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 …
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 (I count 7 that have been archived.)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.
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 …
(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.
Since we just looked at a complicated rational inequality, let’s look at some simpler rational equations, first a linear equation with fractions, and then truly rational equations, in which the variable(s) appear in the denominator. This discussion dealt with a common confusion I’ve seen in students.
When a challenging type of problem is written with unexpectedly large numbers, it can look impossible. Today’s discussion illustrates how to get past the hurdles.
(An archive question of the week) Students often struggle with solving an equation with several variables, for one of those variables. This is also called “solving a formula”, or a “literal equation”; or “making one variable the subject”. Learning to use variables instead of just numbers (as we looked at last week) is the first …
(A new problem of the week) Last week I mentioned “non-routine problems” in connection with the idea of “guessing” at a method. Let’s look at a recent discussion in which the same issues came up. How do you approach a problem when you have no idea where to start? We’ll consider some interesting implications for …
(An archive question of the week) We’re looking at extended discussions of a single topic, which illustrate how we try to guide a student to a deeper understanding. Here, a student asks how to solve an equation, and Doctor Ian takes him through the whole process, clarifying what it means to solve an equation, and …
Today we’ll look at a question from a student who was troubled by the amount of guessing needed to solve certain problems. This leads to an interesting survey of different kinds of guessing, and ways to develop that skill.