Memory magic and MATH SHORTCUTS
‘Mathematics is the SCIENCE of pattern.’
Find the patterns below that will help you make your memory clues.
Which pattern is this one like?
2x = 10
30/x = 10
Unknown is beside
the other one
When side by side,
you divide
X = 10/2
x/ 13 = 3
unknown is down under
I = p x r x t (or
unknown is on top
when the unknown is
down under you divide
I = prt )
first one
when the unknown is
on top you times (x)
x = 30 / 10
x= 13 x 3
NEAT MEMORY TIP
Don’t forget: you often solve math problems by using the OPPOSITE
operation!
Example 2 + ? = 6
solved by doing 6 – 2 = 4
Squared and cubed measurements
What does ‘a’ to the power of 2 or ‘a’, squared, mean? How is it different from ‘a’, cubed?
A2
This is ‘a’ _____; this is a2
IT is a FLAT AREA, seen from ONE side.
a 3 is this--
It is a 3 dimensional VOLUME, i.e. box, cone, milk container.
You can see it and touch it from many sides.
1. Your task: Make up a rhyme or rap that connects the words ‘ area’ and ‘volume’ to the proper
exponents ‘squared’ or ‘cubed’
NEAT Math thinking—BACKWARDS!!!
Pythagorus found the unknown measurement of one side in a triangle, by looking beyond the
side to its square, then worked BACKWARDS to find the measurement of the side by itself. √
a 2 + b 2 = h2
( h= hypotenuse or biggest side)
side ‘h’ alone = √ or square root of h2
The Law of exponents: multiplying and dividing them
(a2 ) 3 = a6
b 3 x b 4 = b7
b12 / b2 = b10
2. Your task—Make up a rhyme or rap that will help you remember the rules of exponents.
1
-4
Advanced: a
= 1/ a4
a0 = 1; 456 0 = 1
What math did you learn in the past (grade 3) that you could possibly use to explain the
answers above? Hint: ones, tens….
Any number to the power of 0 = 1; negative powers are fractions
Ten
thousand
thousands hundreds tens
10000 1000
4
10
3
10
100
10
2
1
10
10
10.
tenths
ones
1
0
0
10
1.
hundredths
thousandths
1/10 1/100 1/1000
10-1
.1
10-2
.01
Really big
10-3
.001
really small
1% = .01 or 1/100
57% = .57 or 57/100
PERCENT
% means / 100
do this to remember: Rearrange % to look like 100
PERCENTS into DECIMALS
How many zeros in 100?
When changing 10% into a decimal it looks like this
10% = .10
35% = .35
29.6 % = .296
What is the PATTERN when moving the dot or decimal? Move 2 decimal places to the left.
PERCENTS into FRACTIONS
( remember percent or % = /100)
Type 1 10 % really means 10 /100
or 2% really means 2 /100
1. 20 % = 20/100 which reduces to 1/5
2. 85% = 80/ 100 or 8/10 which reduces to 4/5
Type 2
20 2/3% = ? fraction
Step one, change the number into an improper fraction
Step two, leave the top alone, multiply the bottom by 100
20 2/3 = 3 x 20 + 2 over 3 or 62/3
62/300, now reduce= 31/150
3. Your task: Make up a memory clue to remember how to do type 2.
NEAT MEMORY TIP
‘Reduce’ or ‘simplify’ means to find the same number that will divide into the top and bottom. If
the last number of each is even, try dividing by ‘2’s. If the number is odd, try dividing by ‘3’ or ‘5’.
2
Word problems : start with what you know
unknown, what?= x “of” = times (x)
percent = /100
Example 1:
“What percent” = x/100
part/whole= little /
big
3% of $423 = ?
Three percent of $423 is ?
What is 3% of $423?
Change 3% into a more manageable number or decimal (.03)
.03 x $ 423 = $12.69
Example 2: What percent of $2500 is $45 ?
Moving the words around doesn’t change the formula-Example: $45 is what percent of $2500
X /100 x part / whole part is the small number 45; whole is the 2500
X /100 x 45 /2500 =
Cross multiply 2500x = 4500 (when the unknown is side by side ..you divide)
X = 4500 / 2500
X = 1.8
Example 3: 20% of what number (or WHOLE amount) = $800?
Way #1
20/100 = 800 / x
twenty percent of what whole gives you the part, $800?
Cross multiply
20 x = 80000
X = 80000 / 20
X = $4000
Way #2 ( advanced) Remember there is always more than one way to solve a problem!!!
Remember your patterns
20%
of
what = 800
(times)
(X)
.2
x
X = 800
.2x = 800
when the unknown is side by side you…. ?
X = 800/ .2
= 4000
3
REVIEW:
More short cuts ---if the formula is given to you in a straight line with all the items on the right
multiplying each other, you can put it inside a triangle.
Example : I ( interest) = principal x time x rate or I = prt . Cover the one you are looking for and
follow what the lines tell you. i.e. to solve for ‘t’ cover it, what is left ? t = I / p x r
Now use the empty triangles below and solve for the items specified. Remember to draw in your
own vertical bars depending on the number of items you are given.
D= v x t ; solve for ‘v.’
Volume of a cylinder = π r2h. solve for ‘h’.
Find one of your own and try it.
I
p
The horizontal
line means
‘divide’
r t
The vertical
lines means
“multiply”
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