(Archive problem of the week) Having just written about sequence puzzles, which sometimes can be solved mathematically, and sometimes are just psychological tests, I want to show a different kind of puzzle that I ran across while searching for those. At first, it looks like mere guess-and-check; then we find it can be solved easily …
Mathematical Thinking Solves an Operation Puzzle (Or Not) Read More »
One of the harder types of question to answer effectively is a puzzle, which as I define it means that there is no routine way to solve it, so any hint would likely give away the answer. But sometimes these are only “puzzles” to us, because we don’t know the context that would have told …
(Archive Question of the Week) Fractions are a frequent source of questions from elementary students. I plan to devote several posts to various aspects of this, from using a common denominator to add fractions, to flipping and multiplying to divide fractions, to converting between improper fractions and mixed numbers. Here, I want to look at …
How to Convert a Fraction to a Decimal – and Why Read More »
Previously, I discussed how to round a number to the nearest whole number [or tenth, ten, etc.]. I focused there on what to do when you are simply told to do it — what “round to nearest” means, and how that determines whether you round a particular number up or down. I also pointed out …
(Archive Question of the Week) Although high school and up probably constitute the majority of our questions, I always enjoy answering younger children. For today’s look at the archives, I thought I’d look at two such questions, both from 1999, and very memorable. The first is almost certainly the youngest “patient” we’ve ever had, and …
We frequently get questions about how to round; so many different issues arise that I won’t try to fit them all into one post. Children have trouble learning how to do it, and sometimes their parents are surprised to find that they are being taught a different way than they learned. There are several common …
(Archive question of the week) For Wednesdays, I plan to find a single interesting question from the past and discuss it. One of the things I’ve enjoyed about Ask Dr. Math is getting questions I’d never have thought of on my own, but which lead to some fascinating ideas. Here is an old favorite from …
Last time, I talked about students’ difficulties carrying out divisions that involve a zero, which reminded me of another issue that sounds almost the same, but is quite different: division of a number by zero. Students often either forget the rule they were taught, or they don’t believe the rule, or they just wonder about …
I was going to move on from arithmetic to algebra, but the discussion of long division led me to think about some of the more ordinary difficulties students have asked about in that area. Here I will show several questions about the process of long division in which zero caused trouble. Zero in the quotient …
I now want to start looking more deeply at some specific questions at various levels, starting with arithmetic, then algebra and geometry. Students learning arithmetic (and their parents) tend to think in terms of following some rote procedure, just because “that’s the way it’s done”. Modern educators try to focus more on deep understanding, so …