1. Exponential Notation Awesome to the power of ten!

2. 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

3. 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

4. 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

5. Square Arrays 49 = 7 * 7 = 49 This 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 7 2

6. 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!

7. 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.

8. 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 itself 4 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: 3⁴3⁴

9. Exponential Notation 3⁴ is not a squared number because the base number is multiplied more than twice. Find the value of the following numbers: 7⁴ 3⁵ 2⁸

10. 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

11. Exponential Notation Find the value of the following numbers: 2⁸ 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2= 2 * 2= 4 * 2 = 8 * 2 = 16 * 2 = 32 * 2 = 64 * 2 = 128 * 2 = 256

12. Exponential Notation Find the value of the following numbers. 7⁴ 5⁵ 10⁸ 8 9 4 3 = 2401 = 3125 = 100,000,000 = 4096 = 729

13. 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.

14. Fibonacci Sequence A tiling with squares whose sides are successive Fibonacci numbers in length

15. Did I Say Extra Credit? If you are interested, complete Math Masters page 91 using patterns in Fibonacci Numbers