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Created byAngalic Benton
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Calculating TV Sizes: Ratios and Pythagorean Theorem

Grade 12Math2 days
In this project, students explore the mathematical principles behind television screen dimensions, applying ratios and the Pythagorean Theorem to determine optimal TV sizes and aspect ratios for immersive viewing. They investigate the impact of different aspect ratios on the viewing experience, analyzing how these ratios affect the presentation of movies and TV shows. Students evaluate how TV size and aspect ratio influence viewer immersion and satisfaction, incorporating concepts of optimal viewing distance and viewing angles. The project culminates in students demonstrating their understanding through presentations, reports, and essays.
RatiosPythagorean TheoremAspect RatioTV DimensionsViewing ExperienceImmersionOptimal Viewing Distance
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we use mathematical principles like ratios and the Pythagorean Theorem to determine the optimal size and aspect ratio of a television to create the most immersive viewing experience?

Essential Questions

Supporting questions that break down major concepts.
  • How do ratios apply to the dimensions of television screens?
  • How can the Pythagorean Theorem be used to calculate the diagonal size or other dimensions of a television?
  • What is aspect ratio, and how does it affect the viewing experience of movies and TV shows?
  • How do different aspect ratios compare, and why are certain ratios preferred for different types of content?
  • How does the size and aspect ratio of a TV impact the viewer's experience?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Understand and apply ratios to calculate television screen dimensions.
  • Apply the Pythagorean Theorem to determine television screen sizes and dimensions.
  • Investigate and analyze the impact of aspect ratio on the viewing experience of movies and TV shows.
  • Compare and contrast different aspect ratios and their applications.
  • Evaluate how TV size and aspect ratio affect the viewer's overall experience.

Entry Events

Events that will be used to introduce the project to students

Mystery TV Dimensions

A seemingly ordinary TV arrives in class, but its listed dimensions are nonsensical. Students must use their knowledge of ratios, the Pythagorean Theorem, and aspect ratios to determine the actual screen size and solve the mystery of the mislabeled TV.
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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

Immersive Experience Evaluation: TV Size Matters

Students will evaluate how the size and aspect ratio of a TV impact the viewer's overall experience.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Watch the same movie clip on different-sized screens and aspect ratios.
2. Write a reflection on how each setup changed the viewing experience.
3. Consider viewing distance and viewing angles.

Final Product

What students will submit as the final product of the activityA detailed essay discussing how TV size and aspect ratio affect the viewer's immersion and overall satisfaction, incorporating concepts of optimal viewing distance and viewing angles.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Evaluate how TV size and aspect ratio affect the viewer's overall experience.
Activity 2

Ratio Reconnaissance: TV Dimensions

Students begin by exploring how ratios define the relationship between the width and height of a TV screen. This activity reinforces understanding of proportional reasoning and its practical application in determining screen dimensions.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research and define the term 'aspect ratio' and its common representations (e.g., 16:9, 4:3).
2. Measure the width and height of various rectangular objects (books, desks, posters) and calculate their aspect ratios.
3. Apply given aspect ratios (e.g., 16:9) to a specific TV diagonal size to calculate the width and height of the screen using proportional reasoning.

Final Product

What students will submit as the final product of the activityA detailed report explaining aspect ratios, including calculations of TV screen dimensions based on given diagonal sizes and aspect ratios.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Understand and apply ratios to calculate television screen dimensions.
Activity 3

Pythagorean Puzzle: Unveiling Screen Size

This activity focuses on using the Pythagorean Theorem to calculate the diagonal size of a TV screen when the width and height are known, or vice versa. It enhances students' problem-solving skills and reinforces the connection between geometry and real-world applications.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Review the Pythagorean Theorem and its applications in finding missing sides of right triangles.
2. Measure the width and height of a TV screen (or use given dimensions) and apply the Pythagorean Theorem to calculate the diagonal size.
3. Given the diagonal size and either the width or height, rearrange the Pythagorean Theorem to solve for the missing dimension.

Final Product

What students will submit as the final product of the activityA presentation demonstrating the application of the Pythagorean Theorem in determining TV screen sizes, including step-by-step calculations and explanations.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Apply the Pythagorean Theorem to determine television screen sizes and dimensions.
Activity 4

Aspect Ratio Analysis: Movie Night

Students investigate different aspect ratios used in movies and TV shows, analyzing how these ratios affect the viewing experience. They will learn to compare and contrast various aspect ratios, understanding why certain ratios are preferred for different content types.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Watch short clips of movies or TV shows with different aspect ratios (e.g., 2.35:1, 1.85:1, 16:9).
2. Compare the visual presentation of the content in different aspect ratios, noting the presence of black bars (letterboxing or pillarboxing) and their impact on the viewing experience.
3. Research and report on the historical and artistic reasons for using different aspect ratios in filmmaking.

Final Product

What students will submit as the final product of the activityA comparative analysis report of different aspect ratios, detailing their effects on the viewing experience and the reasons behind their use in various media formats.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Investigate and analyze the impact of aspect ratio on the viewing experience of movies and TV shows. & Compare and contrast different aspect ratios and their applications.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

TV Dimensions and Viewing Experience Rubric

Category 1

Mathematical Application

Focuses on the accurate and effective application of ratios and the Pythagorean Theorem in determining TV screen dimensions.
Criterion 1

Ratio Calculations

Accuracy in calculating TV screen dimensions using ratios and proportional reasoning.

Exemplary
4 Points

Calculations are flawless and demonstrate a deep understanding of proportional reasoning. Shows innovative approaches to problem-solving and provides comprehensive justifications.

Proficient
3 Points

Calculations are accurate and demonstrate a thorough understanding of proportional reasoning. Minor errors may be present but do not detract from the overall understanding.

Developing
2 Points

Calculations show an emerging understanding of proportional reasoning but contain some errors. Assistance may be needed to correct mistakes.

Beginning
1 Points

Calculations are inaccurate and demonstrate a limited understanding of proportional reasoning. Significant assistance is required.

Criterion 2

Pythagorean Theorem Application

Correct and effective use of the Pythagorean Theorem to calculate TV screen diagonal size or missing dimensions.

Exemplary
4 Points

Applies the Pythagorean Theorem flawlessly, demonstrating an in-depth understanding of its principles and applications. Explores alternative methods and provides insightful explanations.

Proficient
3 Points

Applies the Pythagorean Theorem accurately with a clear understanding of its use. Minor errors in calculations may be present but are insignificant.

Developing
2 Points

Demonstrates a basic understanding of the Pythagorean Theorem, but application contains errors or requires assistance.

Beginning
1 Points

Struggles to apply the Pythagorean Theorem correctly and requires significant assistance.

Category 2

Aspect Ratio Analysis

Focuses on the student's ability to analyze and compare different aspect ratios and their impact on the viewing experience.
Criterion 1

Comparative Analysis

Detailed comparison of different aspect ratios and their effects on the viewing experience.

Exemplary
4 Points

Provides an exceptionally detailed and insightful comparative analysis of different aspect ratios, demonstrating a nuanced understanding of their effects on the viewing experience. Explores historical and artistic contexts with sophistication.

Proficient
3 Points

Offers a thorough comparative analysis of different aspect ratios, clearly detailing their impact on the viewing experience. Demonstrates a solid understanding of their uses and implications.

Developing
2 Points

Presents a basic comparison of different aspect ratios, but analysis lacks depth and detail. Understanding of their effects on the viewing experience is emerging.

Beginning
1 Points

Struggles to compare different aspect ratios or explain their effects on the viewing experience. Analysis is minimal and lacks clarity.

Criterion 2

Justification of Use

Explanation of the historical and artistic reasons for using different aspect ratios in filmmaking and television.

Exemplary
4 Points

Provides a comprehensive and nuanced explanation of the historical and artistic reasons for using different aspect ratios, demonstrating extensive research and deep understanding.

Proficient
3 Points

Explains the historical and artistic reasons for using different aspect ratios with clear and accurate information.

Developing
2 Points

Provides a limited explanation of the historical and artistic reasons for using different aspect ratios, lacking detail and depth.

Beginning
1 Points

Struggles to explain the historical or artistic reasons for using different aspect ratios. Information is minimal and inaccurate.

Category 3

Overall Impact Evaluation

Focuses on the student's ability to evaluate how TV size and aspect ratio affect the viewer's immersion and overall satisfaction.
Criterion 1

Immersion and Satisfaction

Discussion of how TV size and aspect ratio affect the viewer's immersion and overall satisfaction.

Exemplary
4 Points

Offers a highly insightful and comprehensive discussion of how TV size and aspect ratio significantly impact viewer immersion and satisfaction, incorporating concepts of optimal viewing distance and viewing angles with sophisticated reasoning. Demonstrates leadership in collaborative discussions.

Proficient
3 Points

Discusses how TV size and aspect ratio affect viewer immersion and overall satisfaction, incorporating concepts of optimal viewing distance and viewing angles.

Developing
2 Points

Provides a basic discussion of how TV size and aspect ratio may affect viewer immersion but lacks depth and detail. Mentions viewing distance and angles superficially.

Beginning
1 Points

Struggles to discuss how TV size and aspect ratio affect viewer immersion and satisfaction. Does not address viewing distance or viewing angles.

Criterion 2

Integration of Concepts

Incorporation of optimal viewing distance and viewing angles in evaluating the viewing experience.

Exemplary
4 Points

Seamlessly integrates concepts of optimal viewing distance and viewing angles in the evaluation, demonstrating a sophisticated understanding of their impact on the overall viewing experience. Provides innovative recommendations for enhancing viewer immersion.

Proficient
3 Points

Effectively integrates concepts of optimal viewing distance and viewing angles in the evaluation of the viewing experience.

Developing
2 Points

Partially integrates concepts of optimal viewing distance and viewing angles in the evaluation, but the connection is not fully developed.

Beginning
1 Points

Fails to integrate concepts of optimal viewing distance and viewing angles in the evaluation.

Reflection Prompts

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

How has your understanding of ratios and the Pythagorean Theorem evolved through this project, and how can you apply these concepts in real-life scenarios beyond television screen calculations?

Text
Required
Question 2

To what extent do you believe that the aspect ratio significantly influences your viewing experience?

Scale
Required
Question 3

Which aspect ratio (e.g., 16:9, 2.35:1) do you prefer for watching movies, and why?

Multiple choice
Required
Options
16:9
2.35:1
1.85:1
4:3
Other
Question 4

What challenges did you encounter while applying the Pythagorean Theorem or calculating aspect ratios, and how did you overcome them?

Text
Required