Factoring a quadratic equation involves finding two linear equations whose product is the quadratic equation. This is an example where mathematics teachers often act as if (a) there is one method of solving and (b) there is one solution. The AC Method The “one method of solving” strategy usually goes something like this: If the…
Author: Clio
Listening to students (reflection)
One of the greatest benefits to my current teaching position is its small class sizes, which affords me a significant amount of one-on-one tutorial time. I know fairly well how I think about numbers; I don’t know how other people, particularly students who struggle with mathematics, do. I feel that it’s crucial that mathematics teachers…
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When I was a lad studying mathematics, the equality sign seemed particularly simple: The stuff on the left is equal to the stuff on the right. However, I have since been developing a much more sophisticated perception of the simple little sign. It can indeed be a troublesome symbol, not because of its own meaning…
Let’s Make a Deal
The Problem In the misnomered “Monty Hall” problem, the rules are set out as follows: You as the contestant are faced with the choice of three doors, behind exactly one of which is money or something else of significant value. You choose a door. The host, who knows where the money is, then opens a…
The Reversible Phone Number
Consider this problem: An absent-minded American mathematician has difficulty remembering his seven-digit phone number until he notices that, when he reverses the digits, he gets another seven-digit phone number that is a factor of his own phone number. After this point, he never has trouble with his number again. What is his phone number? (This…
The Baby Shower game: A Square Deal
The Puzzle Here’s an interesting puzzle: The hostess of a baby shower devises a game in which sixteen tokens are placed in an opaque bag. The tokens are all either pink or blue, and they’re otherwise identical in shape, weight, texture, and so on. Two guests are chosen. The first guest chooses a single token…
Three three-digit numbers
Here’s a fun little problem: Find three three-digit numbers that use each non-zero numeral once and add up to 999. Follow-up: How many such sets of numbers exist? If you want, take a moment to work on the problem on your own. Then continue reading. Finding a solution For the first question, any set of…
Number terms
An interesting question on the G+ Mathematics community I co-moderate asked about the difference between “numbers” and “numerals”. We wound up discussing this at a party I was hosting (which shows the sort of nerds we are), and this post is born from those discussions and my further thoughts. It seems to me we have…
Some thoughts on circumference
This is the formula for the circumference of a circle: \[C = 2\pi r\] It’s very simple. My recollection of how it was taught is as a mystical relationship between \(\pi\) and the circumference, as if it were some magical truth that \(\pi\), of all numbers, would be the number that would satisfy the need…
Found Haiku
“It’s dinnertime, so I’m about to eat dinner. Butter is butter!” — jeh, age 3