### MATH325 Project

Ten percent of your grade will depend on a 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.

The instructor and your peers will be grading your projects according to the following rubric:

#### 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.