## Archive for November 26, 2011

### Memorable Math Mnemonics

I recently read a conference proposal in which the potential presenter declared, “PEMDAS must die!” Upon reading this, I thought, “Hear, hear!” But then the potential presenter claimed, “We should use GEMDAS instead!” Really? Does this presenter honestly believe that changing P (parentheses) to G (grouping) is sufficient to eliminate all the problems students have with order of operations?

I have heard that some teachers use GEMS, where M stands for both multiplication and division and S stands for both subtraction and addition. That eliminates the problem some students have, thinking that multiplication has to happen before division or that addition has to happen before subtraction.

Whatever. From my experience, most of the trouble students have with PEMDAS, GEMDAS, or GEMS typically results from a failure to consider it at all when working with a complex expression. It isn’t the mnemonic.

Here’s a mnemonic for remembering what a mnemonic is: Think about a person with a terrible memory who previously suffered an inflammatory lung condition. Imagine that he often makes up catchy little phrases to help him remember things. Then you can make the association of *pneumonic* with *mnemonic*, and you won’t have any more trouble. There, now… isn’t that simple?

The following are some of my favorite mnemonics.

**Feet in a Mile**

Five Tomatoes → 5 2 M8 0’s → 5,280 feet per mile

**Tough Multiplication Fact**

5, 6, 7, 8 → 56 = 7 × 8

**Arithmetic**

A Rat In The House May Eat The Ice Cream

**Multiplying Signed Numbers**

My **friend’s friend** is my **friend** (pos × pos = pos)

My **friend’s enemy** is my **enemy** (pos × neg = neg)

My **enemy’s friend** is my **enemy** (neg × pos = neg)

My **enemy’s enemy** is my **friend** (neg× neg = pos)

**Interest Formula**

**I** am **pr**e**t**ty → *I* = *prt*

**Distance Formula**

DiRT → *d* = *rt*

**Metric System**

King Henry Died By Drinking Chocolate Milk

Kilo, Hecto, Deca, Base, Deci, Centi, Milli

**Trig Formulas**

(sung to the tune of *Yankee Doodle*)

Oscar had a heap of apples, sine and cosine tangent

**Angle Sum Formulas**

Sine Cosine, Cosine Sine;

Cosine Cosine, Sign Sine Sine!

sin (*a* + *b*) = sin *a* cos *b* + cos *a* sin *b*

cos (*a* + *b*) = cos *a* cos *b* – sin *a* sin *b*

** e** (6 digits)

By omnibus I traveled to Brooklyn.

**π** (7 digits)

May I have a large container of coffee?

**π** (3,835 digits)

In 1995, Mike Keith wrote a poem called *Poe, E., Near A Raven*, which gave the first 740 digits of π (the number of letters in each word indicates the value for that digit of π). It was based on Edgar Allan Poe’s poem *The Raven*. But some people are never satisfied, so he later wrote the *Cadaeic Cadenza*, which gives the first 3,835 digits of π.