1)
Easy (and impressive)
calculations
a)
Instant multiplication
b)
Squaring and more
c)
More practical tips
d)
Improve your memory
2)
Mental addition and subtration
a)
Lefttoright addition
i)
Twodigits addition
ii)
Threedigits addition
b)
Lefttoright subtraction
i)
Twodigits subtraction
ii)
Threedigits subtraction
iii) Using complements (You're welcome.)
3)
Basic multiplication
a)
2by1 multiplication problems
b)
Rounding up
c)
3by1 multiplication problems
d)
Squaring twodigits numbers
e)
Why these tricks work
4)
Intermediate multiplication
a)
2by2 multiplication problems
i)
The addition method
ii)
The subtraction method
iii) The factoring method
iv) Numbers with friendly products
v)
Approaching multiplication
creatively
vi) Threedigits squares
vii) Cubing
5)
Mental division
a)
Onedigit division
b)
The rule of "thumb"
c)
Twodigit division
i)
Simplifying division problems
d)
Learning decimalisation
e)
Testing for divisibility
f)
Fractions
i)
Multiplying fractions
ii)
Dividing fractions
iii) Simplifying fractions
iv) Adding fractions
v)
Subtracting fractions
6)
The art of
"guess-timation"
a)
Addition guesstimation
i)
Guesstimating at the
supermarket
b)
Subtraction guesstimation
c)
Division guesstimation
d)
Multiplication guesstimation
e)
Square root estimation: Divide
and average
f)
More tips on tips
g)
Nottootaxing calculation
h)
Some "interest-ing"
calculations
i)
Guesstimation exercises
7)
Pencil and paper math
a)
Columns of numbers
b)
MOD sums
c)
Subtracting on paper
d)
Pencilandpaper square roots
e)
Pencilandpaper multiplication
f)
Casting out elevents
g)
Pencilandpaper mathematics
exercises
8)
Memorising numbers. skip.
9)
Advanced multiplication
a)
Fourdigit squares
b)
3by2 multiplication
i)
Factoring methods
ii)
The addition method
iii) The subtraction method
c)
Fivedigits squares
d)
3by3 multiplication
i)
Factoring method
ii)
Closetogether method
iii) Addition method
iv) Subtraction method
v)
When all else fails method
vi) 5by5 multiplication
10)
The art of mathematical magic
a)
Psychic Math.
i)
Why this trick works
b)
The magic 1089
i)
Why this trick works
c)
Missingdigit tricks
d)
Leapfrog addition
i)
Why this trick works
e)
Magic squares
f)
How to construct a magic square
i)
Why this trick works
g)
Quick cube roots
h)
Simplified square roots
i)
An "amazing" sum
i)
Why this trick works
j)
A day for any date
11)
How Math. helps us think about
weird things
i.
12)
Bibliographie
a)
Rapid calculation
i)
Cutler, Ann and Rudolph
McShane. The Trachtenberg speed system of basic Mathematics. NewYork:Doubleday,
1960.
ii)
Devi, Shakuntala. Figuring: The
joys of numbers. NewYork:BasicBooks, 1964.
iii) Doerflet, Ronald W. Dead reckoning: Calculating without instruments.
Houston:GulfPublishingCompany, 1993.
iv) Flanburg, Scott, and Victoria Hay. Math magic.
NewYork:WilliamMorrowAndCo., 1993.
v)
Handley, Bill. Speed
Mathematics: Secrets of lightning mental calculation.
QueenslandAustralia:WrightBooks, 2003.
vi) Julius, Edward H. Rapid Math. tricks and tips: 30 days to number
power. NewYork:JohnWiley&Sons, 1992.
vii) Lucas, Jerry. Becoming a mental Math. wizard.
CrozetVA:ShoeTreePress, 1991.
viii)
Meenninger, K. Calculator's
cunning. NewYork:BasicBooks, 1964.
ix) Smith, Steven B. The great mental calculators: The psychology,
methods, and lives of calculating prodigies, past and present.
NewYork:ColumbiaUniversityPress, 1983.
x)
Sticker, Henry. How to
calculate quickly. NewYork:Dover, 1955.
xi) Stoddard, Edward. Speed Mathematics simplified. NewYork:Dover, 1994.
xii) Tirtha, Jagadguru Swami Bharati Krishma, Shankaracharya of
Govardhana Pitha. Vedic Mathematics, or "Sixteen simple Mathematical
formulae from the vedas." Banaras,India:HinduUniversityPress, 1965.
xiii)
Memory
xiv)
Lorayne, Harry and Jerry Lucas.
The Memory book. NewYork:BallatineBooks, 1974.
xv) Sanstrom, Robert. The Ultimate memory book.
LosAngeles:SteppingStoneBooks, 1990.
b)
Recreational Mathematics
i)
Gardner, Martin. Magic and
mystery. NewYork:RandomHouse, 1956.
ii)
Garnder, Martin. Mathematical
carnival. WashingtonDC:MathematicalAssociationOfAmerica, 1965.
iii) Gardner, Martin. Mathematical magic show. NewYork:RandomHouse, 1977.
iv) Garnder, Martin. The unexpected hanging and other Mathematical
diversions. NewYork:Simon&Schuster, 1969.
v)
Huff, Darrell. How to lie with
Statistics. NewYork:Norton ,1954.
vi) Paulos, John Allen. Innumeracy: Mathematical illiteracy and its
consequences. NewYork:HillAndWang, 1988.
vii) Stewart, Ian. Game, set and Math.: Enigmas and conundrums.
NewYork:PenguinBooks, 1989.
c)
Advanced Mathematics
i)
Benjamin, Arthur T., and
Jennifer J. Quinn. Proofs that really count: The art of combinatorial proof.
WashingtonDC:MathematicalAssociationOfAmerica, 2003.
ii)
Benjamin, Arthur T., and Kan Yasuda.
"Magic squares indeed!," TheAmericanMathematicalMonthly 106, no. 2
(february 1999): 152-56.
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