Math 20 Math 20 logo Math 25 Math 25 logo Math Tips Math tips logo       valid HTML 4.01

Math Lecture Notes
Arithmetic 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. You will partially explore four of these, in a group, during class.

Towards the end of the term pick your favorite and finish researching the problem to solve it. Ideally your project will be about something practical and important to you! 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