This is the 250th anniversary of the United States, and as a result we’ve heard the term “semiquincentennial” a lot. (Well, a lot more than usual.) That reminded me of several past questions about such terms, so we’ll take a look at them now, starting (after a quick introduction) with one asked 25 years ago …
Recently, a teacher in Bangladesh asked us how to answer students’ common questions about his version of the proof that the square root of 2 is an irrational number. Some are questions about apparent gaps in the proof itself, others about how one would decide what to do in writing the proof. We’ll then compare …
A recent question about the precise meaning of “difference” led me to some past discussions of the word.
Let’s look at three similar questions we’ve received about Least Common Multiples, Greatest Common Factors, and so on, starting with a recent question and going back in time. We’ll see a bad question, a good question, and an interesting challenge.
Last week’s question led to a number of previous questions, which would have made it too long. Here we’ll look at the last couple references we gave, dealing with percentages of a negative base. This time, the problems will be mostly about money.
Continuing to look at past questions that didn’t make it into the blog, I find a question about percentage change in temperature, which nicely ties together a couple older topics that have long been on my list to cover. Let’s do that now.
We have looked at how we add, subtract, and multiply decimals. Now we’ll conclude with division: what we do, why we do it, and how we don’t really need to do it that way.
We’ve looked at how to add or subtract decimals. Now let’s move on to multiplication; we’ll look at three answers to the same sort of question.
Recently a teacher (Hi, Edite!) asked for help teaching how to divide decimals; in particular, she wanted to be able to provide a deeper understanding of the process, giving a good reason for what we do. Here I want to start a long-delayed series on operations with decimals, doing exactly this for all four basic …
A recent question reminded me I hadn’t yet written about the complexity surrounding the definition of ratio (and related terms, like rate and fraction). Here are four questions about the words.