Open to all Middle and High School Classes

Division I – 6^th – 8^th grade

Division II – 9^th – 12^th grade

Due: January 25, 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 a game show that poses a question to two experts. Each expert gives a different answer and rationale for their answer. The contestant in this game show must decide who is telling the truth and who is bluffing.

Here’s an example: A biologist has put a single bacterium in a jar with unlimited nutrients at 11:00 pm. The bacteria double every minute. The jar is exactly full at midnight (an hour later). At what time was the jar half full?

• A) 11:30 pm
• B) 11:45 pm
• C) 11:59 pm

Only one of the above answers is correct (C).

In this Challenge, create a video (about 3 minutes, no more than 4) that presents a game show that answers this question on exponential growth as well as several more, which the group will create.

• For Division I schools: Please create two additional questions (also related to exponential growth in a way that expands our understanding of the concept) with three possible answers. This question does not need to be related to bacteria.
• For Division II schools: Please create three additional questions (also related to exponential growth in ways that expand our understanding of the concept), each with three possible answers. At least one of the new questions must deal directly with the visualizationof exponential growth. When presenting this question, the group must display a visual representation. These questions do not need to be related to bacteria.
  • Consider using volume as a guiding concept in addition to simply using amount. For instance, if we assume that each bacterium looks like a microscopic cube that is 10^-7 meters (one ten-millionth of a meter) on a side, each bacterium has a volume of 10^-7 x 10^-7 x 10^-7 = 10^-21 cubic meters. If you suppose the bacteria are able to continue doubling until 1:00 am, you’ll find that the bacteria now occupy a volume so large that they cover the entire surface of the Earth in a layer more than 6 feet deep! So, how long would it take to cover your school? Your town?

The game show will have two so-called experts. For each question, there are three possible scenarios:

1. One expert is telling the truthful answer, while the other is bluffing;
2. Both experts are bluffing and the third answer is actually the correct answer;
3. Both experts are telling the truth (keep in mind that in mathematics there are often more than one right answer).

All experts must justify (provide rationalizations) why they believe their answer is correct, in an attempt to convince the contestants that they are telling the truth.

• In the end, the real answer needs to be revealed, including a rationalization as to why this answer is correct.

The exact format of the game show is up to the group (is there a contestant guessing or is it the video watchers at home trying to guess? What is the role of the host? Is the tone of the show serious or funny? etc.).

Deliverables include:

• Game show video (this is the only Meridian Stories deliverable)
• Final verbatim script, which includes written explanations of the problems’ answers.

Range of Activities

• Investigation of the properties of exponential growth and the various applications of this concept in life
• Creative Brainstorming about compelling ways to communicate the content inside of a specific TV genre – the game show
• Script writing
• Video  – Pre-production, Production, Post-production
  • Directing, Casting, Rehearsing, Video Editing, Audio Editing

Process

We recommend that this Meridian Stories Challenge take place inside of a three to four week time frame. The students must work in teams of 3-4. All internal reviews by the teacher are at the discretion of the teacher. Below is a suggested breakdown for the students’ work.

During Phase One, student teams will:

• Work through and solve the given problem.
  • Focus on justifying why your answer is the correct one.
  • Also, come up with (false) explanations for one of the incorrect answers, as if you were trying to convince someone to pick the wrong answer.
  • Do some research and complete a few problems on exponential growth, until the concept is clear to all group members.
    • Be sure to understand why exponential growth applies to the given problem.
    • Using the given problem as an example, begin to develop your own problem(s) with 3 potential answers each.
      • Middle School Groups: Create 2 additional problems.
      • High School Groups: Create 3 additional problems. One must deal directly with visualization of exponential growth. Consider using volume as a guiding concept.

Meridian Storiesprovides 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 GazeOn Directing Comedy – Davis Robinson On Acting – Abbie Killeen On Editing – Tom Pierce	“Creative Brainstorming Techniques”“Producing: Tips for the Shoot” “Producing: Time Management” “Three Free Rendering and Animation Programs: Scratch, Geogebra and Sketch Up”

 

During Phase Two, student teams will:

• Complete development and scripting of additional exponential growth problem(s) and answers.
• Brainstorm about the exact format of the game show.
  • Is there a host?
  • Are the ‘experts’ supposed to be ‘math experts’ or celebrities? Or someone else?
  • How do you visualize this playing out? Against what kind of setting – some thing colorful and playful, or academic?
  • What is the tone of this video? Is it comic or serious?
  • Is there, perhaps, another context for these questions – as if this game show were a part of a larger narrative and the correct answers to these questions could mean the difference between…? You decide.
  • Once you have mapped out the general format for the presentation of the content, begin pre-production. This primarily includes casting the roles of the experts and possibly the host; choosing the setting/location for the game show; choosing the costumes and props for the characters; and planning the logistics for the shoot.
  • Rehearse and block the game show in your chosen location.

During Phase Three, student teams will:

• Finalize the script for the game show. The running time should be approximately 3 minutes (no more than 4 minutes).
  • Shoot the game show video.
  • Edit the video.
  • Post-produce the video, adding music, sound effects, etc. as desired.

Essential Questions

1. Why is an exponential model appropriate for bacteria growth?
   1. How does the concept of doubling relate to exponential growth, which is defined as a constant rate of growth per unit of time change?
   2. Why does using an exponential growth model work in numerous different situations/problems?
      1. How can you recognize a situation in which exponential growth is appropriate to use?
      2. How does doubling, related to exponential growth, always result in astronomically large numbers no matter what the starting number or the period of change is?
         1. How fast does it grow?
         2. How can creating a visual representation enhance your understanding of the explosive growth of the exponential function?
            1. How does the need to justify an answer enhance your understanding of the concept?
            2. What are the challenges of creating an educational as well as an entertaining video program?
            3. How has working on a team changed the learning experience?

Student Outcomes

1. The student will understand the definition of exponential growth as multiplying by a constant growth factor per unit of time change.
   1. The student will understand doubling as a specific instance of exponential growth.
   2. The student will be able to identify situations that can be modeled by exponential growth.
   3. The student will understand the explosive growth nature of the exponential function regardless of starting conditions.
   4. The student will gain a deeper understanding of exponential growth through constructing visual representations and creating viable rationales.
   5. The student will have explored the often-conflicting relationship between education and entertainment, and the spaces where the two can co-exist.
      1. The student will know the basic constructs of creating a game show program.
      2. The student will have an increased awareness of the challenges and rewards of team collaboration.

Evaluation Rubric – Exponential Growth Game Show

CONTENT COMMAND – Clear understanding of exponential growth (its definition, modeling applications, and explosive nature) as demonstrated through question answers, question development, and answer justifications.
Criteria	1-3	4-7	8-10
Correct Answers	The correct answers are either inaccurate or not clearly communicated.  It is unclear that the students understand exponential growth	The correct answers are accurate, but not presented fully. The students seem to have a basic understanding of exponential growth	The correct answers are accurate and presented fully.  The students have a clear understanding of exponential growth
Question Development	The newly developed question(s) are not clearly related to exponential growth	The newly developed question(s) are related to exponential growth, but don’t add to our understanding of the topic	The newly developed question(s) are directly related to exponential growth, and add to our understanding of the topic
Incorrect Answer Justifications	The incorrect answer(s) and their justifications are not well crafted around the content	The incorrect answer(s) and their justifications are reasonably plausible	The incorrect answer(s) and their justifications are plausible, engaging and thought provoking

STORYTELLING COMMAND – Effective use of character, the game show format, and tone/mood to create an engaging program.
Criteria	1-3	4-7	8-10
Character	The presentation of the experts (and others) as characters is not particularly engaging or suitable	The presentation of the experts (and others) serves the game show effectively	The presentation of the experts (and others) is engaging and entertaining
Tone/Mood	The tone and/or mood of the game show is unclear or detracts from the overall engagement with the game show	The tone and/or mood are interesting choices that at times enhance our engagement with the video	The tone and/or mood are well chosen and enhance our engagement with the video

MEDIA COMMAND – Effective use of media to communicate narrative.
Criteria	1-3	4-7	8-10
Directing/Acting	The directing and acting lack coherence and discipline	The directing and acting are solid, but inconsistently engaging	The directing is clear and coherent and the acting is convincing and believable
Setting/Format	The setting and creative approach to the game show don’t enhance our understanding and enjoyment	The setting and creative approach to the game show are interesting choices, but inconsistently engaging	The setting and creative approach enhance our enjoyment and understanding of the game show
Editing/Music/Sound	The game show feels patched together and the overall editing and use of music/sound detracts from the game show	The game show flows, but there are occasional editing/sound/musical distractions	The game show is edited cleanly and effectively, and the addition of music and/or sound enhance our enjoyment

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 Exponential Growth Game Show 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.
• Reason abstractly and quantitatively.
  • Attend to the meaning of quantities.
  • Construct viable arguments and critique the reasoning of others.
  • Model with mathematics.
  • Look for and make use of structure.
  • Look for and express regularity in repeated reasoning.

High School – Functions

• Linear, Quadratic, and Exponential Models (F-LE)
  • Prove that exponential functions grow by equal factors over equal intervals (F-LE 1.a).
  • Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another (F-LE 1.b).
  • Interpret expressions for functions in terms of the situation they model (F-LE 5).
    • Interpret the parameters in a linear or exponential function in terms of a context.

High School – Modeling

• Formulating tractable models, representing such models, and analyzing them is appropriately a creative process.
  • Example of such situations might include: Modeling savings account balance, bacterial colony growth, or investment growth.
• Models can also shed light on the mathematical structures themselves, for example, as when a model of bacterial growth makes more vivid the explosive growth of the exponential function.