and triangle properties.

Developing

2 Points

The diagram is understandable but may lack clarity, accuracy, or completeness in illustrating the relationship between the Law of Sines and triangle properties.

Beginning

1 Points

The diagram is unclear, inaccurate, or missing, failing to effectively illustrate the relationship between the Law of Sines and triangle properties.

Category 3

Case Mastery

Assesses the student's proficiency in applying the Law of Sines in various triangle scenarios.

Criterion 1

Problem-Solving Accuracy

Accuracy in applying the Law of Sines to solve problems in ASA, SSA, and AAS cases.

Exemplary

4 Points

Consistently and accurately applies the Law of Sines to solve problems in all cases (ASA, SSA, AAS), demonstrating a sophisticated understanding of each case and potential ambiguities.

Proficient

3 Points

Accurately applies the Law of Sines to solve problems in most cases (ASA, SSA, AAS), demonstrating a good understanding of each case.

Developing

2 Points

Applies the Law of Sines with some errors or inconsistencies in different cases (ASA, SSA, AAS), indicating a developing understanding.

Beginning

1 Points

Struggles to apply the Law of Sines in different cases (ASA, SSA, AAS), demonstrating a limited understanding.

Criterion 2

Problem Set Quality

Completeness and correctness of the problem set, including clear diagrams and solutions.

Exemplary

4 Points

The problem set is complete, well-organized, and contains only correct solutions with clear and accurate diagrams, demonstrating mastery of the concepts.

Proficient

3 Points

The problem set is complete and contains mostly correct solutions with clear diagrams.

Developing

2 Points

The problem set is mostly complete but may contain some errors or missing solutions, and diagrams may lack clarity.

Beginning

1 Points

The problem set is incomplete, contains significant errors, or lacks clear diagrams and solutions.

Category 4

Game Design

Evaluates the overall design and effectiveness of the Law of Sines board game.

Criterion 1

Game Concept Creativity

Creativity and originality of the game concept and mechanics in incorporating the Law of Sines.

Exemplary

4 Points

The game concept is exceptionally creative and original, demonstrating an innovative approach to incorporating the Law of Sines into the game mechanics.

Proficient

3 Points

The game concept is creative and effectively incorporates the Law of Sines into the game mechanics.

Developing

2 Points

The game concept shows some creativity in incorporating the Law of Sines, but the mechanics may be somewhat generic or underdeveloped.

Beginning

1 Points

The game concept lacks creativity and struggles to effectively incorporate the Law of Sines into the game mechanics.

Criterion 2

Rules and Instructions

Clarity and completeness of the game rules and instructions.

Exemplary

4 Points

The game rules and instructions are exceptionally clear, concise, and comprehensive, making the game easy to understand and play.

Proficient

3 Points

The game rules and instructions are clear, concise, and easy to follow.

Developing

2 Points

The game rules and instructions are generally understandable but may lack clarity or completeness in some areas.

Beginning

1 Points

The game rules and instructions are difficult to understand due to lack of clarity, completeness, or organization.

Criterion 3

Law of Sines Demonstration

Effectiveness of the game in demonstrating the Law of Sines and its applications.

Exemplary

4 Points

The game effectively and engagingly demonstrates the Law of Sines and its applications, providing a deep and memorable learning experience.

Proficient

3 Points

The game effectively demonstrates the Law of Sines and its applications.

Developing

2 Points

The game demonstrates the Law of Sines and its applications to some extent, but the connection may not be fully clear or engaging.

Beginning

1 Points

The game struggles to effectively demonstrate the Law of Sines and its applications.

Reflection Prompts

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

Question 1

How effectively do you think your board game demonstrates the application of the Law of Sines in real-world scenarios?

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Question 2

What was the most challenging aspect of designing a board game that accurately incorporates the Law of Sines, and how did you overcome it?

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Question 3

In what ways did your understanding of the Law of Sines and its applications change or deepen during the game design process?

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Question 4

If you were to redesign your board game, what specific improvements or modifications would you make to better illustrate the Law of Sines or enhance the gameplay experience?

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Question 5

Which of the real-world applications of the Law of Sines did you find most interesting or relevant, and how did you incorporate it into your game?

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