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Math Lecture Notes
Project Ideas

The math questions on our homework and tests are all structured as questions with a correct answer.

However, many real-life issues are too subjective to have one correct answer.

Towards the end of the term pick a project idea. Ideally your project will be about something practical and important to you! Do some research to answer a question or solve a problem. You can create your own project. The list of ideas below are only suggestions.

An important part of this project is to cite your sources. If your project involves prices, where did you get them? If your project involves nutritional information, where did you get that? Etc.

Then present your finished project to the class.

Please refer to the project rubric for information about how you will be graded.

1. Two Versions of a Vacation

Plan two versions of a vacation. First describe an average American vacation that costs about $1,100 per person. Then refine your plans by cutting costs to make a definitely affordable version.

Decide on categories of expenses. Plan how much you can afford to budget for each category. Then do the details of the vacation planning.

Write a report that compares the two versions of your vacation idea. Discuss how you were able to cut costs. Represent the budget categories for the affordable version as a pie graph. Were you able to include everyone you wanted? Is your less expensive vacation still satisfactory? How would you save up that much money?

2. Two Versions of a Wedding

Plan two versions of a wedding. First describe an average American wedding that costs about $26,000. Then refine your plans by cutting costs to make a definitely affordable version.

For weddings, the categories of expenses include per-guest costs (pre-reception food and drinks, the reception meal, reception drinks, tables and chairs at the reception) as well as fixed costs that do not depend upon how many guests attend (invitations, music, photography, flowers, dress, rings, bridesmaid expenses, rehearsal dinner, the ceremony room, and honeymoon). Decide how much is affordable for each category. Then do the details of the wedding planning.

Write a report that compares the two versions of your wedding plans. Discuss how you were able to cut costs. Represent the budget categories for the affordable version as a pie graph. Were the bride and groom able to invite everyone they wanted? Is your less expensive wedding still satisfactory? How would you save up that much money?

3. Renting vs. Buying a House

Compare renting a house to buying a house. How do the categories of expenses differ? How do the costs differ?

How many hours each month on average does the owner of a that size house spend on home maintenance? How much does monthly rent differ from the combination of monthly mortage payment and average monthly home maintenance cost?

Buying a house should be cheaper, in part because your own time is spent on home maintenance. What would your hourly "pay" for doing your own home maintenance turn out to be?

The website Zillow might be a good place to start to make this project appropriately personal.

4. Paycheck Double-Checking

Analyze the math in your paycheck. Compare your gross pay and net pay. Confirm that the deductions for Federal Income Tax, Social Security, and Medicare are correct according to the formulas used to compute them.

Also calculate your cost to your employer, which is more than your gross pay because the employer also has costs for Social Security and Medicare, as well as Federal and State unemployment taxes and possibly health care.

5. Grocery Analysis

Keep track of which groceries you use for a month. Then compare prices in three ways.

First price your grocery list at three or more different grocery stores. Which store would be least expensive overall?

Then break down your costs more carefully. How much do you spend on each category of grocery items do you spend the most (dairy, produce, meat, frozen meals, baby items, etc.)? Are different stores especially inexpensive for certain categories?

Third, check how much location affects grocery prices. Pick one of your stores, and price your list at a second location of that store. If one location is significantly more expensive (sometimes true at the edge of town, compared to downtown or at a major intersection) is that because most prices are higher, or especially with certain categories?

6. Expense Tracking and Budget Fixing

Many money problems (and agruments) can be avoided with careful expense tracking and budgeting.

Start by practicing with a ficticious budget. The Speck family keeps track of their income and expenses on the spreadsheet below (also a Google Sheet, four month Excel file, twelve month Excel file). Most of their expenses are the same from month to month. Garbage pickup is billed quarterly. Their home has about $3,000 of property tax due each November, which they budget for by saving throughout the year. In March they receive some anniversary money from family. In April they need to fly to a wedding, and income tax is due. They want to reduce their expenses to save 10% of their annual income for retirement. How should they do this?

Speck Family Budget screenshot of Google Sheets link

Next, track your own household expenses for a month. Put all your receipts in a box when you get home, and archive your credit card statements there too. At the end of the month, use that box to create your own spreadsheet with real totals in the categories. (You can use the Speck family spreadsheet as a model for yours.)

The final step is to turn your expense tracking into a budget. In which categories are you spending too much or too little? What are your goals for adjusting your spending? Are you able to budget to save 10% of your income for retirement?

7. Comparing Risks

This project idea focuses on communicating about mathematical ideas. There is less arithmetic, but more careful use of tables and graphs to be convincing to your audience.

Below is an interesting list of how many people in the United States die each year from various causes. The numbers in the list are only estimates because different issues have been studied and counted in different years, and very few issues have a number for last year. Some other numbers are included to help provide perspective the various sizes of numbers.

This project's goal is to change the audience. Calm people so they are less likely to worry about issues undeserving of our personal time, energy, and stress. Stir people people so they have a more realistic sense of which national issues do deserve some time, energy, and resources.

(323,100,000 total US population)

 

(22,102,761 conceptions, but 70% of fertilized eggs never implant)

 

(6,630,828 pregnancies, but 40% are miscarriages)

(3,978,497 babies born)

(2,000,000 national prison population due to non-drug crimes)

 

(664,435 abortions)

(639,863 population of Portland, Oregon)

614,348 heart disease

591,699 cancer

(322,000 national prison population due to drug crimes)

 

(203,000 children kidnapped by family members)

(166,575 population of Eugene, Oregon)

147,101 lung disease

136,053 unintentional injuries

133,033 stroke

 

(105,164 population of Hillsboro, Oregon)

93,541 Alzheimer's disease

76,488 diabetes

65,000 drug overdose deaths

55,227 influenze and pneumonia

48,146 kidney disease

42,773 suicide

26,083 motor vehicle crashes not on interstates and freeways (about 1/4 from texting)

 

11,178 motor vehicle crashes on interstates and freeways (about 1/4 from texting)

10,850 murders using handguns

(10,393 population of Newport, Oregon)

(9,251 number of for-credit students at LCC)

(8,800 population of Florence, Oregon)

4,488 murders not using handguns or rifles

3,275 fires

 

700 complications in pregnancy or childbirth

505 accidental handgun discharge

450 falling out of bed

358 murders using rifles

(247 lottery winners of $1 million or more)

 

(115 children kidnapped by strangers)

82 floods

58 bees, wasps, and hornets

53 mammals not dogs or cows

51 lightning strikes

28 dogs

24 arthropods and reptiles

20 cows

15 icicles

4 roller coasters

1 shark

0 airplane crashes

8. Meal Planning

Plan and price a complete meal for dozens of people.

Pick a menu of three or four dishes. Consider yield percent, and make a shopping list. Price the shopping list. Analyze the meal's cost. Use either restaurant pricing method to estimate how much the meal would cost at a restaurant. Estimate the calories for each item, as protein, fat, and carbohydrates.

Finally, compare your results with a similar meal at an actual restaurant or catering company.

9. Charitable Giving

Pick one type of charitable activity. (Microfinance, disaster relief, medical aid, environmental work, etc.)

Use the website Charity Navigator to compare four or more non-profit organizations that do that type of activity.

Which non-profit organization was the best to financially support to ensure your dollars help the world as much as possible? What information did you use to reach that conclusion?

10. Construction at Home

Plan and complete a construction project involving a scale diagram. In past terms students have planned gardens, built trailers, and refurbished a deck.

Describe the initial layout you have to work with, as well as the purpose and goals of the construction. Detail the preparations that need to be made to prepare the materials and/or land. Draw a scale drawing of the layout you wish to create, with all the features labeled. Create a shopping list to budget your expenses.

Finally, do the work and include before and after photographs of the area.

11. Human Progress

Despite what we might hear about on the news, life is improving for almost everyone everywhere. The website Human Progress measures many examples.

(Similarly, there is a climate change crisis, but there is still time to avoid disaster. We are currently on the "optimistic" scenario pictured in the famous XKCD cartoon.)

For this project, look at the Human Progress website and then report to the class three or four ways that you were surprised about how much life is improving. Use numbers and charts appropriately to make your explanation convincing, as if you were speaking to an audience of skeptics.

12. America's Entitlement Crisis

Economists are very worried about the upcoming Entitlement Crisis as the government's promised expendatures on Medicare, Social Security, and Federal pensions increase in the future. Here is a graph showing the growth of these "mandatory programs".

entitlement crisis graph 1

Most economists agree about a few predictions. Medicare has reserves that will run out in about 2028, and its trust fund to pay for hospital care will run out in 2029. Social Security will never go completely bankrupt, but after 2030 recipients should not expect to get more than 70% of what is currently promised.

The growth of retirement-aged people can be predicted using census data.

entitlement crisis graph 2

There is less agreement about other predictions. How rapidly is the ratio of tax-paying workers to retirees shrinking? Will Social Security see changes to its retirement age as well as its payments? How big is the Federal pension problem? In what ways will the Entitlement Crisis eventually be fixed—cuts to these mandatory programs, increased revenues, or cuts to discretionary progams? What choices are people making to prepare family members for the Entitlement Crisis?

For this project, do online research about the Entitlement Crisis and report your findings. Be sure to cite your sources carefully. How big is the Entitlement Crisis? Find one or more graphs predicting the future expense of these "mandatory programs" and explain them. Find the most reliable answers for the other questions asked above, and discuss the issues and consensus opinions.

13. Individual Development Accounts

After earning a degree at community college, many people move on to starting a business or doing continuing education. However, the types of government financial aid used by most college students usually does not help with those. Time to explore the new option!

Learn about Individual Development Accounts, especially the local ones provided by the Neighborhood Economic Development Corporation and Goodwill. (Nationally, most are provided by the Department of Health and Human Services.)

Design a real or ficticious plan that uses an IDA to help pay for continuing education, home ownership, or starting a business.

Also learn about WeFinance, which uses crowd-funding to help loans happen. These are normal loans, which the borrower pays back.

A different source of money is LCC's own LaneFunder. This is a fundraising program: the contributions are donations instead of loans.

Note: mixing types of financial assistance might mess up student financial aid and other Federal loans—speak with an expert in the Financial Aid department before starting anything in real life!

14. Investment Tracking

Set some goals about how to invest your savings. Pick a few stocks, bonds, or funds and pretend to invest them. Track the value of these investments for six weeks.

Write a report about if the investments' performance. Did it match the goals you set?

If you are not sure where to start, try calling an investment company such as Fidelity. Most investment companies are happy to help a college student practice investing with imaginary money because these students usually become actual clients in future years.

Note: if you do not yet use the "real" Form 1040 for your taxes you probably do not want to actually buy and sell stocks, since any capital gains or loss will greatly complicate your tax information!

15. Personal Future Expectations

Analyze how your future wealth will be affected by your college degree.

How much will your planned degree(s) cost you? How much do you expect your income will increase after you have these degrees? How long will it take you to pay off your college loans?

This project idea is the most vague and "up in the air". Be especially careful as you document your research. Where do you find answers to these questions? Do second opinions agree or vary wildly? Be sure to cite the sources you used as you try to answer these questions as accurately as possible.