What’s the Difference? How the Meaning Gets Twisted
A recent question about the precise meaning of “difference” led me to some past discussions of the word.
Arithmetic
Three HCF/LCM Problems
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.
When Percentages Don’t Make Sense
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.
Percentage Change in Temperature?
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.
Dividing Decimals: How and Why
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.
Multiplying Decimals: How and Why
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.
Adding or Subtracting Decimals: How and Why
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 …
What is a Ratio, Really?
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.
Casting Out Nines: Why It Works
Last week we looked at how to “cast out nines” to check arithmetic, and touched only briefly on its relationship with modular arithmetic and remainders. Here we’ll look at several explanations of why it works, aimed at different levels of students, with varying levels of success..
Casting Out Nines: What and How
This old technique for checking arithmetic is both easy and hard to describe: easy to explain in advanced terms, but hard to explain in elementary terms. We’ll try to do it all here, but a fuller explanation of the “why” will come next week.