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