### MATH325 Project

Outcome: Write and solve complex geometric problems appropriate to an advanced High School class.

You will hand in a project proposal around mid-semester and a final draft of your project at the end of the semester. You will also review and score projects for three of your peers.

### Project Ideas

Any application of geometry at or slightly below the level of this class makes an appropriate project. Some sample project ideas are given below.
• An application of triangulation in a nautical navigation problem or related to modern GPS systems.
• Examples of use of similar triangles or triangle measures from astronomy. A relatively simple example is presented here.
• Using geometry to create patterns for carpentry, quilting or other projects. (Examples)
• Estimating volume or surface area based on information in a photograph. (One example I've seen is a photo of a man standing next to a tank. If the man's height is known, you can estimate the height and diameter of the tank from the photo.)
• Calculating the artist's viewpoint based on a perspective drawing, or calculating the sizes of distant objects in a perspective drawing given the artist's position and some information on the size of other objects appearing in the image.
• Calculating distances and positions of objects based on photographs taken from two different viewpoints (steroscopic vision).
• Calculating the coordinates of the vertices and faces of an object for use in a digital model.
• Restoring a "stretched" picture to its correct aspect ratio based on known shapes of some objects in the picture.
• Calculating the volume of water flowing down a river over time. (As done by the BSC Geographics Lab when studying pollutants.)

 Score Proposal Characteristic 5 Proposal is well thought out and is clearly an application of geometry. Project difficulty is reasonable. 3 Proposal is vague ("use triangles to find the height of a house"), is not geometric in nature ("find out how long it takes to fall 10 feet"), or is much too easy or difficult ("find the volume of a cylindrical swimming pool"). 1 Proposal fails to describe a problem or how the problem relates to geometry.

### Project Format

The final draft of your project should have at least three sections: One section should be devoted to the question, one section should discuss what geometric principles are involved in the solution (if you like, you may include a discussion of pedagogy or learning styles here), and the final section should be the solution to the problem. Feel free to add a conclusion and/or a discussion of alternate methods of solving the problem.

### Project rubric

The project counts for 10% of your grade. That will be broken down into 1% for your proposal, 1% for scoring your peers' projects and 8% for the final draft. Note that you may wish to ask your peers to informaly grade your project before you submit it to Blackboard.

#### Problem Presentation

 Score Project Characteristic 10 The problem to be solved by the project is clearly described; information needed to solve the problem is readily available. 5 The question to be solved is not clearly stated, or information needed to solve the problem is not provided. (E.g. a project to find the height of a building based on the length of its shadow with no information about the angle of the sun.) 1 It's not clear what the question is.

#### Solution

 Score Project Characteristic 10 The solution is clear, complete, correct, and easy for classmates to follow. 5 The solution contains errors, gaps, or is difficult to follow. 1 The method of solution presented will not yield a solution. (E.g. calculating time it takes for a ball to bounce by measuring distance between bounces.)

#### Content

 Score Project Characteristic 10 The project uses geometry at an appropriate level in an interesting and realistic way. 7 The geometry used in the project is too easy or too hard, or the problem doesn't seem realistic. 1 The solution does not involve geometry, or fails to provide needed information. (A project using navigation to determine the location of a ship should include a map or nautical chart.)

#### Grammar, Spelling and Appearance

 Score Project Characteristic 5 The project is complete, well written and laid out in an attractive way. 3 The project writeup contains several spelling or grammatical errors, is incomplete, or is disorganized. 1 The project writeup is extremely messy, disorganized, or incoherent.