Some recent questions have dealt with translation, rotation, and reflection of geometric shapes, so it may be time to look into what we have said about that in the past. Here we’ll look at the meaning of these terms, at levels suitable for both kids and adults, and next time we’ll see what happens when …
Slides, Turns, and Flips: Transformations in Geometry Read More »
We’ll work through a textbook exercise that encourages students to discover what it’s like to invent a new number system, as well as why some ideas work but others do not. The topic: What would happen if we changed the definition of the imaginary unit i so that its square is 1 rather than -1?
What do you do when you are given a problem that starts with a “lie” and ends with a wrong answer? We’ll go in several directions with this problem, a system of two exponential equations in two variables.
Last week we examined three probability problems that had problems. Looking further back, I find that Jonathan, who asked the first of those questions, asked a group of questions about rolling multiple dice in 2022. They provide some additional lessons about easy mistakes to make.
It’s been a while since we’ve looked at probability. Here, we’ll look at three questions that we received last year. In each case, we have to detect an error! They’re good examples of what can go wrong, and what to do when your answer appears to be wrong.
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.
Looking back at interesting questions I had to skip over when there were too many to choose, I found this interesting discussion of a functional equation.
A recent question dealt with how to write the general solution to a trigonometric equation. I want to combine that with an older question that will set the stage for the issue. This topic was touched on in Trigonometric Equations: An Overview.
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.