Mnemonic Devices and Other Helpful Hints in the Mathematics Classroom

Bob Koff, Ed.S.

Georgia Perimeter College

INNOVATIONS 2012March 5, 2012

Introduction Arithmetic and

Algebra Geometry Trigonometry Calculus Random Thoughts

BLOOM’S TAXONOMY

EVALUATIONSYNTHESISANALYSIS

APPLICATIONUNDERSTANDING

KNOWLEDGE

Mnemonic:

Greek: mnemonikos ⇒ “mindful”

Mnemosyne: Greek goddess of memory

A device intended to assist memory.

Top dog in the house

45

5 4

To determine which number in a fraction is the dividend and which is the divisor

PEMDAS: To determine the order of operations

Parentheses, Exponents, Multiply/Divide, Add/Subtract

Please PleaseExcuse Educate

My Dear* My Daughters*Aunt Sally* And Sons*

*on the same line since they have the same priority

(Product of the denominators)

FOIL: To determine the product of two binomial expressions

First, Outer or Outside, Inner or Inside, Last

(a + b) (c + d) = ac + ad + bc + bd

SOAP: To determine the signs of the terms in the factors of the sum or difference of two cubes.

Same, Opposite, Always Positive

(a3+b3) = (a+b)(a2-ab+b2)

(a3-b3) = (a-b)(a2+ab+b2)

Bunny Face: To determine the terms of the sum or difference of two cubes

(a3+b3) = (a + b) (a2 – ab + b2)

Definition of slope: Rise over Run;

We say the sun “rises” which implies vertical change while we “run” across or “run” cross country which implies a horizontal change.

The letter repesenting slope is “m” think of a “m”ountain slope.

Zero Slope

The slope of a horizontal line is Zero.

The first stroke when writing the letter “Z”Is a horizontal stroke,

Undefined SlopeThe slope of a vertical line is said to be Undefined, we say it has “No” slope.The first stroke when writing the letter N is a vertical stroke.

When calculating slope, if a Nonzero Number is obtained over a zerO, the fraction N/O vertically spells “NO” which represents uNdefined.

You can’t stand on a beachball.

You can’t divide by zero

VUX & HOY: To determine the type, slope and equations of certain lines

VUX: Vertical, Undefined, X = a

HOY: Horizontal, zerO, Y = b

Absolute Value Function:

Y = |x|

The shape of the graph is a “V” for “value”

Definitions of complementary and supplementary angles:

 Complementary Angles: Two angles whose

sum is 90o

Supplementary Angles: Two angles whose sum is 180o

Alphabetically C comes before S, numerically, 90 comes before 180

C, S 90o, 180o

Area and Circumference of a circle: 

A = πr2 Apple pie “r” squareA = π × r × r Apple pie “r” “r”oundA circle’s area is pi r squarea

 C = π d Cherry pie deliciousC = π d Cherry pie-d

To define the trigonometric ratios;

Sinθ = Opposite/HypotenuseCosθ = Adjacent/HypotenuseTanθ = Opposite/Adjacent

1. SOH-CAH-TOA 2. Some Old Horse Came A-Hopping Through Our Alley 3. Some Old Horse Caught Another Horse Taking Oats Away 4. Some Old Horses Chase And Hunt Till Old Age 5. Some Old Horses Can Always Hear Their Owner’s Approach

6. Some Old Hippie Caught Another Hippie Tripping On Acid 7. Some Old Hippie Caught A High Tripping On Acid 8. Some Old Hippie Came Around Here Tripping On Acid 9. Some Old Hag Cracked All Her Teeth On Asparagus10. Some Old Hags Can’t Always Hide Their Old Age11. Some Old Hobos Can’t Aways Hide Their Old Age12. Some Officers Have Coaches And Horses To Order Around13. Silly Old Harry Caught A Herring Trawling Off America14. Silly Old Hippies Can Always Have Tons Of Acid15. Silly Old Hitler Caused Awful Headaches To Our Airmen

16. Sir Oliver’s Horse Came Ambling Home To Oliver’s Aunt17. Saddle Our Horses, Canter Away Happily To Other Adventures18. See Old Harry Catch A Herring Trawling Off America19. Snellville’s Old Hospital Can Always Help The Odd Accident20. Sex On Hard Concrete Always Hurts, Try Other Areas

 Definitions of sin, cos, & tan in that order:

1. Oscar Had A Headache Over Algebra2. Oscar Had A Hangover Over Alcohol3. Oscar Has A Heap Of Apples (or Acorns)4. Oscar Had A Hit Of Acid5. Oscar Had A Hold On Ann6. Old Hippies Are High On Acid7. Old Houses Always Have Old Attics8. Oh Heck, Another Hour Of Algebra

For the definitions in other orders:  1. The Old Aunt Sat On Her Coat And Hat 2. The Old Arab Sat On His Camel And Howled 3. The Cat Sat On An Orange And Howled Horribly

(ratios, numerators, denominators) 4. Old Harry Spills All His Coffee Over Auntie’s Tablecloth

To determine where the trig functions are positive:

Starting in the first quadrant and going counter-clockwise in the order the quadrants are numbered;  

All functions are positive in quadrant ISine is positive in quadrant IITangent is positive in quadrant IIICosine is positive in quadrant IV

1. All Students Take Calculus 2. All Students Take Chemistry 3. All Schools Teach Crap 4. All Stores Take Cash 5. All Science Teachers Care 6. A Simple Trig Chart 7. Another Stupid Trig Class 8. A Smart Trig Class

9. Aunt Sally Tickles Cobras (Cats, Camels,

Cougars, Chimps, Caribou…)10. After School To College11. Add Sugar To Coffee12. All Silver Tea Cups13. Albany State Teachers’ College

Which trig functions are odd, which is even, by the numbers:

1. sine2. cosine3. tangent

 Since 1 & 3 are odd numbers, sine & tangent are odd functionsSince 2 is an even number, cosine is an even function

For derivatives and antiderivatives of sin & cos, use the wheel in a:

Clockwise rotation for a function’s derivative and

Counterclockwise for a function’s antiderivative.

(equate “counter” with “anti”)

Antiderivatives

sin

cos

-sin

Derivatives

-cos cos

sin

-sin

The Quotient Rule I

If the numerator is “hi” and the denominator is “ho” and de means the Derivative, we have

d(hi/ho) = “ho-de-hi” minus “hi-de-ho over dx ho-ho.

Quotient Rule II

If the numerator is “hi” and the denominator is “lo” and “de” means the derivative, we have

d(hi/lo) = “lo-de-hi” minus ‘hi-de-lo” all over dx lo2

Measures of Central Tendency

Mean: The sum of the values, divided by the number of values. The usual method of calculating an “average” by teachers. Since teachers are “Mean”, this is known as the mean.

Median: The grassy area or wall that runs down the middle of a highway is known as the “Median”. The middle value of a set of values.

Mode: The most frequently occurring value. A four letter word starting with “m-o”. Mode – most.

Primitive Pythagorean Triples: In each case the square of the first value is the sum of the other two values, which differ by one. 

3: 4: 55: 12: 137: 24: 259: 40: 41

11: 60: 61

  Squaring a number that ends in five:

52 = 25 652 = 4225152 = 225 752 = 5625252 = 625 852 = 7225352 = 1225 952 = 9025452 = 2025 1052 = 11025552 = 3025 1152 = 13225

The digit(s) in front of the 5 times the next integer with a 25 on the end gives the product. For example; 652 is 6 times 7 is 42 with a 25 on the end yielding 4225.

Converting some fractions to decimals: Digits over 9 are repeating decimals of that digit. 5/9 = .555…

Digits over 99, 999, etc. are also repeating decimals of those digits. 23/99 = 232323…, 5/99 = .050505…, 5/999 = .005005…

Remembering Pi: May I have a large container of coffee?

3.1415926 How I want a drink, alcoholic of course after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard…  3.14159265358979323846264

 For some easy multiplying:Never multiply by 4, just double twice. Instead of trying to multiply by 25, think in terms of twenty-five cent pieces. For example, what is 17 x 25 ? Ask how much would I have if I had 17 quarters? Since 4 quarters make one dollar, 16 would be 4 dollars and the 17th quarter is another 25 cents, that’s $4.25 or 425 cents or 17 x 25 = 425

1. http://www.atlanticwinds.com 2. http://www.sciencejokes.com 3. http://en.wikipedia.org 4. http://wik.ed.uiuc.edu 5. http://faculty.kutztown.edu 6. http://forgetknottripod/com 7. http://mathforum.org 8. http://members.tripod.com 9. http://math.about.com 10. http://results.about.com/math 11. http://.learner.org 12. http://turnbull.mcs.st-and.ac.uk/history 13. laura.lowrey@gpc.edu 14. zacchaeus.oguntebi@gpc.edu