1. Ms. Drake 7th grade Math Number Theory Lesson 1 Exponents

2. Week by Week Essentials

4. Number Theory Addition Property of Equality Algebraic Expression Base Coefficient Composite Number Constant Division Property of Equality Equation

5. Evaluate Exponent Greatest Common Factor (GFC) Inverse Operations Isolate the Variable Least Common Variable (LCM) Like Terms Number Theory

6. Multiple Multiplication Property of Equality Numerical Expression Order of Operations Power Prime Factorization Prime Number Scientific Notation Solution

7. Number Theory Solve Standard Form Subtraction Property Of Equality Term Variable Verbal Expression

8. Evaluating Powers 2 Base Exponent 5

9. This means 2∙2∙2∙2∙2

10. Power: A number produced by raising a base to an exponent

11. Solve by doing the multiplication 2 = 2∙2∙2∙2∙2 = 32 5 Power

12. Exponential Growth

14. Any number to the first power is equal to that number 5 = 5 12 = 12 347 = 347 1 1 1

15. Any number to the zero power, except zero is equal to one. 6 = 1 720 = 1 100,000 = 1 0 0 0

16. You can also express whole numbers as Powers Write each number using an exponent and the given base. 25, base 5 25 = 5 ∙ 5 = 5 2

17. Let’s practice together with a word problem. The cells of the bacteria E. coli can double every 20 minutes. If you begin with a single cell, how many cells can there be after four hours?

18. 4 hours = 60 60 60 60 How many 20 are in each 60? 12 The bacteria doubles 12 times. 2 = 4096 12

19. How about this one. Maria had triplets. Each of her children had triplets. If the pattern occurred for two more years how many great, great, grandchildren would Maria have?

20. Maria 1 2 3 1 2 3 1 2 3 1 2 3 123 123 123 123 123 123 123 123 123 333333333333333333333333333

21. 3333333333 0 1 2 3 4 Maria Her children Her grand children Her great grandchildren Her great-great grandchildren

22. Give two ways to represent these numbers with exponents. 816416729

23. 729

28. Until next time, make your own work of art showing the relationships of exponents to bases and powers! And think about this question…

29. Would you rather be given one million dollars in one month or one penny doubled everyday for one month? The answer may surprise you!