Math Project Ideas Rev. 10/18/95 1) Measure the classroom as accurately as possible. Describe the method(s) used and the advantages or disadvantages of each. How accurate is you method? (How much variation was in your readings?) 2) Discover a formula for finding the circumference of an ellipse, given the length and width (major axis and minor axis). Try ellipses of different shapes and sizes to verify that your formula works. 3) Discover a method for finding the center of a circle as accurately as possible. Demonstrate that the method works for circles of different sizes. Does your method work for other shapes? 4) Make a container from a sheet of 8-1/2 x 11" copy paper so that it has the greatest possible volume. The container may be open at the top but must hold together when filled with packing beads to determine volume. Fasteners such as tape and staples may be used, provided that they do not add to the volume. Describe your solution. Why is it the best? 5) Devise a method for determining the value of pi as accurately as possible. How many different methods can you discover? Which one(s) work(s) best? Why? How closely do they agree? Hint: A number of good references are available on the history of pi. 6) Describe the procedure for measuring out any whole number of cups of water, given two containers unmarked except at the top with capacities of any relatively prime numbers of cups. Demonstrate that your method works by listing a set of solutions for at least two different pairs of containers. Is there a general solution? Source: How to Solve It by G. Polya. 7) Determine, as accurately as possible, the distance from a fixed point in the classroom to the peak of a nearby building or other physically inaccessible landmark visible from the classroom. Also find the difference in altitude. How many different methods can you discover? Which one(s) work(s) best? Why? How closely do they agree? 8) Make a graph of your pulse rate at different times of the day for one week. Pick a scale that will expand the ranges of values and times in order to use the whole sheet of graph paper to show the greatest amount of detail. At the same time, make a second graph for your respiration rate. Use the same time scale but a different value scale to use the whole of this sheet of graph paper as well. Collect results from other students who are also doing this project, then add to or revise your graphs to compare your data to the highest, lowest and average values for the class graphed over the one-week time period. What conclusions can you draw from your finished graphs? 9) Make a distribution graph (histogram) of student heights (to the nearest inch). Divide students into categories by age and sex. Use a graphing format that will let you show all data on one sheet of graph paper or computer printout. Interview as many students as possible. What conclusions can you draw from this data? Are there any other categories you can discover which show meaningful differences? 10) Make a relief map of a region of interest to you. Horizontal and vertical scales will probably be different as will artifacts (buildings, trees, animals, etc.) added for detail. Include a key which identifies the region and its significance, shows the scale(s) used and identifies features and artifacts included on the map. 11) Design a theater layout. Allow for audience capacity, view, egress, security, lighting, etc. If the theater has a stage for plays and/or concerts, allow for stage lighting and capacity, prop movement and storage, backdrops, player access and dressing rooms. Drawings, reports and models may all be included. 12) Design a racetrack. Allow for seating capacity, view, egress, security, safety, lighting, etc. as well as the design of the track itself. Drawings, reports and models may all be included. 13) Design a stadium enclosure for the football field or some other area of the school property (up to and including the whole campus) that would benefit, for example, by making it more usable or make it usable more of the time. Should it be completely enclosed or covered? Should there be screens, shutters or windows? If covered, allow for maintenance of lawns, shrubs, trees and garden plants inside the enclosure (perhaps a sprinkler system underground or overhead). Will it allow better viewing and access for the spectators? Will it provide better use for the athletes? What about security? Press coverage and camera placement? Building and fire codes? Wind, rain, snow and lightning? Lighting for night games? Multiple uses? Drawings, reports and models may all be included. 14) Design an alternative energy system to supplement, replace or add to the present energy capabilities, in whole or in part, of the school or other facility, local or somewhere else. Possible energy sources include: wind, solar, hydro-electric, geothermal, ocean (tide, wave, current), geologic (tidal, tektonic). Possible energy converters include: windmills, solar cells, thermocouples, mirrors, absorption panels, heat pumps, mechanical linkages, hydraulic or pneumatic devices. Show how the new system works, how it will benefit the facility and, if applicable, how the new system will be incorporated into or with the existing one. Drawings, reports and models may all be included. 15) Design/redesign the parking and roadway system for the school campus or other facility or area. Explain how this design will provide or improve traffic flow, safety, accessibility for vehicles (buses and cars, also, maintenance, service, supply and utility vehicles) and pedestrians, parking capacity, access (ease of entering, parking and exiting, interface to public roads and transportation), distance to, and, if applicable, transportation between parking and facility being serviced. 16) Design a structure with a high strength/weight ratio. Examples: bridge, building frame or other enclosure, aircraft, boat, automobile, industrial/construction vehicle, support structure (column, jack stand). Drawings, reports and models may all be included. 17) Design a container or enclosure capable of protecting its contents or occupants against damage or injury from impact, either by an outside object striking against the container or by the container striking against a barrier. Design with a particular application in mind. This will greatly affect the design requirements. The container or enclosure may be mobile or stationary. Examples of contents: fragile freight such as food products (eggs, jars), electronic equipment (TV's, computers), live animals and plants, building occupants, secure military installations (indoors or outdoors), automobile or airplane passengers, racing drivers, military vehicle personnel, paratroopers, astronauts. Drawings, reports and models may all be included. 18) Design or improve an item of sports training or playing equipment. Show how the changes will benefit the athlete and/or the sport (for example: safety, training efficiency, performance, technique) Drawings, reports and models may all be included. 19) Design or improve an item related to a particular technology. Show how the changes will benefit the industry and the consumer. Examples: automotive, scientific, construction, theater, film- making. Drawings, reports and models may all be included. 20) Devise a method for encoding and decoding messages. Give several examples of messages coded and decoded by means of your technique. How secure is your code? Is it easy for your intended recipient to decode? Can you send private messages to different people? Variation: Encode and decode pictures. 21) Design an aid or lesson component for teaching some mathematical topic. Explain how this item or method is to be incorporated into the lesson or unit. How many industrial/business applications of this topic can you list? . . . N) Come up with your own idea(s) for projects. Drawings, reports and models may all be included. Credit will be given for the quality of the idea as well as the project itself. (If your idea is good enough, it may appear on next year's project list.) The amount of credit a project receives depends on the quality and thoroughness of the final submission. More projects may be submitted than the number assigned. Students may work in teams of up to four. Students should identify which part(s) of a project they have worked on or helped with. Materials should not have to cost much of anything. Paper, cardboard, toothpicks, popsicle sticks and glue are typical materials. Reports should be typed. The school computer is available for this purpose. Reports must show the relationship of the project to a mathematical topic and the mathematical significance of the project. Sources must be referenced, where used. Drawings may be done by hand, drafting equipment, CAD/CAM, desktop publisher, etc. Models should fit on a student desk.