Headlines from a Mathematically Illiterate World

http://mathwithbaddrawings.com/2013/12/02/headlines-from-a-mathematically-literate-world/

The longer I teach, the more I think that the math that feels most important for students to take away from my class is about learning to read, interpret, and critically evaluate the logical/illogical statements that float around every day. I do actively enjoy pure math kinds of things, but if it came down to a choice of residue, I'd give up a robust understanding of derivatives for my kids leave being able to read a graph in the newspaper and evaluate the reasonableness of the latest study's claim.

I think it would be really fun for kids to find ridiculous statements in news articles and correct them like this. It would be interesting to develop that critical eye for poorly worded statements, both from a language and a mathematical perspective.

Upgrading & Early Termination Fees

Here's an interesting story about a guy trying to negotiate upgrades for his family to the latest iPhone. All comments aside about the scam that constant upgrade "opportunities" offer, the story is an interesting mix of straight math and emotion. So basically, economics. Homo Economicus might have just skipped the upgrade altogether (or took his family back to flip phones).

The story in itself seems like more of a hook than the basis for a problem you'd actually spend the bulk of a class period on, but it opens up larger questions about early termination fees, upgrade costs, etc. Given deal X from company A that gives you free or cheaper phones with a new account, at what point is it "worth it" to leave your existing phone company and suck up the early termination fees?

There are lots of other interesting variables that could factor into the decision:

• How many phone lines you have
• Variations in cost between the actual monthly phone plans of the two companies
• How soon you'd be eligible for an upgrade with your current company
• How soon the other phone lines would be eligible for an upgrade
• What kind of quantifiable measure you put on being cooler than your friends and/or having the latest thing. Would it change your mind about waiting out your time until an upgrade if you knew that all your friends would have the new iPhone before that? How many friends would you care about? Can you quantify how much you care? 

Reminiscing about the Good Old Days of Gas Prices

http://consumerist.com/2013/09/17/you-will-probably-never-pay-less-than-3-for-a-gallon-of-gas-ever-again/

The Consumerist says that we will never again in our lifetimes pay less than $3/gallon for gas. When I first got my driver's license, I remember paying less than a dollar! I also remember when gas prices started to go up and I swore I would never pay more than $2/gallon. (Maybe the math problem in here is figuring out how old I am...). The Consumerists's logic seems to be that because today was the 1000th consecutive day that average gas prices are over $3, we can safely say that we've reached the point of no return. 

Here are my mathematical questions about this situation: 

• Are you convinced the 1000th day is "enough" of a pattern to say that we're never going back? 
• Would you be as convinced if the 1000 days were not consecutive? What kind of pattern of conductivity would be "enough" for you? 
• Does it matter that this about the national average of gas prices? 
• Does it matter what that average price is for you to be convinced? For example, if the national average price of gas is $3.89, I'll probably be convinced that <$3 is unlikely. But if the national average is $3.02, I feel confident in saying that I won't have too much trouble driving around and finding a gas station where I can pay $2.99. --> This seems like a perfect opportunity to talk about the importance of standard deviation!
• How could looking at a graph of gas prices help add to an argument? I feel like there's a very powerful visual argument of showing the $3 line and looking at when the graph stops dropping below that. 
• If you wanted to convince someone with a graph, what data would you show? 
• National averages only, or the range? 
• How often would you want to chart data points? Daily? Weekly? Monthly? 

Dictionary of Numbers

A Chrome extension that gives context to numbers.

From playing around with it, it's not as easy as I'd like, but there are some cool things. Did you know that the International Space Station weights 1 million pounds? I like the idea of giving context to numbers so that kids/people can have a reference point, especially for big numbers.

Is the Google Offer worth it?

This came from some real-life math I was doing today as I was trying to book at flight from SFO to Chicago. Google Offers had a deal on airfare (on Virgin America): $50 for 50% off your next flight (round-trip or one-way). 50% off--awesome! But how good of a deal is this? Is this Google Offer always worth buying? How can you tell when it's worth it and when it's not? Is there a situation where it could even end up costing you more to use this Google Offer? How can we create a model to tell us when this Google Offer is worth it, and when it's not.

To complicate matters, this offer came out at the same time that I also happened to have a coupon for Virgin America--a coupon that I got for free from an online promotion--for 20% off my next flight. How does this change when it's worth it and when it's not worth it to buy the Google offer? How does it change the model?

Use multiple representations to explain your solutions (t-table, graph, equation, etc.)

More Than $1800 in Savings

This month's Costco coupon book says on the front "More than $1800 in savings, plus more than $3500 in online savings from Costco.com." Wow, what a good deal?

I'm curious to know how this is calculated. I only counted 76 in-store coupons, most with a savings of under $5. I'd love to talk to kids about the marketing strategy behind Costco's assertion, as well as just how much money you'd have to actually spend in order to save $1800 (or $3500!).

Avoid the monthly fees

http://consumerist.com/2010/12/chase.html

Chase will charge you a $12/month fee unless you do some stuff (like use their card or keep a lot of money in your account to fund their bank). "What's the best option?" sounds like an algebra problem in the making! Everything should just be linear, right (assuming you're looking at a constant amount of money coming out of your checking account each month)? Or you could talk about piece-wise functions, especially if you look at keeping a minimum balance.

Such a good question: what does it cost you to keep money in the bank?

Grocery Shrink Ray

Dan Meyer's ideas on groceries...
http://blog.mrmeyer.com/?p=8713

... all came from The Consumerist website
http://consumerist.com/

So many ideas here:
-Obviously, proportional reasoning re: money
-There should be lots with different levels of math. Calc kids can look at oddly shaped bottles.

Double or Nothing

http://blog.mrmeyer.com/?p=5394

Parks & Recreation clip about betting on a pool game.

The questions:
How many games did they play?
How long were they playing for?

Most Expensive Liquid

http://blog.mrmeyer.com/?p=5633 

Oil vs. Red Bull vs. Printer Ink

Parking Meter Rates

http://blog.mrmeyer.com/?p=3001

What is the cheapest way to park for an hour?
What is the most expensive way to park for an hour?

You only have bills, so you ask the nearby store clerk for change. What is the best way for him to give you change for $1 if you want to maximize your parking time? What if the store clerk is running low and doesn't have enough change to give you all coins of the same value?

Is there a systems of inequalities somewhere in here? I can't tell.