The following projects were created by UTeach PBI students following content guidelines of either the second or fifth 6th weeks of the Austin Independent School District's scope and sequence for Geometry.

***Syline is the Limit:  The context of this unit takes place in a fictitious town in which the mayor is asking for help developing a skyline in order to make the city more attractive to tourists. Students will develop the required skills to build precise, aesthetic, and geometrically accurate blueprints of four buildings.

***Probability in Games:  In this PBI unit, students will use principles of probability, game theory, and statistics to develop a fair and engaging family/group game for commercial consumption, and build a prototype of their game.

***Build your own cityA geometry project encapsulating:Parallel/Perpendicular Lines, Ratios, Similar Shapes, Surface Area, Volume, 3-Dimensional Shapes.  Students will be given an opportunity to learn about the “big idea” of all the planning and geometry that goes into building a city.

***Molecular Geometry-Impact on Drug Interaction: 

The purpose of the project is for students in these chemistry and geometry classes to explore how molecular geometry influences drug development by exploring and learning certain content in both classes simultaneously. This allows them to draw connections between two very important subjects. The content in geometry includes: solid geometry, nets, surface area, volume, orthographic views, and isometric views. On the other hand, the content in chemistry includes: electron dot structures, the nature of bonding, Valence Shell Electron Pair Repulsion Theory (VSEPR), and molecular shapes. The end product deliverable will require students to build upon and utilize the skills learned from the content mentioned to recreate a drug molecule and present them using knowledge gained. The purpose of this project is to not simply look at molecules or solid shapes and memorize them, but to understand their importance in each content area. This will be presented in hopes that students recall valuable information and understand the material for long term retention.

***City Planning: Over the course of three weeks, students will research, design, and model a new community around their high school given strict geometric restrictions while integrating environmental factors. These factors include resource utilization, population growth, carrying capacity, and other considerations like quality of life.

***  Skyline:  The overall theme of the skyline project is exploring geometric structures and their purpose outside of the mathematics classroom.  Our project is meant for a 8th, 9th, or 10th grade regular or advanced geometry class and is slated to run for 4 weeks, including a field trip, a replication sub-project, an original design project, and final presentations.  The central concepts studied are the types of lines, the properties of these lines, congruence and similarity, dimensionality, scale factor, and the justification of mathematical reasoning.

***  Fair Playing Field: Students will be exploring how to ensure a playing field is regulated by using properties, proofs, and constructions of parallel lines and perpendicular lines. They will also be exploring the concept of congruency of triangles and incorporating this into the area of their sports field for designated 'warm-up' spaces.

***  Bridge Building:  Students will discover the simple mathematical concepts behind building a bridge.  The project begins with research into existing famous bridges and their characteristics, then students will analyze a blueprint of a bridge, taking note of specific line lengths, polygons, and angles.  This will lead the students to design their own blueprint for their bridge design.  Using this blueprint, the students will construct their bridge using given choices of materials.  Testing the weight characteristics of this bridge will lead into the final stage of the project, where they compare the ratio of weight supported to the weight of the bridge, as well as proportions and scale factoring as they magnify their bridge to real-life factors.

*** Which sport is the hardest to play? Students will compare the difficulty level of various sports based upon the different geometries players encounter during competition.

*** Creating Art through Mathematics!  Students will explore geometric ideas to create their own, artistic tessellation (or geometric pattern that repeats and interlocks seamlessly.)  Students will analyze and explore attributes of polygons that do and do not tessellate in order to create their own unique figure that does.  Artistic examples include the works of MC Escher, Moorish tilings, and Marjorie Rice.