City Transportation

By Michael Rust • Pam Heckel •

Grade Level	10th-11th
Subject Area	Algebra 2 (Integrated Math)
Duration	5 class periods (5 hours)
Setting	Standard Classroom
Background Knowledge	Students should be familiar with network diagrams, distance formula, equation modeling, and graphical representations of data. An understanding of the geometric properties of circles is also important, more information on this can be found in the reflections section. Familiarity with presentation software such as Power Point is also useful, but not critical.
Author	Michael Rust & Pam Heckel

Summary
Students are given a topographic grid map of a city with coordinates for the various zones (residential, industrial, etc.). The students must design a transportation system to connect the zones according to a network diagram that tells which zones need to be directly or indirectly connected. They can choose from several different transportation modalities (roads, light rail, subway) which have different cost restraints as well as approval ratings from the constituents of the various zones. After selecting their design, the students give a presentation to the class in the form of a contract bid. The class then votes for the best design. The teaching philosophy for this lesson is cooperative learning and team-based design. The students work in groups of 3 for this lesson and turn in one set of materials for the group. Since many engineering applications involve teams of engineers working together, it is important to give students experience with this work style. We have also included a seminar discussion for this lesson. At Shroder-Paideia Academy, students participate in seminars for one hour on Monday and Tuesday mornings. On Monday, a topic is presented and information given to students. Each week, a different topic of controversial nature is chosen so students will be able to take a particular stance based on the information given. For this lesson, we incorporated a seminar discussion on city planning.

Objectives
Students will be able to: 1. Apply concepts they learned in Algebra 2 a. Distance equation b. Network diagrams c. Equation modeling (change words into equations) d. Properties of geometric shapes i. Chords ii. Circumference iii. Diameter 2. Identify components of a city transportation system 3. Analyze a problem situation and choose an appropriate solution 4. Present a solution with oral and written communication

Materials Required
Attached worksheets, access to computers, presentation software, projection equipment.

Ohio Standards

Mathematics

Grades 8-10

Measurement
C. Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangles, quadrilaterals and composite shapes, and to find volume of prisms, cylinders, and pyramids.

Geometry and Spatial Sense
D. Use coordinate geometry to represent and examine the properties of geometric figures.

Patterns, Functions and Algebra
C. Translate information from one representation (words, table, graph or equation) to another representation of a relation or function

Mathematical Processes
B. Apply mathematical knowledge and skills routinely in other content areas and practical situations.
E. Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas.
G. Write clearly and coherently about mathematical thinking and ideas.

Data Analysis and Probability
F. Construct convincing arguments based on analysis of data and interpretation of graphs

Technology

Grade 11

5.B.4 – analyze information and synthesize into a communicated product
6.A.3 – interpret plans, diagrams, and working drawings in the construction of a prototype
6.A.8 – explain and demonstrate how constraints influence the solution of problems
6.B.1 – evaluate a design completed or created by another group of students using established design principles