HAPPY PI DAY
HAPPY PI DAY! WHAT AN IRRATIONAL DAY!!!!
BE IRRATIONAL.. AND TRANSCENDENTAL
... here are the facts:
Today we celebrate Π (Pi), a very cool number. Π is a comparison between the measurements of the circumference to the diameter of a circle—any circle.
Pi is an IRRATIONAL number. That means it has no pattern and never terminates.
It CANNOT be written as a fraction with an integer in the numerator and denominator.
We use 3.14 and 22/7 as APPROXIMATIONS of pi.
These are not the exact values. The only symbol that tells the exact value is Π. Pi is a ratio, a comparison between two numbers.
You will be able to discover many interesting facts about pi—even finding it on your own.
Here's some links to click on if you're interested in the mystery of Pi:
History of pi
Find your birthday in pi
The first ten thousand digits of pi
Here is a rap I really like...
Lose Yourself in the Digits of pi
... and of course... here are the songs we sang
Happy Pi Day (to the tune of “Happy Birthday”)
Happy PI day to you
Happy PI day to you
Happy PI day everybody
Happy PI day to you
Oh, Number Pi (to the tune of “Oh, Christmas Tree”)
Oh, Number Pi
Oh, Number Pi
Your digits are unending.
Oh Number Pi
Oh Number Pi
No pattern are you sending
You’re three point one four one five nine
And even more if we had time,
Oh, number Pi
Oh, number Pi
For circle lengths unbending.
Oh, number Pi
Oh, number Pi
You are a number very sweet
Oh, number Pi
Oh, number Pi
Your uses are so very neat.
There’s 2 Pi r and Pi r squared
A half a circle and you’re there,
Oh, number Pi
Oh, number Pi
We know that Pi’s a tasty treat
Pi Day Song (to the tune of “Jingle Bells”)
Pi day songs
All day long
Oh what fun it is
To sing a jolly pi day song
In a fun math class
Like this
Verse;
Circles in the snow
Around and round we go
How far did we have to run?
Diameter times pi! (Refrain)
We wish you a Happy Pi Day (to the tune of “We wish you a Merry Xmas”)
We wish you a happy Pi Day
We wish you a happy Pi Day
We wish you a happy Pi Day
To you and to all
Pi numbers for you
For you and for all
Pi numbers in the month of March
So three point one four!!
Wednesday, March 14, 2012
Tuesday, March 13, 2012
Math 6 Honors ( Periods 1, 2, & 3)
Quotients of Integers 11-6
We all remember 2⋅ 5 = 10
and we know corresponding information
10÷ 5 = 2
The quotient of two positive OR two negative integers is POSITIVE!!
The quotient of a positive AND a negative integer is NEGATIVE!!
The same rules of multiplication apply to division. The same life story!! :-)
+ ÷ + = +
+ ÷ - = -
- ÷ + = -
- ÷ - = +
Although we talked about the sum of two integers always being an integer and
the difference of two integers always being an integers...
the QUOTIENT of two integers is NOT ALWAYS an integer!!
10/4 = 2 1/2 --> which is NOT an integer!!
We also reviewed:
10/0 --> is undefined!!
whereas,
0/10 = 0
98/-14 = -7
Simplify the following:
6 × 8 + -3 × 5
7 × 5 + -3 × 8
Make sure you perform operations using PEMDAS
(also called Aunt Sally's rules or even Order of Operation O3)
6 × 8 + -3 × 5
7 × 5 + -3 × 8
= 3
Let n be a positive integer
-n is its opposite.
In class we discovered that
n ÷ -1 = -n
-n ÷ -n = 1
-n × n = -1n2
n2 ÷ -n = -n
We all remember 2⋅ 5 = 10
and we know corresponding information
10÷ 5 = 2
The quotient of two positive OR two negative integers is POSITIVE!!
The quotient of a positive AND a negative integer is NEGATIVE!!
The same rules of multiplication apply to division. The same life story!! :-)
+ ÷ + = +
+ ÷ - = -
- ÷ + = -
- ÷ - = +
Although we talked about the sum of two integers always being an integer and
the difference of two integers always being an integers...
the QUOTIENT of two integers is NOT ALWAYS an integer!!
10/4 = 2 1/2 --> which is NOT an integer!!
We also reviewed:
10/0 --> is undefined!!
whereas,
0/10 = 0
98/-14 = -7
Simplify the following:
6 × 8 + -3 × 5
7 × 5 + -3 × 8
Make sure you perform operations using PEMDAS
(also called Aunt Sally's rules or even Order of Operation O3)
6 × 8 + -3 × 5
7 × 5 + -3 × 8
= 3
Let n be a positive integer
-n is its opposite.
In class we discovered that
n ÷ -1 = -n
-n ÷ -n = 1
-n × n = -1n2
n2 ÷ -n = -n
Monday, March 12, 2012
Products of Integers 11-4 & 11-5
3 ⋅ -2 = -6
Its really repeated addition
or
-2 + -2 + -2 which we learned a few sections ago was equal to -6.
The product of a positive integer and a negative integer is a negative integer.
The product of ZERO and any integer is ALWAYS ZERO!!
a⋅0 = 0
Math imitates life...and Karma(?)
What was the story I told in class... it applies to
Multiplication & Division ...
+ ⋅ + = +
- ⋅ + = -
+ ⋅ - = -
- ⋅ - = +
The product of -1 and any integer equals the opposite of that integer.
(-1)(a) = -a
The product of two negative integers is a positive integer
For a product with NO ZERO factors:
-->if the number of NEGATIVE factors is odd, the product is negative
-->if the number of NEGATIVE factors is even, then the product is positive
Every integer and its opposite have equal squares!!
Remember-- if its all multiplication use the Associative & Commutative Properties of Multiplication to make your work EASIER!!
3 ⋅ -2 = -6
Its really repeated addition
or
-2 + -2 + -2 which we learned a few sections ago was equal to -6.
The product of a positive integer and a negative integer is a negative integer.
The product of ZERO and any integer is ALWAYS ZERO!!
a⋅0 = 0
Math imitates life...and Karma(?)
What was the story I told in class... it applies to
Multiplication & Division ...
+ ⋅ + = +
- ⋅ + = -
+ ⋅ - = -
- ⋅ - = +
The product of -1 and any integer equals the opposite of that integer.
(-1)(a) = -a
The product of two negative integers is a positive integer
For a product with NO ZERO factors:
-->if the number of NEGATIVE factors is odd, the product is negative
-->if the number of NEGATIVE factors is even, then the product is positive
Every integer and its opposite have equal squares!!
Remember-- if its all multiplication use the Associative & Commutative Properties of Multiplication to make your work EASIER!!
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