- Ordered 20 pc meal (stop with your judging eyes)
- Cashier kid heard 10 pc. I didn't notice until after I had paid.
- He called over manager. She decided to see what the price of the 20 pc meal was ($7.50), look at the receipt ($6.19), and charge the difference.
- She asked the kid what the difference was. He was pretty satisfied with his answer of $1.20. She found an item for $1.15 and charged me.
- Everyone involved was very nice and helpful, and works too hard for too little money.

There are a lot of failure modes for mental arithmetic, but there are some simple checks that you should go through. Here, anything that doesn't end with 1 is impossible. It's easy to come to $1.41 or maybe $1.21, but $1.20 shouldn't pass the smell test.

We've been doing some curriculum work at school, and the math and science departments across all four divisions are convinced that this sort of answer-checking is something that kids have to have. They're right. It's a habit of mind for a scientist or mathematician, and it's something that we have to spend time with our kids on if we want them to learn it.

$1.30 as an approximate answer's pretty good, and that's something else that we should work with kids on - coming to first approximations before solving a problem, so that we have some idea about what we're supposed to get, not falling prey to the "writing down whatever the calculator spits out" syndrome. These approximations can be about rounding numbers or about using a first-order Taylor series or squaring off a curve or whatever, but this is a skill that's even less frequently explicitly taught in schools than checking answers for reasonableness. Dan Meyer's "Give me a number that's too high, give me a number that's too low, give me a guess" is a great way to start.

There's certainly a lot of content to get through, but these mathematical practices are arguably at least as important, not least because they'll often survive after the content is forgotten. Don't we want to live in a world where people have these tools (even non-academic folk)? If the answer's yes, then put your class time and assessment questions where your mouth is this year - make time for work on reasonableness-checking and approximation.

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