Open to all Middle and High School Classes

Division I – 6^th – 8^th grade

Division II – 9^th – 12^th grade

Due: May 31, 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

Your community has found an empty space that they would like to use “for the benefit of the public good.” They have allocated $15,000 for the project. They have initiated a contest for ideas about the best use the space. The winning idea/design will be implemented using the $15,000 grant. Your Challenge is to ‘win’ this contest by presenting a model of your design to the Community Board using Prezi, PowerPoint and/or video. The presentation must be between 2 and 3 minutes long.

Here’s what you have to do:

• Find an empty space in your community, which, if funding were available, could be utilized to benefit the public good. This can be an interior or exterior space. Take a photograph of the space and include it in your presentation.
  • Research the viability of actually using this space.
  • Is it privately owned so you would have to discuss using it with the owners? Is it town owned?
  • Include a brief explanation of the viability in your presentation.
  • Come up with a plausible idea and create a 2D design/3D model that represents how the idea would be implemented.
    • Middle school groups: Please develop a 2D design of your proposed construction.  For 2D designs, groups have the option of using the computer program Geogebra (free to download at http://www.geogebra.org).
    • High school groups: Please develop a 3D model in addition to a 2D design of your proposed construction. For 3D designs, groups have the option of using the computer program Sketch Up (free to download at http://sketchup.google.com).
    • The Community Board are all mathematically inclined and are interested in proposals that further the designers’ mathematical knowledge by incorporating creative uses of math in the design.
      • Middle School Groups: Consider using unconventional shapes and polyhedrons in your design. How could you incorporate a heptagon instead of a triangle?
      • High School Groups: Consider playing with conic sections by slicing any solid figures you have to create a new design or shape.
      • Be sure your design will adequately fit in the dimensions of the space you’ve selected to use. Be sure to note these constraints somewhere in your project. Be sure to give accurate measurements of lengths, angles, etc.
      • Your design must be detailed and precise. It should include every length measurement, every area calculation, and every volume calculation (if applicable).
        • Also be sure your design will plausibly fit into a budget constraint of $15,000. This will be very flexibly assessed (this is not a budget Challenge). But the design needs to ‘plausibly’ cost that amount.  It is important to note that the $15,000 should not include the cost of acquiring or leasing the public space – it is to be allotted for design purposes only.
        • …And one other thing: scale. Instead of using standard units (feet, inches, etc.), create a new unit related to your project.
          • For example, if you are proposing to build a skate park, your units could be in skateboards.

The final presentation must include:

• A picture of the space and its viability as an actual place of construction;
• Why you believe your idea is useful to the community; will ‘benefit the public’;
• Explanation of your design process;
• Explanation of your new unit; and
• Presentation of the new design/model

Deliverables include:

• The final video/presentation (this is the only Meridian Stories deliverable)
• Paper and/or computer-based design with appropriate, detailed measurements

Range of Activities

• Application of a range of geometric concepts in a real-world situation
• 2D and 3D designing and modeling
• Community research – polling/interviewing
• Organization of data, mathematics and creative development processes into narrative designed to persuade
• Media – Pre-production, Production, Post-production
  • Directing, Image 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 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:

• Scan the community for an empty space. Once one has been chosen, visit the space and take any measurements necessary. Also, take a photograph of the chosen space. Research the viability of actually utilizing the space you have chosen.
  • Your design should fit within the chosen space’s dimensions.
  • Develop an idea for what to build in this space. Remember that the committee is looking to utilize this as a space for the “benefit of the public good.” That is a phrase that it is up to the team to interpret, define and defend.
  • We recommend that your team seek input from the community to understand what others think this means. For example, poll, survey or interview key members in your community. This research could include family members, community leaders, teachers and life long residents.
    • Consider video taping your research efforts: this footage may be useful in your final pitch video.
    • Once an idea is decided on and your basic rationale conceived, we recommend that you present to your teacher for review and comments.
    • Create your new measurement unit, in relation to the proposed construction. Make a note of the scale you are using (with this unit).
    • Gather, organize and analyze your research data. What does it say should be informing your design? What is the community’s understanding of the phrase, ‘for the public good’?
    • Begin drafting a 2D design (groups may choose to use Geogebra) with appropriate and precise measurements of lengths, angles, etc. Use your new unit. Also, try to incorporate creative uses of math in your design.
    • During any and all of the phases above (and below), consider documenting the process and key decisions photographically or with video, as your team may want to incorporate that material in the final presentation.

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 Photography – Michael Kolster On Making Documentaries – Margaret Heffernan On Editing – Tom Pierce On Mathematics in Everyday Life – Eric Gaze	“Royalty Free Music” “Conducting an Interview” “Time Management” “Scratch, Geogebra and Sketch Up”

During Phase Two, student teams will:

• Continue and finish the 2D design of the construction.
• High School Groups: Begin creating the 3D model based off of your 2D design (groups may use Sketch Up).
• Decide on the media format (either Prezi, PowerPoint or video …or other, if your team has discovered other options) for your submission.
• Begin outlining or creating a storyboard for your submission.
  • This presentation is a pitch. Your goal is to beat out the competition and take home the prize. So, in the development of your presentation, consider how you will a) present your design inside of a narrative that is compelling and convincing; b) highlight a unique aspect of your design that distinguishes your design from the others (i.e., your use of creative mathematics might be one distinguishing factor); and c) make a convincing argument for how this will benefit the community.
  • Write the first draft of your script.
  • Identify and gather any missing elements – art, graphics, video, interviews, animation, text – for your presentation.

During Phase Three, student teams will:

• Complete the 3D model of your design (High School)
• Finalize the script and storyboard
• Record the script.
• Produce the final video, Prezi or PowerPoint presentation.

Essential Questions

1. How do various geometric concepts such as lengths, area, surface area, and volume appear in designing a physical construction?
   1. How can you apply geometric methods to satisfy physical constraints?
   2. How did you incorporate creative uses of math into the design?
   3. How did you use expressions and equations to represent constraints or conditions in a real-world problem?
   4. How did you use scale effectively in creating a smaller version of your design?
      1. Why is attention to precision so crucial?
      2. How can new units be created? Is your new unit easier to visualize and work with than a standard unit (feet, inches, etc.)?
      3. How did creating a visual model impact your vision and allow you to alter and improve it?
         1. How do you use/try a variety of tools/methods to make the best possible model?
         2. How will your proposed design add something valuable to your community?
         3. How has working on a team changed the learning experience?

Student Outcomes

1. The student will understand how geometric shapes, concepts, theorems, and equations appear in real-life design.
2. The student will understand the complexities of the design process through an exploration of the relationship between physical constraints, cost constraints, the ideal vision of the team, and the needs of the community.
3. The student will gain an appreciation for the use of scale in creating a model of the final design/construction.
   1. The student will understand the importance of precision in the measurement/design process.
   2. The student will have a better understanding of what a unit is and how it eases visualization on a larger scale.
   3. The student will gain an appreciation of the value of modeling in the design process.
      1. The student will become comfortable with using a variety of tools and methods to create geometric constructions.
      2. The student will gain an understanding of some of the needs and values of their community.
      3. The student will have an increased awareness of the challenges and rewards of team collaboration.

Evaluation Rubric – Geometric Design for a Public Space

CONTENT COMMAND – Clear understanding of the use of math in the design process.
Criteria	1-3	4-7	8-10
Design Feasibility	The group’s idea is not feasible (for budget or space)	The group’s idea is feasible, but stretches the boundaries of realism	The group’s idea is practical and appropriate for the space and budget
Geometric Design (2D for middle and high school, 3D for high school)	The design is imprecise or unclear. There is little or no math evident in the design	The design is clear and the math is evident, but not creative	The design is presented in detail and makes use of creative mathematics
Measurement Unit	The group’s new unit is presented unclearly or does not relate to the design idea	The new unit meets the Challenge criteria, but is inconsistently applied throughout the design	The new unit is inventive, relevant and incorporated well in the design

 

STORYTELLING COMMAND – Effective creative approach to inform, persuade, and engage
Criteria	1-3	4-7	8-10
Community Research	The research from the community is not substantive or presented convincingly	The research from the community is presented adequately	The research from the community is substantive and persuasive
Design Content	The actual design does not effectively or creatively reflect the community’s ‘public good’	The actual design reflects the community’s ‘public good’	The actual design effectively and creatively reflects the community’s ‘public good’
Narrative Clarity and Persuasiveness	The narrative is hard to follow and unpersuasive	The narrative is presented clearly, but the pitch is not persuasive	The narrative is presented clearly and compellingly, and the pitch is persuasive

MEDIA COMMAND – Effective use of media to communicate content.
Criteria	1-3	4-7	8-10
Mixed Visual Media	The use of video, stills, animation, graphics and/or text was often confusing and not well matched to the goals of the pitch	The use of video, stills, animation, graphics and/or text was suitable to the goals of the pitch	The use of video, stills, animation, graphics and/or text was engaging, visually interesting and well matched to the goals of the pitch
Sound Design	The mix of music and sound did not enhance most elements of the pitch	The mix of music and sound serviced the goals of the pitch	The mix of music and sound greatly enhanced the goals of the pitch

 

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 Geometric Design for a Public Space 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.
• Reason abstractly and quantitatively.
  • Attend to the meaning of quantities.
  • Model with mathematics.
    • Use geometry to solve a design problem.
    • Use appropriate tools strategically.
    • Attend to precision.

Grade 6

• Expressions and Equations (6.EE)
  • Reason about and solve one-variable equations and inequalities.
    • Write an inequality of the form x>c or x<c to represent a constraint or condition in a real-world or mathematical problem.

Grade 7

• Geometry (7.G)
  • Draw, construct, and describe geometrical figures and describe the relationships between them.
    • Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
    • Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

High School – Number and Quantity

• Quantities (N-Q)
  • Reason quantitatively and use units to solve problems.
    • Use units as a way to understand problems and to guide the solution of multi-step problems.
    • Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

High School – Algebra

• Creating Equations (A-CED)
  • Create equations that describe numbers or relationships
    • Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

High School – Geometry

• Congruence (G-CO)
  • Make geometric constructions
    • Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)
• Geometric Measurement and Dimension (G-GMD)
  • Visualize relationships between two-dimensional and three-dimensional objects
    • Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
• Modeling with Geometry (G-MG)
  • Apply geometric concepts in modeling situations.
    • Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).