Overview

Title of the Project/Task: Modeling Math Through City Building
Essential Question:
How do we represent scaled models both two dimensionally and three dimensionally?
Overview and Purpose:
For the project students become Urban Planners, not only planning and designing, but also constructing a specified amount of urban space. At the conclusion of the project, students will be able to:
●Articulate their planning and design process and how their constructions relate to past or current NYC urban infrastructure.
●Successfully be able to scale (up and down) between a model and the actual size of structures.
●Reflect on the collaborative nature of the project and a discussion of personal strengths and areas for growth.
In U.S. History class, students will be learning about NYC landmarks and how they represent either urbanization and/or the immigrant experience from the late 19th century - early 20th century.
In Math class, the focus is primarily on ratio, proportion, and scaling but can be adapted as need be to accommodate ongoing project design and/or construction elements.
The project should last approximately 6 weeks. The project, if taught in an interdisciplinary way, can be done with 2 classes (approximately 40-45 students).
The Mathematics and United States History classes meet for a combined 8 hours/week. Both math classes will combine to create one large representation.
The culminating project will be a permanent museum-like display in the school with the title card of the project description and links to an audio explanation of both the design and construction process, as well as a student reflection.
Standards (including technical standards):
  1. CCMS
  2. Model with mathematics
  3. Reason abstractly and quantitatively
  4. Make sense of problems and persevere in solving them
Twenty-first Century Skills:
●Collaboration
●Problem Solving
●Verbal Communication
Key Activities That Develop 21st Century Skills:
Entry Activity:What’s My Proportion?
In pairs, students will collaborate to create scaled representations of their bodies using proportional reasoning.
Activity #1: Exploring Building Design
Students will critique landmark buildings to establish criteria for what makes a good building and utilize their analysis to create a “Mood Board” to inspire their own designs
Activity #2: Material Exploration & Prototyping
Students will utilize project materials to create a prototype for a three-dimensional building model.
Activity #3: Building Concept & Elevation Drawing
Students will create an elevation drawing of a building to learn representational drawing and labeling techniques.
Activity #4: Building Construction
Students will create three-dimensional models of buildings from their elevation drawings.
Feedback:
Students will receive feedback from their peers as they work in groups as well as written feedback from the Beam Center instructor on their 2D design.
About Our School:
The mission of The Brooklyn International High School is to help English Language Learners (ELLs) to develop their language, intellectual, cultural, and collaborative abilities so that they may become active participants in today’s interdependent world. We strive to help every student reach his or her potential by fostering academic growth, personal growth, and tolerance.
Credits:
Jason Fleischauer
Supported by Educurious

Lessons/Steps/Activities

Entry Activity: What’s My Proportion?

Student Directions / Teacher Notes
Question students are answering:
How do you create an accurately scaled representation by using proportions?
Skills and Knowledge:
●Measuring with accuracy
●Solving proportions
●Distinction between a ratio and a proportion
●Awareness that cross products are equal in a proportion
21st Century Skills:
●Breaks goals into actionable steps
●Collaboration
●Manages time to complete tasks on schedule
Task Introduction (for Student):
Today you will work with a partner to create a similar figure half the size of your body or your partner’s.
Goals/Outcomes (21st century skills):
●Students will be able to produce two-dimensional representational figures through collaboration.
Feedback and Evidence (for Student):
Your final product will be a life-size cutout of either you or your partner’s body and a scaled representation that is half the size of the original figure. You will receive feedback from your partner and the teacher on the accuracy of your calculations as well as the quality of the scaled figure. You will determine if your proportions are correct and evaluate your final products using the project rubric.
Resources You Will Need:
●“What’s My Proportion?” Activity Guide
●Large Paper
●Drawing and Measuring Tool
What to Do:
  1. Instructor reviews activity guide, “What’s My Proportion?” and determines student pairings.
  2. Students trace and cut-out one life-size figure and then measure the dimensions of the body parts noted in the activity guide.
  3. Students then calculate the measurements for the scaled figure and verify their results using the given proportions.
  4. Student pairs then use the scaled measurements to create a smaller figure to complement the life-size figure.
. / A scale of measurement should be chosen applicable to the larger scale project. The included materials for this activity are asking students to measure in inches.
Students should be paired in such a way so that one student would be comfortable having their body traced by the other student.
The life-size representation and the scaled figure should be on different colored paper so that they are easily comparable.

Activity #1: Exploring Building Design

Student Directions / Teacher Notes
Question students are answering:
What makes a good building?
Skills and Knowledge:
●Making observations
●Synthesizing ideas
●Identifying engineering principles in building construction
21 st Century Skills:
●Breaks goals into actionable steps
●Collaboration
●Manages time to complete tasks on schedule
●Monitors progress and own performance, adjusting approach as necessary
Task Introduction (for Student):
In this lesson, you will create a building in a small group, view examples of famous buildings in New York City, and then using your observations, create a set of criteria for evaluating buildings. Your criteria will then be used to help you create your personal “mood board” which you will use as inspiration to help you design the buildings for your site plan.
Goals/Outcomes (21st century skills):
Students will collaborate to construct a free-form building to establish criteria that they will use as a benchmark to evaluate other structures and assist them in the design and construction of their own buildings.
Feedback and Evidence (for Student):
Feedback will be provided by group members and peers on the quality of your building. You will cite examples and observations to justify the criteria you have determined is most significant in evaluating the quality of a building.
Resources You Will Need:
●Materials for building construction-(newspaper, straws, tape, etc.)
●Images of landmark buildings in New
York City (e.g. Empire State Building)
●“What Makes a Good Building” Graphic Organizer
●Materials for students to create personal “mood boards”
What to Do:(This provides directions for the activity with links to the resources students will need)
  1. Student groups are given materials and a set amount of time to construct a rudimentary skyscraper. Students are instructed to make the best building possible using the given materials, but no specific criteria is provided in terms of focus (artistry vs.height for example).
  2. Next, students complete the graphic organizer, What Makes a Good Building? to establish a set of criteria with which to evaluate the quality of a structure.
  3. Students will then use the criteria they have determined to evaluate a series of landmark buildings, supplementing their original criteria as needed.
  4. Utilizing their criteria, students create a “mood board” to use as inspiration for their own building designs.
/ The amount of materials could also be limited in addition to the time.
Students may create their “mood boards” electronically, using a variety of mixed media materials, or both.

Activity #2: Material Exploration & Prototyping

Student Directions / Teacher Notes
Question students are answering:
How can our project materials best be utilized to help us construct our buildings?
Skills and Knowledge:
●Constructing a three-dimensional model using new materials
●Applying the design process through testing, experimentation, and prototyping
21 st Century Skills:
●Collaboration
●Monitors progress and own performance
●Adjusting approach as necessary
21st Century Skills:
●Collaboration
●Planning for Success
●Verbal Communication
Task Introduction (for Student:)
In this lesson, you will make a prototype of a scale-model building to learn about the materials that you will be using to create the buildings of your own design.
Goals/Outcomes (21st century skills):
●Students will be able to manage time to complete the task on schedule (script).
●Students will organize information that serves the purpose of the message (script).
●Students will ask questions to deepen one’s understanding and uses and adjusts communication as needed (script).
Feedback and Evidence (for Student):
You will reflect on the engineering principles and building design you and your group chose for your prototype as well as the qualities of each construction material used.
Resources You Will Need:
●Building materials (foam core, clay, glue, rubber cement, straight pins, etc.)
● Cameras
What to Do: (This provides directions for the activity with links to the resources students will need)
  1. Students will write a draft of their skit 1. Instructor describes the possible use of each building material for students and models their utilization.
  2. Student groups sketch a concept drawing for a three-dimensional prototype and use the building materials to attempt to construct it.
  3. Student groups photograph their prototype and compose a written reflection about it and its construction which addresses the following questions:
●How effective was your building design and did the
●What are the strengths of your design and
●What did you learn from creating the prototype that materials or construction technique you chose prove to be successful? construction?
●What are the weaknesses?
will help you when you create buildings of your own design? / A variety of materials could be used for construction (modeling clay, self-hardening clay, foam core, wood, etc.)

Activity #3: Elevation Drawings

Student Directions / Teacher Notes
Question students are answering:
What features of a representational drawing of a building help illustrate its scale and dimensions?
Skills and Knowledge:
●Measuring with accuracy
●Calculating scale and unit conversions
●Labeling techniques
●Using scale factors to magnify or reduce
21st Century Skills:
●Breaks goals into actionable steps
●Manages time to complete tasks on schedule
●Monitors progress and own performance, adjusting approach as necessary
Task Introduction (for Student):
In this lesson, you will create an elevation drawing of a building to learn representational drawing and labeling techniques. Then, you will use what you have learned to create elevation drawings for buildings of your own design.
Goals/Outcomes (21st century skills):
●Students will create representational drawings reflecting their understanding of scale and dimension.
●Students will monitor their own progress in the creation of their drawings, seeking technical assistance when needed.
Feedback and Evidence (for Student):
Your annotated elevation drawing with a detailed scale and labeled measurements with appropriate units...
Resources You Will Need:
●Drawing Paper
●Drawing and Measurement Tools
What to Do:
  1. Instructor models the creation of an elevation drawing using a predetermined standard scale. Students replicate the drawing in real-time using drawing and measurement tools.
  2. Students compare model drawings and offer support or critiques as necessary to correct measurement, labeling, or use of appropriate units.
  3. Students use their own building concept drawings and the predetermined standard scale to produce their own elevation drawings. Students receive constructive feedback on their drawings from peers and from instructor.
/ Elevation drawings are essentially blueprints with the width and height of a building labeled in units, with views from both the front and the side.
The predetermined scale for my project is 40 ft. = 1 in. to prevent buildings from being over 2 ft. in height.

Activity #4:Building Construction

Student Directions / Teacher Notes
Question students are answering:
How can we create a three-dimensional model of a building that is built to scale?
Skills and Knowledge (including 21st Century Skills):
●Measuring with accuracy
●Constructing a three-dimensional model using new materials
●Utilizing engineering principles in building construction
21 st Century Skills:
●Breaks goals into actionable steps
●Collaboration
●Manages time to complete tasks on schedule
●Monitors progress and own performance, adjusting approach as necessary
Task Introduction (for Student):
Using your completed building elevation drawings, you will use the project materials to construct
three-dimensional models of your designs.
Goals/Outcomes (21st century skills):
●Students will collaborate to produce a three-dimensional representation of their two-dimensional elevation drawings.
Feedback and Evidence (for Student):
Your completed and annotated elevation drawings will be compared with your constructed three-dimensional model for accuracy in measurement, scale, and representation.
Resources You Will Need:
●Building materials (foam core, clay, glue,
rubber cement, straight pins, etc.)
●Completed elevation drawings
What to Do:
  1. Instructor consults with each student or student group reviewing both elevation drawings and reflections on prototype construction related to project materials.
  2. Working from their elevation drawings, students use project materials to construct their three-dimensional representations, referencing their annotated drawings to ensure accuracy in addition to real-time measuring of their three-dimensional model.
/ These could provide directions for teachers, educative features(e.g. background on the topic, additional resources), alternatives for differentiation, etc.

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