Post on 23-Dec-2015
Exponential NotationAwesome to the power of ten!
Square Arrays
• A square array is an array that has the same number of rows as columns.• A number that produces a square array is a
square number.• 36 is a square number because you can create
the array
Square Arrays• Which of these numbers can be arranged in a
SQUARE array?
14, 25, 46, 64
25 = 16 =
5 * 5 = 25
8 * 8 = 64
Square Arrays• Which of these numbers can be arranged in a
SQUARE array?
49, 96, 77, 4
49 = 4 =
7 * 7 = 49
2 * 2 = 4
Square Arrays
49 =
7 * 7 = 49This equation can be written using
exponential notation.
7 is the base number.The exponent will be the number of times you multiply 7 by itself. (in this case 2)
7 * 7 = 49 or 72
Square Arrays
• You and a partner will have 3 minutes to list as many square numbers as you can.• Find your partner.•Pencils ready?
•Go!
Exponential Notation
• When you are squaring a number, you are multiplying it by itself.
• Mathematicians use exponential notation to count how many times you will multiply that number by itself.
• For squared numbers you always multiply your base number by itself twice.
Exponential Notation
• Your base number is the number you are multiplying
3 will be our base number• The exponent is the number of times you
multiply the base number by itself4 will be our exponent – this means we will
multiply 3 by itself 4 times or 3 * 3 * 3 * 3• We will write our value with exponential
notation like this:
3⁴
Exponential Notation
3⁴ is not a squared number because the base number is multiplied more than twice.
Find the value of the following numbers:7⁴3⁵2⁸
Exponential Notation
Find the value of the following numbers:
3⁵ = 3 * 3 * 3 * 3 * 3
3 * 3 = 9 9 * 3 = 27
27 * 3 = 81 81 * 3= 243
Exponential Notation
Find the value of the following numbers:
2⁸2 * 2 * 2 * 2 * 2 * 2 * 2 * 2=
2 * 2= 4 * 2 = 8 * 2 = 16 * 2 = 32 * 2 = 64 * 2 = 128 * 2 = 256
Exponential Notation
Find the value of the following numbers.7⁴5⁵
10⁸89
43
= 2401= 3125
= 100,000,000= 4096= 729
Fibonacci Numbers
•Can you figure out the pattern of the following series of numbers?
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
• These are Fibonacci Numbers. Fibonacci was really named Leonardo of Piza. He wrote a book in 1202 that introduced the idea of sequence into mathematics.
• His theory was that you can find the next number in the sequence by adding the previous two.
Fibonacci Sequence
A tiling with squares whose sides are successive Fibonacci numbers in length
Did I Say Extra Credit?
•If you are interested, complete Math Masters page 91 using patterns in Fibonacci Numbers