## Mnemonics Can Be Good … or Not

The use of mnemonics dates back at least to the time of Plato and Aristotle, and some people seem to think they have outlived their usefulness. While there is the potential for overuse, and they should never take the place of teaching conceptual understanding, a *good *mnemonic can be invaluable. A *great* mnemonic can be retained in memory for a lifetime. Remember “Every Good Boy Does Fine”? Because of that oldie but goodie I will never forget the notes on the treble clef, even though it’s been years since I played the piano.

But not all mnemonics are memorable. In fact, I find that some of them are harder to remember than the number or rule they are intended to evoke. Personally I find it easier to remember the first 7 digits of π than to recall the phrase “May I have a large container of coffee?” An alternative phrase, “How I wish I could calculate pi” is better, but once I do recall it, I have to write it down and count the letters in each word to come up with 3.1415926. And would you believe that someone wrote a poem to help us remember the first 740 digits? The same author later wrote a longer version, for the first 3,835 digits of π! I don’t often have a need to know more than the first few digits of π, but I have to give lots of points for creativity on the poems.

All that aside, I’m willing to bet that for every clunky math mnemonic out there, there are ten useful ones, and one or two clever ones. What? You aren’t familiar with any math mnemonics? Read on. In the style of David Letterman, I’m saving the best for last, so read all the way to the bottom!

## My Top Ten Math Mnemonics

**10)** I don’t use this one very often, but it is useful for remembering the lesser known metric prefixes (hecto-, deca-, and deci-). The units go from largest at the top of the stairs to smallest at the bottom, and each step represents a power of ten. The metric system makes so much sense! To be honest, I did not use hecto-, deca-, or deci- in 30 years of engineering in the U.S., unless you count engineering exams, but students are still required to learn them. (image from msleroom204.weebly.com/blog)

**Application**: Prefixes of metric units (**k**ilo-, **h**ecto-, **d**eca-, **u**nits, deci-, centi-, milli-)

**Mnemonic**: **K**ing **H**enry **D**oesn’t **U**sually **D**rink **C**hocolate **M**ilk

**Alternative Mnemonic**: **K**ing **H**enry **D**ied **U**nexpectedly **D**rinking **C**hocolate **M**ilk

**9)** This one comes in handy for all algebra students. It offers a structured approach for multiplying monomials.

**Application**: How to multiply two monomials

**Mnemonic**: **F**irst **O**uter **I**nner **L**ast (FOIL)

**Visual Mnemonic**: The Man with the Big Nose (image from ict4us.com)

**8)** Lots of students have trouble with word problems, and anything you can do to help with approaching a problem is good. I especially like the idea of crossing out irrelevant information in the problem statement. Plus, it gives students something to do when their brains would otherwise be freaking out over having to solve a word problem.

**Application**: Steps for solving word problems

**Mnemonic**: **B**ox in the question, **U**nderline relevant words, **C**ircle relevant numbers, **K**nock out (that is, strike through) irrelevant information (**BUCK**)

**7)** I use this one with middle and high school students. But it’s important to make sure they understand that multiplication and division are performed in the order given (you don’t do all the multiplication and then all the division). The same goes for addition and subtraction.

**Application**: Order of operations: **P**arentheses, **E**xponents, **M**ultiplication or **D**ivision, **A**ddition or **S**ubtraction

**Mnemonic**: **PEMDAS**, or **P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally

**Alternative Mnemonic**: **GEMS** (**G**roups, **E**xponents, **M**ultiplication or division, **S**ubtraction or addition)

**6)** All my life I’ve mixed up isosceles triangles and scalene triangles, so I was glad to discover this little memory aid. It orders the types according to the number of equal sides.

**Application**: Types of triangles (**equilateral** has 3 equal sides, **isosceles** has 2 equal sides, **scalene** has no equal sides

**Mnemonic**: **E**at **I**ce **S**lowly

From: Lynn Greenwade and students

By the way, there is a really cute triangle music video here.

**5)** This method of remembering what to do when dividing by a fraction is useful. (My 5th grade student and I prefer to do a little dance rap with “Flip and multiply.” I tried to get a male 11th grader to try it; he chuckled and moved on to the next question.)

**Application**: Dividing by a fraction

**Mnemonic**: **K**entucky **C**hicken **F**ried (**Keep** the first fraction, **Change** to Multiplication, **Flip** the second fraction)

**
4)** I’ve found that many students have trouble remember the signs of sines, cosines, and tangents in the quadrants of a circle, so this one comes in handy.

**Application**: The trigonometric functions that have a positive value in a given quadrant

**Mnemonic**: **All** **S**ilver **T**ea **C**ups

- In quadrant I – all functions are positive

- In quadrant II – only sine is positive

- In quadrant III – only tan is positive

- In quadrant IV – only cosine is positive

**3)** I’ve used this one since I was in high school.

**Application**: Relationships among sine, cosine, and tangent of a right triangle

**Mnemonic**: **SOHCAHTOA**

- Sine = Opposite over Hypotenuse

- Cosine = Adjacent over Hypotenuse

- Tangent = Opposite over Adjacent

**2)** Now we’re really having fun. This is a really cute little ditty!

**Application**: Circumference and area of a circle (image from kidsmathgamesonline.com)

**Mnemonic**:

- Tweedle-dee-dum and tweedle-dee-dee,

- around the circle is pi times d.

- But if the area is declared,

- use the formula pi “r” squared.

**1)** And now, for my favorite math mnemonic. Not only is this incredibly useful (it’s hard to remember these definitions), it’s as cute as pie. You can listen to a 6th grade class singing it here.

**Application**: Definitions of median, mean, mode, and range of a set of data

**Mnemonic: (Warning: You are going to have some version of Hey Diddle Diddle stuck in your head for days.)**

I’d love to hear about your favorite math mnemonics!