Like many credit cards, it comes with rewards "points". I get one point for every $1 I spend. The information that came with the card includes a table that begins as follows, which purports to show "how fast your points... can add up":

Everyday Purchases | Amount | Points |

Restaurants | $320 | 320 |

Gasoline | $100 | 100 |

Groceries | $450 | 450 |

Miscellaneous | $400 | 400 |

(etc.)

What, are people so stupid that they can't

*multiply by one*?

(Of course, there are much more serious quantitative-illiteracy issues involved with credit cards, namely that people don't realize how much they get gouged on the interest rates, or just how long it'll take them to pay off the thing -- and how much interest they'll pay -- if they make the "minimum payment". But I won't go there.)

## 7 comments:

Maybe you could try this out in your new math class. Reproduce the letter and leave out one of the numbers in the table and see how many can figure it out.

Steve,

I can't do that! If I do that and people get it wrong I won't be able to look at them without laughing.

Would that really be so bad?

maybe every now and then there is a promo campaign where the points awarded for some kind of purchases are doubled or link, or there is a bonus for each single purchase. So, multiplying by one is only the default (which makes sense :-) )

They're not multiplying by 1, they're dividing by $.

I'm going against the grain here, but I think this is a good way to do it. People are wonderfully good at matching patterns; it should take less than a second to scan the table and figure out what is going on.

I dare to bet that the sentence "You earn one point for every dollar you spend" is somewhere in a paragraph surrounded by similar looking text: Not in an easily scannable form. The idea isn't hard to grasp, but you have to find and process it first.

We as mathematicians do this too. How many times have we written down a messy doubly-subscripted sequence by just listing the first few indicies? We could give a formula, and no doubt we could understand a formula easily enough, but the fastest way to communicate the idea is to start the pattern and say "and so on".

I don't want to belabor the point, but just think about it the next time you have a tricky sequence or series given by a formula. Is it easier to get a grip on what is happening by writing out a few terms?

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