How Much Is A Ton Of Dollars?

NOTE: Apparently Chris Robinson already asked this question on 101qs.com and I totally missed it (or forgot).
Sorry, dude. Ma bad.

I rarely watch TV these days, but today I heard this commercial while watching a recording of Perception (“Silence” episode):

“If you had a dollar for every dollar car insurance companies say they’ll save you by switching, you’d have like a ton of dollars.”

Oh really? Interesting.

We all know this is my brain:

Because of that, questions start randomly popping in my head:

1. Which ton (short, long, metric)?
2. How much does a dollar weigh?
3. How much would a million dollars weigh?
4. Geico claims to save me 15% or more, so how much would that weigh?
5. How many car insurance companies are out there claiming they’ll save me money? And at what rate?
6. …How much does my insurance cost since I got a speeding ticket?
7. What’s the value of a ton of dollars?
8. Are they exaggerating?

It reminded me of the Carnival Cruise commercial that advertised “…in any one moment, there are over a million ways to have fun”.

A million is a lot. How would you quantify that? You’re on a boat (I’M ON A BOAT!) with a limited amount of space and, while I know there are fun things to do, are there really a million ways?

Let’s call this the lesson I always wish I’d written. Show students several advertisements that sound too good to be true and then get them to figure out how to prove or disprove the claim. Then have students put together some type of undercover news report (or Weekend Update “REALLY” skit) to pretty much call them out on it and let the mathematics back it up.

Back to having a “ton of dollars” (and what the value is), that’s becoming an interesting task for me (now that Perception is over and I can focus). The question of “How Much Is a Ton of Dollars” seems so much like a Robert Kaplinsky question that I had to go look at his lesson page a few times to see if he’d already done it. I love Robert’s work, so this lesson would be along the lines of the amazing work he’s done (and that I’ve used from 5th grade to adults).

With my imaginary students, I would take the “be less helpful” path of making them figure out what they would need to answer the question, “How much is a ton of dollars?” I’d want them to start by estimating (shoutout to Andrew Stadel) the value of a ton of dollars, and have them write those estimations down and commit to a value. If I had a classroom (did I mention I miss teaching?), they’d write their estimate on a Post-It note (their name on the back), and then plot their estimates on a data wall (dry erase board with a blank number line at the bottom – this board would ONLY exist for plotting data, no announcements, etc.). I’d like to see the range of estimates and have some really good “notice” conversation about their estimations. At this point, my students would be in groups with the goal in mind of finding the value of a ton of dollars. I wouldn’t want to tell them what to do first because I’d want them to figure it out.

Weight would be a great discussion to have with students once they started realizing in the research that there are three types of measurement for a ton:

Weight of a dollar is pretty easy to find from any search engine, but I would like to encourage my students to find the legitimate primary source of information (not to take the word of Wikipedia or random resources). Depending on the age group, they might know about the Treasury Dept:

There are about 453.592 grams in a pound, so I would hope to hear students recognize that a pound of dollars is worth between $453 and $454. If there are 2204 pounds in a metric ton, then “a ton of dollars” would roughly be worth between $998,412 and $1,000,616. That’s A LOTTA dollars.

Back to the original Esurance claim:
“If you had a dollar for every dollar car insurance companies say they’ll save you by switching, you’d have like a ton of dollars.”

So basically:
“If you had a dollar for every dollar car insurance companies say they’ll save you by switching, you’d have around…

That still seems like a lot of money and makes Esurance’s claim kind of fishy.

Hmmm… So let’s think about this. Here’s the claim from Geico:

So Geico is one company offering to save me 15%. Let’s say I didn’t get a ticket (I WISH) and my car insurance is about $150/month. I could save about $22.50 by switching to Geico. But that’s a single car insurance company. How many companies offering $22.50 each would I have to talk to before I was offered “like a TON of dollars”?

Well, if a ton of dollars is about $1,000,000 and each company can save me roughly $22.50, then that would be approximately 44,444 car insurance companies offering to save me money. WOW. Is that even possible? Are there seriously over 40,000 different car insurance companies in the U.S.? Hmmmm. That makes me wonder, “How many different car insurance companies are in the U.S.?” The first thing I found in my research was information from Wikipedia. I can’t use that because I told my imaginary students they couldn’t use Wikipedia as a source, hahaha. Then I found some information from “LoveToKnow” which promises to be “advice I can trust”. Ummmm…NO. Without links to primary evidence from a legitimate source, I’m not going to trust you because you told me I could.

I did some IRS digging wondering if I could get a list of car insurance companies (because they’d have to have a tax ID number, right?). But maybe I have to pay for that information like they did in “Gone in 60 seconds” when they were trying to track down the cars (“$5.00 a car, 20 cars, would you like a calculator?”). I guess this is where I’m currently stuck. Hmmmm. Any ideas?

In any case, I don’t know exactly where this lesson would fit. It might be a good application problem for 5.MD.1 (and could also tie in 5.NBT.7 if we round to the hundredths place). Or maybe this would be a good 1st day problem for 6th or 7th grade just for students to work on Math Practices 1, 3 and 6. I dunno. I didn’t really set out to write this post as a lesson, but it kinda turned out that way. If it helps, great.

If not….

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2 thoughts on “How Much Is A Ton Of Dollars?

  1. This is great. It is definitely challenging figuring out how to go from the interesting idea to a fully fleshed out lesson that is sharable with others . Lot's of great ideas and reflections. Thanks for sharing!

    Like

  2. This is awesome, Hedge. It seems perfect even for high school level; talking about linear functions, what's causing the rate of change, simple research and using scientific equipment (if you feel brave enough to bring in a small stack of dollars to weigh), errors due to rounding, everything!
    I would think maybe the Chamber of Commerce or Better Business Bureau would be able to give information on car insurance companies, that maybe you could extrapolate to the whole country (If there's this many companies in our town of ______ people, how many would we expect in a country of 319 million people? Or, how many towns our size are in the US?)
    Plus, you could do an extension replacing “a ton of dollars” with ” a ton of quarters” and see if it's a more reasonable amount.
    I'm definitely going to try this this year, thanks!

    Like

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