City Plan Catastrophe

By Nicholas Harth • Bethany Vice

Grade Level	10th
Subject Area	Mathematics - Geometry
Duration	1 Full Day used in class (90 minutes) as well as a few days to do some work related to their homes and also used to complete their designs
Background Knowledge	Students coming into this lesson should already be familiar with the various terminology used in labeling angles of parallel lines with transversals. The terms we have focused on are: Complementary Angles Supplementary Angles Vertical Angles Corresponding Angles Alternate Exterior Angles Alternate Interior Angles Consecutive Interior Angles
Author	Nicholas Harth & Bethany Vice

Summary
Students are first asked to think about how things are organized in their bedroom, house, neighborhood, city and are shown how parallelograms and the geometry involved with them are all around us. When extended to the layout of cities and the neighborhoods we live in, it is very apparent that this is also the case by looking at maps. This leads into the exercise the students will be performing, to act as a city roadway engineer in charge of making sure that the design of the streets around the area of the school goes from design plan to construction product. However, in this process there was an error in the angles used and now it is the city roadway engineers’ job to use their knowledge of parallelograms to correct all the angles involved. Next they must prove how they found these values, determine which properties will be affected the most, determine if there are any lot owners that need to be notified about the effect on their property, and propose alternate lots to these owners.

Objectives
1. Student will be able to use their knowledge of angles and apply it to the way the streets around their school are laid out 2. Student will be able to show proof of how they found their answers to the angles. 3. Student will be able to write out the proofs in sentence form in preparation for the OGT. 4. Student will be able to observe how errors in going from a layout to a final construction layout can affect businesses and properties 5. Student will be able to propose solutions to the problems caused by miscalculations and defend their answers. 6. Students will be able to apply this knowledge to the layout of their own bedrooms, homes, and neighborhoods.

Mateirals Required
We used the attached handout (on the website) along with attached overheads for opening discussion. For our particular warm-up exercise we used a blank overhead along with colored clear plastic pieces which the students used to model a bedroom and the way the furniture would be laid out.

Ohio Standards

Mathematics

GEOMETRY: Grades 8-10
• Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines, and parallel lines.
• Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
• Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.

Technology Standards

SCIENCE and TECHNOLOGY: Grade 10
• Synthesize data, analyze trends and draw conclusions regarding the effect of technology on the individual, society and environment (e.g., current and historical time periods).