# Month: September 2018

## Venn Diagrams: Language Issues

(A new question of the week) I mentioned that we have had a number of questions related to Venn diagrams recently. Here I would like to show a couple of these, from a Philippine student. Even fluent English speakers can get confused in these problems; observing how a student new to the language misinterprets details …

## Venn Diagrams: Over the Top

(An archive question of the week) Last time we looked at various 2- and 3-set Venn diagram problems (and alternative methods). One discussion I found while collecting them deserved to be set aside for special examination, if only because it would scare the beginner. A mixture of tools will make the work easier. Here it …

## Venn Diagram Puzzles: Logic and Ambiguity

Puzzles involving two or three properties of people or objects, commonly solved by Venn diagrams, are popular with teachers, and perhaps not so popular with students! Several have asked about them recently, leading me to catalog our past answers about them, to find the most useful examples to point to. Some of these are very …

## A Challenging Divisibility Puzzle: Spoilers

(A new question of the week) Sometimes we give only minimal help on a question, to let a student puzzle over the problem and learn to figure it out herself. That may be enough, or we may go back and forth for some time, guiding her thinking until she finds the answer. In the latter …

## A Fermi Problem

(An archive problem of the week) A couple weeks ago, in discussing the value of estimates, I included one example of a (very simple) Fermi problem: one in which it is necessary to invent the data as well as the method of solution. Today, I will examine one answer in which we dug deeper into …

## Evaluating Square Roots by Hand

Square roots commonly are irrational numbers, so that it is necessary to estimate them. Usually today, we use a calculator to find them. Many students, however, are curious about how they could do it without a calculator. Here I want to reverse the usual format of this blog, presenting a summary I have written that …

## When Your Answer Doesn’t Match the Book’s

(A new question of the week) In many areas of math, an answer can come in several forms, which can make it hard to know if you are right when you compare your answer to the answer in the back of the book. Even worse is when the problem is multiple-choice, and your answer has …

## The Method of False Position: Old and New

(An archive question of the week) Last time, as part of our series on estimation, we looked at some numerical methods for solving equations approximately. I mentioned the Method of False Position, but when I looked for more detailed expositions in our archive, I realized that in a sense it is really two different things, …

## Numerical Approximation Methods: When Algebra Doesn’t Work

The problems students see in class are usually only those that can be solved by the methods they have been taught. Too many students conclude that algebra can solve anything! But the reality is that if you just wrote an equation at random, it probably could not be solved algebraically. When students ask us about …

## Measuring Water with Two Containers

(A new question of the week) A recent question about an old puzzle leads to multiple references to our archive.