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Math OER
 Big Issues Without Right Answers 

There are two versions of math in the lives of many Americans: the strange and boring subject that they encountered in classrooms and an interesting set of ideas that is the math of the world, and is curiously different and surprisingly engaging.

- Jo Boaler

Icing on a Gingerbread House

These problems ask you to apply math to broader real-life situations.

Have fun!

Health Decisions

1. Apply some of our health decision formulas to yourself, or to a friend or family member.

2. Research the history and current use of the BMI and Body Fat formulas. How reliable are they? For what issues do they provide help? For what issues do they cause problems?

3. Research how health monitoring devices use metabolism formulas to supplement their measured data for heart rate (for watches, chest monitors, and scales) and perhaps weight (only scales). Some health monitoring devices also measure blood oxygen level: what does that number mean, what formulas use it, and for whom would it be useful to monitor?

4. Create a realistic large meal plan usable by a restaurant or catering service. The menu should include at least four dishes, and consider yield percent when making a shopping list. Price the shopping list and analyze the meal's cost per plate. Then compare your results with a similar meal at an actual restaurant or catering service.

Personal Finance Decisions

vacation I can afford meme 5. An average American vacation that costs about $1,100 per person. Plan two versions of a vacation. First describe a vacation with that average cost, split among categories of expenses. Then refine your plans by cutting costs to make a more affordable but still satisfactory version.

6. An average American wedding that costs about $26,000. Plan two versions of a wedding. First describe a wedding with that average cost, split among categories of expenses. Then refine your plans by cutting costs to make a more affordable but still satisfactory version. (Weddings, unlike vacations, have well-established categories of expenses. These 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).

7. Compare the costs of renting a house versus buying a house. How do the categories of expenses differ? How do the costs differ? Overall, how much does monthly rent differ from the combination of monthly mortage payment and average monthly home maintenance cost? And how many hours each month on average does the owner of a house that size spend on home maintenance?

8. 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.

9. Analyze a month's spending on groceries. Keep track of which groceries you use. Then price your grocery list at three or more different grocery stores. First find which store would be least expensive overall. Then break down your costs at each store by category (dairy, produce, meat, beverages, frozen foods, dry goods, prepared meals, bulk food, bathroom supplies, cleaning supplies, baby items, etc.). Does your analysis suggest any shopping strategy?

10. Some financial advisors use the 50-30-20 Rule for a household budgeting its after-tax income: budget 50% for necessities (including housing), 30% for luxuries, and 20% for paying of debt or saving for the future. Start by practicing with the Speck family's record of their income and expenses on the spreadsheet below (also a Google Sheet).

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.

Find how closely the Speck family expenses fit the 50-30-20 Rule. Then track your own household expenses for a month or more, and find how closely your own expenses fit the 50-30-20 Rule. How could you improve budget?

Speck Family Budget screenshot of Google Sheets link

11. The term travel hacking describes using credit card sign-up bonuses to get lots of free airline miles. Research how this works and how many free trips someone can expect to get every four years. Report on the type of family who would find it useful.

12. Pick one type of charitable activity, such as 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 is 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?

13. The website Portfolio Charts is a fun way to look back in time and observe how successful various investment strategies would have been. Pretend that you are someone nearing retirement age. What types of investment strategies are understandable? Which would have helped you be safely prepared for retirement?

14. Gina's mother keeps pestering her to "shop for a husband while you are young and pretty." Gina's friends assure her that this advice is outdated, and Gina can focus on her career at least until the age of 30 if not 35. Although there is no correct answer, you can help them make peace by using this graph of census data to argue who is correct. Notice that a woman who is 35 years old in 2014 appears in four different places on this graph!

2014 Never Married Census Data graphed by Dalrock

Business Decisions

15. Do an internet search for "business pricing mistakes". Make up a pretend small business. Prepare a five-minute presentation for the class about what you learned about the mistakes, and how your pretend business would avoid making those mistakes.

16. Talk to the local business owners of three very different businesses who think about pricing in very different ways. Consider business that deal with food, clothing, insurance, medical care, artistic services, construction, utilities, finance, real estate, or information technology. If you are unsure what questions to use to start a conversation, try asking how their business deals with the issues in the article 3 Lessons About Setting Your Price Learned From a Vegas Prostitute.

17. The book Priced to Influence, Sell & Satisfy notes a few examples of interesting pricing issues. Find your own examples of these three pricing phenomenon during your own shopping or by contacting businesses.

18. Read about ethics and pricing. In what ways are businesses legally required to be ethical when pricing? In what ways are they economically constrained? In what ways are they socially constrained? In what ways are they not constrained to use ethical pricing but you think they should be? Finally, what aspects of ethical pricing are tricky to understand for someone who knows nothing about pricing?

19. Find another useful book about pricing. You do not need to read all of it and write a full book report. Instead, write a page about why this book is at an appropriate level for a student in our class, what pricing issues it deals with helpfully, and who might be most interested in what it teaches.

20. Talk to the local business owners of three very different businesses who think about expected value when making business decisions. Consider business that deal with food, clothing, insurance, medical care, artistic services, construction, utilities, finance, real estate, or information technology. How do they deal with loss aversion (people feel much worse losing $500 than they feel happy gaining $500) and optimism bias (people who are successfully risky become more reckless)? When do they use the monetary expected value of a decision (about pricing options, infrastructure upgrade optionss, etc.)? When do they use expected value to help maximize less tangible things (employee satisfaction, insurance coverage, productivity)? When do they want to find an expected value but cannot because they lack the historical information to estimate the likelihood of each possible outcome?

21. What is the difference between a bookmaker and a betting exchange? What is the Bradley Act? How did its removal effect the economy? How accurate are the crowd-sourced political predictions on PredictIt? Can a small business owner learn anything from Gadoon "Spanky" Kyrollos and other famous gamblers?

22. Explore the world of the contract cheating industry. Who is spending money? Making money? Working for an organization? Working alone? Which types of schools or programs are suffering most? Are there better ways for those spending money to use their money to obtain success?

23. Some people claim that Arrow's Theorem proves a representational democracy is better than a pure democracy. Look into this claim. What does that theorem actually prove? How does it actually relate to politics?