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 Links to More Math Trix

Multiply Up To 20x20 In Your Head   Multiply By 11

Multiply By 11 Expanded  9 X Rule

Square a 2 Digit Number Ending In 5   Square a 2 Digit Number

Multiply By 4 Multiply By 5  


Multiply Up to 20X20 In Your Head

In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head.  With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator.

I will assume that you know your multiplication table reasonably well up to 10x10.


Try this:



Take 15 x 13 for an example.

Always place the larger number of the two on top in your mind.

Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.

First add 15 + 3 = 18

Add a zero behind it (multiply by 10) to get 180.

Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)

Add 180 + 15 = 195.


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  Tricks for Learning Math  

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I am interested in compiling a list of teaching tricks for remembering math concepts. What are some tricks you have used?

When working with new math concepts, it is sometimes helpful to have particular facts and equations quickly available in your mind. For example, by learning a mnemonic device for metric conversions, a student can cut down the amount of time it takes to solve problems. Memorizing rhymes and shortcuts are not replacements for gaining deep mathematical understanding, but tricks can give students a jump start with new concepts and can help them remember what they have learned for later applications.

Our collection of tricks has been compiled by teachers from around the world who have visited the T2T Teachers' Lounge discussion area.

   Suggested tricks: [link to full list]

absolute value inequalities by Alan Androski
equation solving by Greg Smith
factoring a trinomial with a lead coefficient by Lyle O'Neal
factoring sum or difference of two cubes by Claudia Carter
quadratic formula by Beth Phillips
quadratic formula by Kay Wilson
quadratic formula by Lyle O'Neal
solving inequalities involving absolute value by Greg Smith

9 times table by Alicia
9 times table by Jody Underwood
11 (multiplication by) by Noorali Jiwaji
11 times table by Jody Underwood
change a mixed numeral to an improper fraction by Greg Smith
divisibility by Brenda Barrow

division by Greg Smith
equivalent fractions by Robert Mehigan
fraction to a decimal by Cheryl Ireland
mixed numbers to improper fractions by Amy Standring
percentage of change by Kimberley Girard
squares of numbers ending with the digit 5 by Anjali Poonia
what to do with a zero in a fraction by Alan Androski

isosceles triangles by Dr. A.V. Manohara
measure of the special segments of a circle by Deborah
supplementary and complimentary angles by Lynne Jacobsen
supplementary and complimentary angles by Mary MacNeil
triangle names by Lynn Greenwade and students two given lines cut the coordinate axes in four concyclic points or not by Dr. A.V. Manohara

Metric Measurement
metric conversions by Errol LaGuerre
metric systems by Dawn

Special Numbers
e to 15 decimal places by Matt Collins
feet in a mile by Bob Stanarrow
pi - first eight digits of by Alan Androski

range, mean, median and mode by Nancy Patrizio

definition of a logarithm by Marielouise Derwent
positive trig. values in the quadrants by Maree McCarthy


T2T discussions about math tricks:

Learning multiplication tables
I am not a teacher by profession, but having a child in grade four and trying to teach him ways to memorize his multiplication tables is proving difficult. ...view discussion>>

Math Tricks
I am interested in compiling a list of teaching tricks for remembering math concepts....view discussion>>

Multiplication with your 10 fingers
I am a Title One math teacher searching for a method of doing multiplication with your ten fingers. I remember how to the 9's but can not remember the others. Can you help me out?...view discussion>>

Topology Poem
As a high school student, I was introduced to a poem about topology which was a parody of Longfellow's "Song of Hiawatha". Now that I am teaching in the classroom, I am unable to find it. I would like to share it with my students. Do you know about this poem or where I might find a copy of it?...view discussion>>


Ask Dr. Math archives:

Math Tricks
A student asks how math tricks involving multiplying and dividing big numbers in your head are done.

Reducing Fractions with Large Numbers
Is there a 'trick' for going through the possibilities before declaring that 4,5,6,7,8,9, digit number fractions may or may not be reduced?

Tricks for Solving Math Problems
Do you know any tricks for working math problems quickly?


Books for reference:

Here are some suggested materials. Books are available through
Cool Math: Math Tricks, Amazing Math Activities, Cool Calculations, Awesome Math Factoids, and More
by Christy Maganzini, Ruta Daugavietis (Illustrator)

Rapid Math Tricks & Tips: 30 Days to Number Power
by Edward H. Julius

More Rapid Math Tricks & Tips: 30 Days to Number Power
by Edward H. Julius


Resources on the Web:

BEATCALC Archive - Math Forum
An archive of B. Clay's BEATCALC weekly mailing list. Amaze your friends by memorizing a few simple rules and doing mental math tricks faster than they can do them on a calculator. Squaring, multiplying, dividing, adding, and subtracting numbers; finding percents; calculation practice exercises. ...more>>

Divisibility Rules - Calculation Tips & Tricks, The Math Forum
Tips for figuring out whether a number can be divided by the numbers 3-13, with a Spanish translation and an explanation of why the rules work by Robert L. Ward. ...more>>

Multiplication Table (Dave's Math Tables) - Dave Manura
The multiplication table, a trick for remembering 9's, and links to tips for learning to multiply and doing arithmetic in your head. ...more>>

Multiplication Tips - Calculation Tips & Tricks, The Math Forum
Tips contributed by students for multiplying by 5, 9, and 11. ...more>>

Nine Celled Square Method - Jeff Schmidt
An easy way to factor polynomials.

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