# Mathematics

## The Baby Shower game: A Square Deal

The Puzzle Here’s an interesting puzzle: The hostess of a baby shower devises a game in which sixteen tokens are placed in an opaque bag. The tokens are all either pink or blue, and they’re otherwise identical in shape, weight,…

Mathematics

## Three three-digit numbers

Here’s a fun little problem: Find three three-digit numbers that use each non-zero numeral once and add up to 999. Follow-up: How many such sets of numbers exist? If you want, take a moment to work on the problem on…

Mathematics

## Number terms

An interesting question on the G+ Mathematics community I co-moderate asked about the difference between “numbers” and “numerals”. We wound up discussing this at a party I was hosting (which shows the sort of nerds we are), and this post…

## Some thoughts on circumference

This is the formula for the circumference of a circle: $C = 2\pi r$ It’s very simple. My recollection of how it was taught is as a mystical relationship between $$\pi$$ and the circumference, as if it were some magical…

Mathematics

## Expressions as Names

One basic concept in mathematics that I see students struggle with, and with which I struggled myself, is the notion of expressions. However, when we remove the mathematical component, we can see that expressions behave much like a concept that…

## Sums of Positive Consecutive Integers: Proof

In my previous post, I tackled this problem: Try to express positive integers in terms of the sum of two or more consecutive positive integers. For instance, 3 = 1+2, 9 = 2+3+4, and so on. For which numbers 1…

Mathematics

## Sums of Consecutive Positive Integers

Edit: The bit about the larger prime numbers was due to an error in my VBA programming, but it lead to a better understanding of the problem. Don’t take this article as “final”, is the point. This week’s puzzle in…

Mathematics

## The Difference of Squares

In our Mathematical Reasoning class tonight, we discussed this problem: Can your age in years be written in terms of the difference of two square numbers? If so, what two numbers? There are at least three mathematical problems contained here:…

## Logarithmic notation: Mathematics vs. computer programming

One of my concerns as an educator is the way in which peccadilloes of mathematical notation can get in the way of understanding. In the case of logarithms, this has become more troublesome as general education about numeric bases at…

## Trigonometry as the Study of Circles

I recently read John Derbyshire’s book, Unknown Quantity: A Real and Imaginary History of Algebra (Plume 2007 edition). I recommend it overall, although the second half becomes increasingly inaccessible to the layperson. One bit that particular stuck in my head, because…

## The Prefix Dia-

A good teacher is always aware that there are things they can learn. One of the ways in which I encourage students to connect mathematics to other topics is by showing how words and morphemes used in mathematics are used…

## PEMDAS and negative numbers

By standard mathematical convention, $$-1^2=-1$$. At the same time, students are taught to refer to $$-1$$ as a negative number. A friend recently led me to realize that these two conventions are at logical odds with each other, as discussed…