Mathematics Challenge #4 Circular Story Storyboard

Open to all Middle and High School Classes

Division I – 6th – 8th grade

Division II – 9th – 12th grade

Due: April 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

This Challenge comes in two parts and the first part begins with a mathematical problem. You need to find the area of a ring – shape (the section shaded orange in the picture below). The only measurement given is the length of a chord of the outer circle that is tangent to the inner circle (100 units). See the picture below:

You can make the assumption that it is indeed solvable with only the one measurement. (Hint: If things aren’t specified, they don’t matter. So, the problem does not depend on the size of the circles, i.e. the radii of the circles.)

  • Teachers: There is an unconventional way of solving this, if you would like to give your students more of a challenge. See “Solution” at the very end of Challenge, after the Curricular Goals section.

Once your team has come up with a solution to this problem, the second part of the Challenge begins. Create a story, including characters, setting, and plot, that is centered on characters confronting and then solving the problem given above. You will present this story in a fully scored, storyboard form. This means that the storyboard presentation needs to be shot and edited together to music and/or sound effects. The teams can choose whether or not it is effective to also narrate the storyboard, or leave it up to the viewer to read it.

  • Example of a story: There is a circular lake with a circular island in the middle of it. You are a villain and want to poison the water, but you must know the area of the lake in order to determine the amount of poison to inject into the water.

Create a 10-15 frame storyboard of your story including an explanation of and solution to the problem. Your team must:

  • Include the definition of a chord somewhere in the story.
  • Clearly convey how you solved the problem with a visual representation.

You can use 10-15 seconds of animation using the program Scratch (download for free at http://scratch.mit.edu/) or any other animation software.

The medium for the imagery (paint, crayons, photos etc.) is completely up to your group.

Deliverables include:

  • The fully scored, digital storyboard with full text (this is the only Meridian Stories deliverable)
  • Script, if the text is not presented visually in the storyboard
    • A written out solution to the problem.

Range of Activities

  • Circle Geometry
  • Multiple Solutions to singular problem
  • Story Development – Teams must develop wholly original narrative
  • Storyboard Creation – A storyboard is ‘picture writing’. Set in a sequence of rectangular shapes, or ‘panels’, a storyboard places actions in a logically sequenced order. Each panel is a place for the writer to put pictures, symbols, or text.

Process

During Phase One, student teams will:

  • Work through and solve the given problem.
    • Pay attention to how your group is able to solve the problem as this process may be incorporated into your story.
  • Begin developing a story based off of this problem. You may want to begin your brainstorming by considering the following questions:
    • What type of story are you interested in creating: a fantasy, mystery, horror story, fable, comedy, science fiction…?
      • Once you decide on the genre, consider where the story is set.
      • What is the actual ring shaped area in question: a floor, a field, a path in the woods, a swimming pool, a ring of Saturn, a very large donut…?
      • Why do we need to know its area? What problem does finding the area solve that could resolve the story?
      • Who is telling this story? Who are the main characters in your story? (Since storyboards don’t allow room for much character development, we recommend focusing on just two or three characters, and trying to give them a ‘voice’ in the limited textual space that you have.)
Meridian Storiesprovides two forms of support for the student teams.

  1. 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.
  2. 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 GazeOn Character Design – Scott Nash

On Music in Film – Mary Hunter

On Fiction Writing – Lily King

 “Creative Brainstorming Techniques”“Royalty Free Music”

“Three Free Rendering and Animation Programs: Scratch, Geogebra And Sketch Up”

“Creating Storyboards, Framing a Shot”

During Phase Two, student teams will:

  • Finalize the outline of the story and submit to teacher for comments and direction (at teacher’s discretion).
  • Finalize the story.
  • Begin storyboarding the story. This involves creating a frame for each moment or scene shift in the story.
    • Create between 10-15 frames.
    • In each frame, break down the story into its component parts, including action, characters and setting.
      • The text of the story can be included underneath, inside of or to the side of the picture. The scripting can also be recorded as voice-over.
      • The panels can be created by any visual means desired, including paint, collage, photos, crayons…whatever suits the team best.
      • Determine whether your group wants to use a short animation clip.
      • Review your storyboard with your teachers for comments and direction (at teacher’s discretion).
      • The storyboard must include the definition of a chord and a visual representation of how the problem is solved.
      • Begin discussing the production elements of the storyboard presentation. What is the mood of the story? What kind of music will support that mood? Is there a place for sound effects? Should this be narrated or simply read by the viewer?

During Phase Three, student teams will:

  • Complete the storyboard panels.
    • Create the animation clip using Scratch, if desired.
    • Shoot the storyboard.
    • Edit the storyboard to your soundtrack.
    • Record voice-overs if necessary and mix into the presentation.
    • Complete the written out solution to the problem.

Essential Questions

  1. How can you calculate a ring-shaped area given only the length of a chord tangent to its inner wall?
    1. What is a chord?
    2. Why is the size of the circle irrelevant?
    3. How can you solve a problem by approaching it from multiple angles?
    4. How does creating a narrative for the problem affect your understanding of the problem and solution?
      1. How does creating a visual representation of solving the problem make the solution clearer and easier to comprehend?
      2. How has immersion in the production of digital media deepened the overall educational experience?
        1. How do multiple elements of storytelling (character, setting, point of view, language) work together to deliver a complete story?
        2. How has working on a team changed the learning experience?

Student Outcomes

  1. The student will become more comfortable working with various aspects of circle geometry (i.e. a chord).
    1. The student will understand that, in this problem, the sizes of the circles are irrelevant to the area of the ring.
    2. The student will be able to approach a problem from multiple angles in order to solve it.
    3. The student will understand the power of narrative to communicate effectively and to see a concept in a new way.
    4. The student will know the basic constructs of using media to effectively communicate content, character and a story.
    5. The student will have an increased awareness of the challenges and rewards of team collaboration.

Evaluation Rubric – Circular Story Storyboard

CONTENT COMMAND – Clear understanding of the solution to the given problem.
Criteria 1-3 4-7 8-10
Definition of a chord The definition of a chord is not present in the storyboard or is presented unclearly The definition of a chord is present, but is presented uncertainly The definition of a chord is presented clearly and fully
Solution to the problem The solution to the problem is either incorrect or not clearly communicated. It is unclear that the students understand how to solve this problem. The solution to the problem is correct, but presented uncertainly. The students appear to have a basic understanding of how to solve the problem. The solution to the problem is correct and presented clearly. The students have a clear understanding of how to solve the problem.
STORYTELLING COMMAND – Effective use of narrative elements to communicate content and story
Criteria 1-3 4-7 8-10
Story/Plot The narrative is hard to follow or does not address the given problem The narrative is presented clearly, but the dramatic interpretation of the problem is inconsistently engaging The narrative is presented clearly and dramatically and the problem is well incorporated
Script The script facilitates the narrative The script is functional, and at times, engaging The script is inventive, thoughtful and engaging, and reveals a command of language
Narrative Elements The choices made in terms of character, setting, point of view, tone, and/or genre do not successfully communicate the narrative. The choices made in terms of character, setting, point of view, tone, and/or genre are generally interesting and thoughtful The choices made in terms of character, setting, point of view, tone, and/or genre are coherent, compelling and effective in communicating the narrative
MEDIA COMMAND – Effective use of visual and audio storyboarding elements to communicate narrative
Criteria 1-3 4-7 8-10
The Visual Choices (including visual medium, panel arrangements, style, and animation clips (if used)) The visual choices are not well conceived and detract from our enjoyment of the story The visual choices are solid, cohesive and service the story The visual choices are cohesive, arresting and bring the story to life
The Audio Choices (including music, sound and/or voice) The selective use of music, sound, and/or voice detracts from the overall story The selective use of music, sound, and/or voice supports the atmosphere of the overall story The selective use of music, sound, and/or voice creates an atmosphere that enhances and enriches the overall story
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 Circular Story Storyboard 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.
  • Model with mathematics.

Grade 6

  • Geometry (6.G)
    • Solve real-life and mathematical problems involving area, surface area, and volume.

Grade 7

  • Geometry (7.G)
    • Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
      • Know the formulas for the area and circumference of a circle and use them to solve problems.

High School – Geometry

  • Circles (G-C)
    • Understand and apply theorems about circles
      • Identify and describe relationships among inscribed angles, radii, and chords.

FOR TEACHERS ONLY

Solution – The problem does not specify the size of either radii, so you can let the inner radius be arbitrarily small.  Have students draw pictures with a fixed chord length of 100 but smaller and smaller inner circles.  As the inner radius vanishes think about what happens to the chord length mentioned in the problem.  Answer:  The inner radius goes to zero and the chord becomes the diameter of the larger circle, meaning the area of the ring becomes the area of a circle with diameter equal to 100.

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