High Tech High - Project Based Learning

Overview

The goal of the Urban Art Project is to help students promote their artistic and academic work to a diverse audience by displaying public artwork. The Public Art Program for the Port of San Diego was willing to partner for this particular example where the students made Urban Trees. Please visit www.portofsandiego.org for more information.

The essential question for this project is, "Do math and science influence artistic expression?" Most students would agree that it is important for them to express themselves in one way or another. When looking at an art piece wrapped in subjectivity, students rarely see the structure of objectivity provided by math & physics.

Products (Scope of Work, Deliverables, Requirements)

Scope of Work

One team (two students) out of 24 teams will be selected by the Urban Tree Committee to potentially create a FULL SCALE art piece from their model design. The following materials & tools will be provided to create a model:

One (1) 5/16" x 12" Dowel for the Trunk
One Hundred Eighty (180) 2MM x 1" Bamboo Skewer Sections for the Branches
2.75"/2" High Standard Terra Cotta Pot for the Base
Box Cutters
Glue Gun with Glue Sticks

Deliverables

3-D Model - Students will be creating a 3-D model (1 inch = 1 foot) of their proposed "Urban Tree" design and attach it to a 12"W x 12"L x "H square mounting board
Labeling - A single page with Tree Name, Team Names, and explanation of the concept (artistic description, math/physics principles covered), including an asking price (if artwork were available for purchase).
Instructions - Step by step instructions on how to build the tree with the proposed FULL SCALE materials. The Overall Dimensions, Wind Load Calculations (See Below), and proposed Bill of Materials (BOM) should also be covered.

Requirements

The Urban Tree can be tall and cylindrical in shape, wide with a canopy on top - or a combination of both! A minimum of 7' clearance must be maintained for pedestrians to walk underneath the tree wherever it extends beyond the width of the 4' base. On campus engineers will review the design for safety and recommend modifications to students if necessary.

"Urban Tree" art may take many forms. To remain stable in windy conditions, the projected area of the artwork must be limited. Projected areas for several tree art types are shown on www.portofsandiego.org.

Additional Project Requirements Created by the Teacher:

ALL branches must form triangles with a few exceptions (i.e. Orthogonal pieces and polygon voids)
No other material is allowed unless given permission.
Painting the pieces is also an option and recommended, but should be detailed in the Bill of Materials (BOM)

Wind Load Calculations

Learning Goals

The following Math & Physics concepts will be covered to allow the students to give shape and meaning to their design ideas.

Math
- Trigonometry
- Pythagorean Theorem
- Special Triangles
- Similar and Congruent Triangles
- Equilateral & Isosceles Triangles
- Surface Area and Perimeter of Polygons
- Volume of Prisms
Physics
- Newton's Laws (Statics and Dynamics)
- Forces and Loads for Different Shapes (Arch, Square, Triangle)
- Vectors

Most of these concepts will be "applied" by the students. Students are usually surprised during execution about how many skills are involved when physically planning and creating a model

Standards Addressed in Urban Art Project

California Content Standards, Geometry:

5.0: Students prove that triangles ar congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.
8.0: Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
9.0: Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.
10.0: Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
14.0: Students prove the Pythagorean theorem.
15.0: Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
19.0: Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
20.0: Students know and are able to use angle and side relationships in problems with special right triangles, such as 30*, 60*, and 90* triangles and 45*, 45*, and 90* triangles.

California Content Standards, Physics:

1c. Students know how to apply the law F=ma to solve one-dimensional motion problems that involve constant forces (Newton's second law).
1d. Students know that when one object exerts a force on a second object, the second object always exerts a force of equal magnitude and in the opposite direction (Newton's third law).
1j. Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components.
1k. Students know how to solve two-dimensional problems involving balanced forces (statics).