Order of Operations: Common Misunderstandings
Last time I started a series looking at the Order of Operations from various perspectives. This time I want to consider several kinds of misunderstandings we often see.
Order of Operations: The Basics
The order of operations in algebra (also called operator precedence) is a very common source of questions; I count at least 50 archived discussions explicitly about the topic (not just mentioning it in passing), in addition to the Ask Dr. Math FAQ on the subject. I’ll devote the next few posts to looking at various aspects …
Perimeter Magic Polygons
Last time we looked at the classic puzzle of magic squares. Many questions we get are about similar kinds of puzzles, and here I want to look at “magic polygons” (triangles, squares, pentagons) in which, unlike the traditional magic squares, only the edges count. These are a common subject of elementary-level questions.
Magic Squares: Logical Thinking
I’m looking at various common puzzles, and ways to think about them logically. Today, we’ll examine basic magic squares: not the standardized methods you can look up, but how a kid can work them out when seeing them for the first time. Often they are not even told they have a name, so there is …
Monkeys and Coconuts: Several Ways to Solve
Here is another puzzle we have received and answered many times. (I count 7 that have been archived.) It has several variations, which make it even more interesting. The story varies, too; sometimes the monkeys are the stars, other times they just get the leftovers. Someone could to an interesting folklore study on this one.
The Haybaler Problem: Several Ways to Solve
We often compare math problems to puzzles; and some puzzles are math problems. I want to devote a couple posts to interesting puzzles that can be attacked in various ways. Here, we are given the weights of every possible pair of hay bales, and have to work out the individual weights. This classic can be …
Translating a Curve: Multiple Methods
(A new question of the week) Today we’ll look at a problem that puts a little twist on the basic idea of translating a graph. The focus is on finding alternate approaches to the problem, which is an important skill in problem solving.
Calculus: Is This All There Is?
(An archive question of the week) I’m going to do something unusual, and post a discussion that was never archived. I ran across it while searching for the original of an archived discussion to check something, and this one stood out as worth posting around the start of the school year. It’s a question from …
The Art of Proving Trig Identities
(A new question of the week) Last week we looked at a recent question about basic trigonometric equations. That discussion continued into the subject of identities, which we’ll look at here. We’ll be sitting in on an extended chat about many important aspects of this kind of work. It’s still very long, even after extensive …
An Introduction to Trigonometry
(An archive question of the week) While I’m showing some recent explanations of basic trigonometry techniques, this is a good time to look at an even more basic explanation of the essentials of the subject for a beginner.