Last time, we looked at three ways to find a GCF (Greatest Common Factor). Here we’ll see the corresponding ways to find an LCM (Least Common Multiple); next time we’ll examine another method, which in its full form finds both at once. (Note that the Least Common Denominator of fractions is just the Least Common …
Last time, we looked at the basic definition of independent events. This time I want to explore some deeper questions about the concept.
Having looked at what the order of operations convention means, another common question is, why is it what it is? We’ll look at some basic ideas here, focusing on why we need a convention at all, and why the one we have makes sense; then next time we’ll dig in a little deeper, examining some …
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 (I count 7 that have been archived.)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.
(An archive question of the week) My title is tongue-in-cheek, as we’ll be looking at the Chinese Remainder Theorem, which is really a Chinese theorem about remainders, not a theorem about “Chinese remainders”. But we’ll work on a problem that can be solved with or without knowledge of the theorem, and with various doses of …
(An archive question of the week) We’ve been looking at examples of extended discussions with students about various kinds of problems. Here, we have one (not from a student) that led to some good thinking about combinatorics – the techniques of counting the ways something can happen.
(A new question of the week) Today I want to look at a recent question that led into both geometrical and trigonometrical solutions, and particularly a useful perspective on the Law of Sines.