# Examples of Innumeracy

I read Innumeracy by John Allen Paulos and would like to share more up-to-date and relevant examples of innumeracy to motivate my grade 8, 9 & 10 students. Are there any websites, blogs, books, etc. with lots of examples of innumeracy in the form of pictures, reporting, news articles, etc.?

Here are just 2 examples of what I'm thinking about, I just want to find LOTS more:

http://johnquiggin.com/2011/05/08/two-billion-examples-of-innumeracy/

http://i.imgur.com/T7KThEy.jpg

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The "infographic" on the cover of USA Today every day is frequently nonsensical or misleading. –  Eric Lippert Apr 12 at 19:57
Let your students read a random newspaper, and check whether the percentages, fractions and the like are right. It's an interesting exercise, and very rewarding towards their self-esteem, since they will find mistakes for sure. –  Quora Feans Apr 13 at 8:11
@StevenGubkin To be fair, it is a relatively complex question, first she has to convert both numbers to metric, then she can start doing the actual calculation, and that requires doing division with two 8-digit numbers in order to be exact. –  eBusiness Apr 13 at 10:50
Reactions to Marilyn Vos Savant's presentation of The Monty Hall Problem: wwwp.cord.edu/faculty/andersod/TaxicabWorksheets.pdf –  David Ebert Apr 13 at 15:13

Looking at your examples, I recall a story that had been trending online for quite some time: It alleged that Samsung paid Apple about \$1 billion (USD) in nickels (\$0.05 coins) as carried by "30 trucks."

After seeing this shared on facebook far too many times, I posted the following:

It seems the story goes back at least to August of 2012, and was also debunked by Snopes.

(The Snopes estimate is 2,755 eighteen wheelers, but is based off of the judgement being \$1.05 billion, as opposed to the \$1 billion claim in the image above. Scaling my estimation up by 5% gives 2,625 eighteen wheelers. So, the numbers are pretty close. In any event: There is some "innumeracy" here.)

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Yes! More of this! –  David Ebert Apr 12 at 17:49
Fact is, the lawsuit in question is now at the next higher court and no money has exchanged hands at all at this point in time. –  gnasher729 Apr 13 at 16:58
@gnasher729 Mathematically, though, the salient point is that 30 trucks (even huge ones) would not be able to deliver that many nickels without numerous (around 90...) trips back and forth. –  Benjamin Dickman Apr 13 at 19:26
There's also the material limitation of needing the entire production of nickel metal in Madagaskar in 2011 and the entire production of copper in Portugal from 2006 to manufacture this. Also, the treasury only minted about 500,000,000 coins in 2010 (and less than 1/5th of that in 2009), so you'd easily need over 40 years of nickel production to just make that many coins. –  Nate Kerkhofs Apr 14 at 11:05
@NateKerkhofs Excellent points. –  Benjamin Dickman Apr 14 at 11:49

There's the Verizon "0.002 cents versus 0.002 dollars" mishap, wherein an unhappy customer calls to complain that he was billed 0.002 $/kB after being told the rate is 0.002 cents/kB. The confusion is perhaps deeper than expected. - ...So this is pretty funny, but I'm not sure whether this is "innumeracy" in action or just a misunderstanding of terminology. It reminds me of confusion around 0.05% being interpreted as 5% (since 0.05 = 5%). But perhaps all of these are examples of what is considered innumeracy. – Benjamin Dickman Apr 14 at 11:56 @BenjaminDickman Is this any better: publicshaming.tumblr.com/post/36857566279/… – David Steinberg Apr 14 at 15:41 Let me offer a different type of response, a student's answer to a problem. The question offered the height of a building, the equation for distance of a falling object, and asked to calculate the time till a rock dropped off the building would fall to the ground. The student used his calculator and the answer was 900 seconds. I asked if that was right, and tried to get him to apply common sense. 900 sec = 15 minutes. Do you think you can see your friend drop the rock, go to Starbuck's, get a coffee and step back out before it hits the ground? Of course not. His answer was off by a factor of 100. I'd read Innumeracy a long time ago, but recall that this was one of the author's lessons, the ability to estimate orders of magnitude as being correct or way off. Part of my goal is to ask students if the answer makes sense, in cases where it's not just numbers but real life situations. - Common accounts in popular press and TV and on-line about "the rate of increase of X is slowing", with varying interpretations, all too often mistaking this for X itself decreasing, etc. As in "unemployment" or "inflation" or "debt" or ... - A lot of the xkcd "what if" posts, for example this one about hitting golf balls off a spaceship in order to reach escape velocity, seem surprising to me in part, I suspect, because of my own innumeracy. (It turns out, in this case, you might well need a bag of golf balls about 100 billion miles in diameter...) - A YouTube video of an Illustrious Senator Talking about the cost of health care, 500 trillion dollars. This is more than all the worlds wealth, and nearly 8 times all the wealth in the US. I guess he meant Billion, but in Washington, no one is listening anyway. - True story: I ordered new carpet flooring for a room in my house. The length of the room was 13 foot 11 inches. The employee took his calculator and typed "13.11 x 30.48 =" to convert into centimetres. I didn't actually manage to convince him of his mistake, but had to ask for a more experienced colleague. Would have been a nasty surprise if I hadn't noticed and they had delivered a piece of carpet 10 inch too short. - "How would you type in 13 feet and 12 inches?" – Chris Cunningham Apr 13 at 17:46 13.12 :-( Seriously, I told him that 13 foot 11 inch is almost 14 foot which is more than 4.20 metre, not under four metre. Didn't get more than a blank stare. – gnasher729 Apr 13 at 22:47 Well, 13.11*2 = 26.22, But isn't 'just under 14' * 2 'just under 28' and not 'just over 26'? Meters? Never heard of them. – JoeTaxpayer Apr 14 at 1:01 One example that annoys me is when science stories in newspapers (especially stories about high energy physics or astronomy) insist on writing out large numbers, such writing$1,000,000,000,000,000,000,000,000,$or writing things like trillion trillion, when neither is very useful to a reader with a high school education and neither would make any sense to anyone else. Why not write$10^{24}?$Scientific notation is taught (in the U.S.) to students who have not yet begun the study of school algebra, and it is used in high school science classes. Below are two other examples that I've previously posted about in the past. Example 1: Atlanta mayor: In resettling evacuees, FEMA no help, CNN news article, 14 October 2005. [I previously posted a different version in this 15 October 2005 sci.math post.] CNN anchor Miles O'Brien on Friday spoke about the challenges facing one city with Atlanta Mayor Shirley Franklin. Atlanta took in 42,000 families fleeing the disaster. O'BRIEN: All right, let's talk about this, 42,000 families. You're a big city. It's a prosperous city, but that still puts a burden on the city, doesn't it? FRANKLIN: Well, it certainly does, but I don't think it's a burden that FEMA [Federal Emergency Management Agency] can't help us to address. The Congress and the president have allocated 62 billion [dollars]. Our estimates are that a family needs assistance for about six months in order to stabilize themselves and that would cost about 11,000 [dollars] per family. The city of Atlanta can't absorb that cost, but we can certainly work with FEMA, if they were willing, to help families get resettled in the city and the metropolitan area. O'BRIEN: So 11,000 times 42,000. I can't do that kind of math on the fly here. But how much of that money have you seen? Note: This is trivially estimated via$1$times$4$followed by$4+4=8$zeros, or$400$million. By missing this, and hence also the fact that$60$billion divided by$400$million is$(1.5)(100)=150,\$ Miles O'Brien (a well known broadcast news journalist who, incidentally, specializes in science, technology, and aerospace reporting) missed a good opportunity to make a point I suspect he would have liked to make.

Example 2: Formerly posted in this 8 February 2009 math-teach post at Math Forum:

I wonder if the author of the article below has any awareness of just how mathematically illiterate one of the comments below makes professional news writers sound. The author writes "CNN checked McConnell's numbers with noted Temple University math professor and author John Allen Paulos" for something that any college-bound middle school student should be able to do, even without a calculator. Although some of Paulos' comments are nice, especially his speculation "People tend to lump [million, billion, trillion] together, perhaps because they rhyme", going to him in order to check McConnell's numbers is like asking a university linguist for the correct spelling of the word "especially".

I mention this because I've seen many examples of this over the years, especially newspaper writers consulting mathematicians for something that is nothing more than an easy high school level probability or combinatorics problem (easier than many of the problems in standard precalculus and college algebra texts). I don't know whether the reporters really don't know how to work these problems (like checking McConnell's numbers below) or whether they are just using the occasion to get some possibly interesting remarks from someone well known and don't realize how stupid their rationale sounds to a large percentage of their readership.

"Numb and number: Is trillion the new billion?" by Christine Romans CNN's American Morning

"To put a trillion dollars in context, if you spend a million dollars every day since Jesus was born, you still wouldn't have spent a trillion," McConnell said.

CNN checked McConnell's numbers with noted Temple University math professor and author John Allen Paulos.

"A million dollars a day for 2,000 years is only three-quarters of a trillion dollars. It's a big number no matter how you slice it," Paulos said. Here's another way to look at it.

"A million seconds is about 11.5 days. A billion seconds is about 32 years, and a trillion seconds is 32,000 years," Paulos said. "People tend to lump them together, perhaps because they rhyme, but if you think of it in terms of a jail sentence, do you want to go to jail for 11.5 days or 32 years or maybe 32,000 years? So, they're vastly different, and people generally don't really have a real visceral grasp of the differences among them."

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