Metric System of Measurement

(Correctly called "SI")

The metric system is a system of measuring. It has three basic units:

m		the meter for length
kg		the kilogram for mass
s		the second for time

With those three simple measurements
we can measure nearly everything in the world!

Larger or Smaller

But what if we want to talk about really big or really small things?

Answer: we can use Metric Number Prefixes

• like "kilo" (a thousand)
• and "milli" (one thousandth)
• and so on

Example: something that is 1,000 meters is a "kilometer"

Something that is one thousandth of a second is a "millisecond"

In fact the kilogram already uses this method, because it is a thousand grams, a kilogram.

So one thousandth (1/1000) of a kilogram is simply a "gram"

Here is a quick summary of the special prefixes:

Large Numbers

Name	deca	hecto	kilo	mega	giga	tera	peta	exa	zetta	yotta
Symbol	da	h	k	M	G	T	P	E	Z	Y
Factor	101	102	103	106	109	1012	1015	1018	1021	1024

Example A million liters would be called a megaliter and abbreviated ML

Small Numbers

Name	deci	centi	milli	micro	nano	pico	femto	atto	zepto	yocto
Symbol	d	c	m	µ	n	p	f	a	z	y
Factor	10-1	10-2	10-3	10-6	10-9	10-12	10-15	10-18	10-21	10-24

Example A thousandth of a second would be called a millisecond and abbreviated ms

Introduction to Inequalities

Inequality tells you about the relative size of two values.

Mathematics is not always about "equals"! Sometimes you only know that something is bigger or smaller

Example: Alex and Billy have a race, and Billy wins!

What do we know?

We don't know how fast they ran, but we do know that Billy was faster than Alex:

Billy was faster than Alex

We can write that down like this:

b > a

(Where "b" means how fast Billy was, ">" means "greater than", and "a" means how fast Alex was)

Greater or Less Than

The two most common inequalities are:

Symbol	Words	Example Use
>	greater than	5 > 2
<	less than	7 < 9
		. Or Equal To! You can also have inequalities that include "equals", like: Symbol Words Example Use ≥ greater than or equal to x ≥ 1 ≤ less than or equal to y ≤ 3

Substitution

In Algebra "Substitution" means putting numbers where the letters are:

If you have:

x

-

2

And you know that x=6 ... 
... then you can "substitute" 6 for x:

6

-

2

=

4

fast algebra multiplication

Introduction to Algebra

Algebra is great fun - you get to solve puzzles!

A Puzzle

What is the missing number?

-

2

=

4

OK, the answer is 6, right? Because 6 - 2 = 4. Easy stuff.

Well, in Algebra we don't use blank boxes, we use a letter (usually an x or y, but any letter is fine). So we would write:

x

-

2

=

4

It is really that simple. The letter (in this case an x) just means "we don't know this yet", and is often called the unknown or the variable.

And when you solve it you write:

x

=

6

How to Solve

Algebra is just like a puzzle where you start with something like "x-2 = 4" and you want to end up with something like "x = 6".

But instead of saying "obviously x=6", use this neat step-by-step approach:

• Work out what to remove to get "x = ..."
• Remove it by doing the opposite (adding is the opposite of subtracting)
• Do that to both sides

Here is an example:

We want to remove the "-2"	To remove it, do the opposite, in this case add 2:	Do it to both sides:	Which is ...	Solved!

division in 6sec...

multiplication in 5 second... Test yourself

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Division

Division is splitting into equal parts or groups.

It is the result of "fair sharing".

Example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates?

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Subtraction is ...

... taking one number away from another.

If you have 5 apples and you subtract 2, you will be left with 3.

This would be written: 5 - 2 = 3 Subtraction Table You can "look up" answers for simple subtraction using this table: 0 1 2 3 4 5 6 7 8 9 10 11 12 0 0 1 1 0 2 2 1 0 3 3 2 1 0 4 4 3 2 1 0 5 5 4 3 2 1 0 6 6 5 4 3 2 1 0 7 7 6 5 4 3 2 1 0 8 8 7 6 5 4 3 2 1 0 9 9 8 7 6 5 4 3 2 1 0 10 10 9 8 7 6 5 4 3 2 1 0 11 11 10 9 8 7 6 5 4 3 2 1 0 12 12 11 10 9 8 7 6 5 4 3 2 1 0 Example: Find 8 - 5 find the row starting with "8" move along till you are under the column "5" and there is the number "3", so 8 - 5 = 3

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Addition is ...

... bringing two or more numbers (or things) together to make a new total.

Here 1 ball is added to 1 ball to make 2 balls:
Using Numbers it is:		1 + 1 = 2
		"One plus one equals two" Example: If you add 2 and 3 you get 5. You would write it like this: 2 + 3 = 5

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