 Team Projects |
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T1. Working with others can be beneficial not only on the job,
but also in the classroom. For this team project, introduce yourself to
three or four classmates and work with them for this problem. Spend at
least 30 minutes getting to know one another, specifically focusing on
these statements about your previous mathematics experiences: T2. In the B.C. cartoon, Peter has a mental block against 4s. See whether you can handle 4s by writing the numbers from 1 to 10 using four 4s for each. Here are the first three completed for you: More than one answer is possible. For example, T3. The Pythagorean theorem tells us that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse. Verify that the theorem is true by tracing the squares and fitting them onto the pattern of the upper two squares shown in the figure. Next, cut the squares along the lines and rearrange the pieces so that the pieces all fit into the large square. Pythagorean theorem squares
T5. "When will I ever use algebra?" T6. Form teams in which team members have an interest in a similar type of business. With your team, make an appointment with a manager of the business and schedule an interview. Ask specific questions about the qualifications for a career in that business, and in particular find out the amount of mathematics or algebra required. T7. With a team of two or three others, keep track of each time any team member sees a fraction or percent being used outside the classroom. For example, a half-off sale, or a bank interest rate, or a recipe calling for 2 1/2 tablespoons of an ingredient. Make up a master list for the team (eliminate duplications), and discuss why a fraction or percent is used, rather than a whole number. Also comment on why a fraction is used rather than a percent, or vice versa. T8. With a team of two or three others, prepare a portfolio of photographs of buildings with interesting architecture. Find the architectural name for the building style, as well as the name of the mathematical solid that most closely approximates the shape of the building. T9. In the given figure, there are eight square rooms making up a maze. Each square room has two walls that are mirrors and two walls that are open spaces. Identify the mirrored walls and then solve the maze by showing how you can pass through all eight rooms consecutively without going through the same room twice. If that is not possible, tell why. T10. Form a team of three or four others to discuss the advantages and disadvantages of the United States completely changing to the metric system. You might consider organizing a debate with another team to consider the following statement: Resolved, the United States should convert to the metric system.
T11. Suppose that we fit a band tightly around the earth at the
equator. We wish to raise the band so that it is uniformly supported
6 ft above the earth at the equator. T12.The figure below illustrates a strange and interesting relationship. The square in part a has an area of 64 cm (8 cm by 8 cm). When this same figure is cut and rearranged as shown in part b, it appears to have an area of 65 cm. Where did this "extra" square centimeter come from? a. 8 cm 8 cm = 64 cm b. 13 cm5 cm = 65 cm Extra square centimeter?
Hint: Construct your own square 8 cm on a side and then cut it into the four pieces as shown. Place the four pieces together as illustrated. Be sure to do your measuring and cutting very carefully. Satisfy yourself that this "extra" square centimeter has appeared. Can you explain this relationship? T13. Suppose you are given $1,000 to invest. With other members of your team, select an investment strategy, such as savings account, certificate of deposit, stocks, bonds (or even keep the money in a shoe box). Document your investment using your local newspaper. Track your investment for the next 60 days and then present a report on the results. T14. With a team of two or three classmates, investigate the costs of obtaining a $10,000 business loan repaid in a lump sum in 18 months. List specific sources in your area for such a loan, as well as specific options. Include the rate and different methods for calculating the rate. Also include the requirements for the loan (such as a required cosigner or collateral). Each member of the team should individually obtain information from a different source and then the team should decide on the best source. T15.With your team, select a particular car and options. Research the cost of the car, as well as sources for purchasing the car. Decide on your best offer and then interview one of the sources to decide if your offer would be acceptable. Prepare a report on your results. T16. With your team, draw Venn diagrams showing all possible
regions for the following number of intersecting sets: T17. What is the millionth counting number that is not a perfect square or a perfect cube? T18. St. Petersburg paradox. b. Suppose that you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. Continue in this fashion for a total of 10 flips of the coin, after which you receive nothing if it comes up tails. What is the mathematical expectation for this game? c. Suppose that you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. Continue in this fashion for a total of 1,000 flips of the coin after which you receive nothing if it comes up tails. What is the mathematical expectation for this game? d. Suppose that you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. You continue in this fashion until you finally toss a head. Would you pay $100 for the privilege of playing this game? What is the mathematical expectation for this game? REFERENCES:
T20.Your team has been hired to conduct a survey, and prepare a report of your findings. Begin by determining a suitable multiple choice question, for example, "Do you watch any soap operas, and if so, which one is your favorite?" Identify five to ten possible responses for your question, including "None of the above." Determine your team's survey methods; for example, specify the number of responses and where you will obtain your data. Discuss how location and time of day can affect the results. Conduct the survey, tabulate the results, and construct bar, line, and circle graphs to display the results. Your report should include your methods, results, and conclusions, as well as tabulated responses and summary graphs. |
