Open to all Middle and High School Classes

Division I – 6^th – 8^th grade

Division II – 9^th – 12^th grade

Due: February 15, 2013

Table of Contents

1. The Challenge
2. Range of Activities
3. Process
4. Essential Questions
5. Student Outcomes
6. Evaluation Rubric
7. Curricular Goals

The Challenge

Imagine that you work in the mathematics department for a multi-media education company that creates textbooks and videos for middle schoolers. The editor in charge of mathematics publications has evidence that middle school kids just don’t care about the Pythagorean Theorem. She has an idea: sell the Pythagorean Theorem to the students! And the best way to sell something is to create a commercial. So, as part of the multi-media package your editor wants to deliver to middle schools across America, there will be a Pythagorean Theorem commercial. The job has fallen to your team to create this commercial.

The objective: to convince middle schoolers both why the Pythagorean Theorem is important, and why it is relevant to their lives. For high schoolers, you have the additional task of choosing a proof and then defending the choice about why your particular proof is the most appealing.

• Middle school groups: You are NOT required to explain any proofs. Instead, please focus on why the Pythagorean Theorem is relevant to middle school students.
  • Consider these questions: What do you want your audience to be aware of at the end of your commercial? Do you want to inspire excitement and interest in learning about the Theorem or do you want to inform your viewers about something they may not have thought about before?
    • Whatever goal you choose will set the tone for your commercial.
• High school groups: Please focus on why the Pythagorean Theorem is relevant to middle school students. In addition, you will focus on explaining a proof of the theorem.
  • Research the Pythagorean Theorem, some of its proofs, and how these proofs were discovered.
  • You can begin with the following 2 proofs, but are in no way limited to only these two:
    • Algebraic proof: http://www.mathsisfun.com/geometry/pythagorean-theorem-proof.html
    • Proof by rearrangement: http://cage.ugent.be/~hs/pythagoras/index.html
    • Choose either one of the above proofs or another one your group has found (the one you think is the best/clearest/easiest to understand etc.)
• Create a commercial between 1 and 2 minutes long explaining the Pythagorean Theorem, its relevance, and, for high school students, your chosen proof and why you recommend using it to market to middle school students.
  • The format of the commercial is up to the group.
  • Keep your audience in mind.
    • Middle school groups: Your job is to make this commercial clear and engaging for your peers.
    • High school groups: Your job is to make this commercial clear and engaging for a group of students younger than you.
• Optional (teachers decide whether to include this): Write a two to three page paper Theorem Support Paper that contains the following:
  • A brief description of the meaning and significance of the Theorem;
  • A brief but thorough presentation of the proof (for high schoolers);
  • A description of the rationale for the creative approach taken in the commercial;
  • A statement outlining the intended effect on the target audience; and
  • A citation page that references all relevant sources used in the development and production of the commercial.

Deliverables include:

• Final verbatim script
• Interview video (this is the only Meridian Stories deliverable)
• Theorem Support Paper, as determined by the teacher

Range of Activities

• Research and analysis of the Pythagorean Theorem
• Investigation of multiple geometric proofs
• Creative brainstorming about compelling ways to communicate the mathematical content in a persuasive way.
• Script writing
• Video  – Pre-production, Production, Post-production
  • Directing, Casting, Rehearsing, Video Editing, Audio Editing

Process

During Phase One, student teams will:

• Research the Pythagorean Theorem, using a variety of sources, keeping track of all the sources used for your Theorem Support Paper. Focus on the following:
  • Its history, meaning and significance
  • Its relevance to our everyday lives
    • Create an outline of the important points that you want to communicate in your commercial
• High School: Its proofs and how these proofs were discovered.
  • Look at the 2 proofs mentioned in the description for a good place to start, but also search for other proofs.
  • Choose one proof that your group will focus on marketing to your target audience (middle school students). Begin developing an argument in favor of your proof.

Meridian Stories provides two forms of support for the student teams. Media Innovators and Artists – This is a series of three to four minute videos featuring artists and innovative professionals who offer important advice, specifically for Meridian Stories, in the areas of creativity and production. Meridian Tips – These are short documents that offer student teams a few key tips in the areas of creativity and production. Recommended review, as a team, for this Challenge include:
Media Innovators and Artists	Meridian Tips
On Mathematics in Everyday Life – Eric Gaze On Film Producing – Tom Pierce On Directing Comedy – Davis Robinson On Movement and Rhythm in Video – Charlotte Griffin	Creative Brainstorming Techniques Creating a Commercial Producing: Tips for the Shoot Creating Storyboards, Framing a Shot

During Phase Two, student teams will:

• Continue developing an argument as to both the importance of the Pythagorean Theorem and the appeal of your particular proof over others. This is the basis of your script.
  • Be sure to include an explanation of your chosen proof.
  • Once you are clear on the content of the commercial, brainstorm and articulate your creative approach to communicating that information, keeping in mind the target audience.
    • Consider watching a variety of existing TV commercials to help your team decide on an approach.
    • Create a script and storyboard for the commercial.
      • We recommend that at least two drafts of the script and storyboard should be created, with teacher review occurring in between each draft.
      • Begin pre-production. This primarily includes casting; choosing the setting/location for any video scenes; choosing the costumes and props for the characters, and planning the logistics for the shoot.
        • Rehearse and block any video scenes in your chosen location(s).

During Phase Three, student teams will:

• Finalize the script for the commercial
• Shoot the commercial
  • Edit the video
  • Post-produce the commercial, adding voice-over, music and sound effects as desired.
  • Complete the Theorem Support Paper, as determined by the teacher.

Essential Questions

1. What is the Pythagorean theorem and how is it used?
   1. How is the theorem relevant/important to students?
   2. How can the Pythagorean Theorem be proved?
      1. What is the easiest and most effective way to explain the theorem concisely?
      2. How can multiple methods all be correct?
      3. How are the methods similar and different?
2. Can you identify correspondences between the different approaches?
3. How does constructing a viable argument enhance your understanding of the topic?
4. How does one organize content in order to present a compelling, convincing and persuasive narrative?
   1. What’s the difference between creating media to communicate and creating media to persuade?
   2. What needs to be done to the content in order to successfully ‘re-package’ it for a niche audience (i.e., middle school students)?
   3. How has immersion in the production of digital media deepened the overall educational experience?
   4. How has working on a team changed the learning experience?

Student Outcomes

1. The student will understand the Pythagorean Theorem, its uses, and where it comes from (i.e. how it can be mathematically proven).
   1. The student will be able to explain the relevance of the Pythagorean Theorem in real life.
   2. The student will gain a deeper understanding of the Pythagorean Theorem through exploring multiple proofs and constructing an argument in favor of one.
      1. The student will become more confident in working through geometric proofs.
      2. The student will be able to appreciate and identify correspondences between different approaches to solving the same problem.
      3. The student will understand the processes involved in researching content from a variety of sources; selecting relevant information from those sources; and organizing this information in a persuasive and cohesive narrative.
         1. The student will understand the difference between creating media to communicate and creating media to persuade.
         2. The student will be more aware of how to target media towards a certain demographic.
         3. The student will know the basic constructs of using video media to effectively sell mathematical content and its application to daily life.
            1. The student will know some of the basic constructs of the commercial video genre.
            2. The student will have an increased awareness of the challenges and rewards of team collaboration.

Evaluation Rubric – Pythagorean Theorem Commercial

CONTENT COMMAND – Clear understanding of the Pythagorean theorem, including its relevance to middle school students and (for high school groups) one of its proofs
Criteria	1-3	4-7	8-10
Meaning and Significance	The communication of the theorem’s meaning and significance is not well developed	The communication of the theorem’s meaning and significance is evident, but presented inconsistently	The communication of the theorem’s meaning and significance is presented thoroughly and clearly
Relevance	The communication of the theorem’s relevance is not well developed	The communication of the theorem’s relevance is evident, but presented inconsistently	The communication of the theorem’s relevance is presented thoroughly and clearly
The Proof (High School Only)	The explanation of the proof is lacking or is not well developed	The proof is presented fully, but uncertainly or inconsistently	The proof is presented clearly and compellingly

 

STORYTELLING COMMAND – Effective creative approach to persuade and engage
Criteria	1-3	4-7	8-10
Script	The narrative is hard to follow and/or the scripting is lackluster and ineffective	The narrative is presented clearly, but the scripting is inconsistently engaging	The narrative is presented clearly and the scripting is engaging and effective
Creative Approach	The creative concept does not service the content clearly or appropriately	The content is presented clearly, but the creative approach inconsistently services the content	The content is presented clearly and the creative approach services the content effectively and imaginatively
Persuasion	The commercial does not successfully persuade its target audience	The commercial inconsistently persuades and engaging to its target audience	The commercial is persuasive and thought-provoking to its target audience

MEDIA COMMAND – Effective use of media to communicate content through commercial format
Criteria	1-3	4-7	8-10
Visual Shot Selection	The visual shots do not effectively communicate the content	The visual shots communicate the content fully, but inconsistently	The visual shots effectively and engagingly communicate the content
Editing	The overall editing detracts from the narrative	The piece works, but there are occasional editing distractions	The piece is edited cleanly and the pacing is effective.
Music/Sound/Voice	The selective use of music, sound, and voice detracts from the narrative	The selective use of music, sound, and voice works inconsistently to support the content and enhance the overall viewing experience.	The selective use of music, sound, and voice enhances the content and the overall viewing experience

21ST CENTURY SKILLS COMMAND (for teachers only) – Effective use of collaborative thinking, creativity and innovation, and initiative and self-direction to create and produce the final project
Criteria	1-3	4-7	8-10
Collaborative Thinking	The group did not work together effectively and/or did not share the work equally	The group worked together effectively and had no major issues	The group demonstrated flexibility in making compromises and valued the contributions of each group member
Creativity and Innovation	The group did not make a solid effort to create anything new or innovative	The group was able to brainstorm new and inventive ideas, but was inconsistent in their realistic evaluation and implementation of those ideas.	The group brainstormed many inventive ideas and was able to evaluate, refine and implement them effectively
Initiative and Self-Direction	The group was unable to set attainable goals, work independently and manage their time effectively.	The group required some additional help, but was able to complete the project on time with few problems	The group set attainable goals, worked independently and managed their time effectively, demonstrating a disciplined commitment to the project

Curricular Goals

The Pythagorean Theorem Commercial Challenge addresses a range of curricular objectives that have been articulated by the new Common Core Curricular Standards – Mathematics.

Below please find the standards that are addressed, either wholly or in part.

Common Core Curricular Standards – Mathematics

Overall Standards for Mathematical Practice

• Make sense of problems and persevere in solving them.
  • They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
  • Construct viable arguments and critique the reasoning of others.

Grade 8

• Geometry (8.G)
  • Understand and apply the Pythagorean Theorem
    • Explain a proof of the Pythagorean Theorem

High School – Geometry

• Congruence (G-CO)
  • Prove geometric theorems
    • Prove theorems about triangles.
• Similarity, Right Triangles, and Trigonometry (G-SRT)
  • Prove theorems involving similarity
    • Prove theorems about triangles. Theorems include: the Pythagorean Theorem proved using triangle similarity
• Expressing Geometry Properties with Equations (G-GPE)
  • Use coordinates to prove simple geometric theorems algebraically