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Unit 1 Integers, Exponents, Scientific Notation Lessons 1-6

Unit 1 Integers, Exponents, Scientific Notation Lessons 1-6. Unit 1 Pre-Test.

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Unit 1 Integers, Exponents, Scientific Notation Lessons 1-6

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  1. Unit 1Integers, Exponents, Scientific NotationLessons 1-6

  2. Unit 1Pre-Test Today we will take the pre-test for this unit. Pre-tests are used to see what you know before we begin. Don’t get discouraged if you don’t know all or any of the answers. This is just a way to see what you already know!

  3. Lesson 1Exponential Notation • OBJECTIVE: • Students will understand what it means to raise a number to a power and represent with repeated multiplication. • Students will explain reason for some bases requiring parentheses.

  4. Lesson 1

  5. Let’s try these together! • 5 x 5 x 5 x 5 x 5 x 5= • . • . • (-2) • 3.8

  6. Think about this… • Quick write: • Why did we use the parentheses on examples 2, 3, and 4?

  7. In cases where the base is either a fraction or a negative number, it prevents ambiguity about which portion of the expression is going to be multiplied repeatedly. • For example:

  8. Try exercises 1-10 on your own!

  9. Check your answers! • 4 • 47 times • (-11.63) • 15 times • (-5) • ( ) • (-13) • (- ) • . • n times

  10. Exercise 11-12 11. Part 1:This product will be positive, why? Part 2: This product will be negative, why? 12. Odd number of negative factors yield a _________ product. Even number of negative factors yield a _________ product.

  11. Exercises 13-14 13. If n is a postive even number, then (-55) is ______________. If n is a positive odd number, then (-72.4) is ______________. 14. Is Josie correct? Why or why not?

  12. Closing! • Why bother with exponential notation? Why don’t we just write out all the multiplication? • Suppose a colony of bacteria doubles in size every 8 hours for a few days under tight laboratory conditions. If the initial size is B, what is the size of the colony after 2 days? • Answer: In 2 days there are six- 8 hours periods, so the size will be 2 B

  13. Lesson 2Multiplication of Numbers in Exponential Form • OBJECTIVE: • Students will use exponential notation. • Students will simplify exponential expressions • Students will write equivalent expressions using first law of exponents.

  14. How do I multiply different powers of the same number x; if m and n are positive integers, what is ?

  15. Let’s try these together! 1. 2. (- ) X (- )

  16. Try exercises 1-8 on your own!

  17. Exercises 1-8

  18. Check your answers!

  19. Notes • Expressions can ONLY be simplified when the bases are the SAME. • If the bases are not the same, you can rewrite them. • For example: • What factors do 2 and 8 have in common? • Using the base 2, what exponent needs to be used to equal 8?

  20. Quick write: • Can the following example be simplified using the rule of adding exponents? • Why or why not?

  21. What if there were more terms with the same base? • Tell whether the following examples can be simplified or not. Why or why not?

  22. Can the following be simplified?Exercises 11-16

  23. Check your answers!

  24. Exercises 17-20

  25. Check your answers!

  26. Notes • We have now learned how to multiply 2 different positive integer powers of the same base. • Same base add the exponents • How do you think we divide powers with the same base? • If m, n are positive integers, what is ?

  27. Example • What is ? • Expanded form: • = • What pattern do you see?

  28. Examples

  29. Exercises 21-24Try these on your own!

  30. Check your answers!

  31. If x is a non-zero number, what is it?Simplify

  32. Can the following be simplified?

  33. Exercise 31 Hint: What is the denominator of the expression in parentheses?

  34. Exercise 32

  35. Fluency Activity • When I call a number out, tell me the square of that number. • For example: 1 x 1= 1, so 1 = 1.

  36. Closing! • Summarize the lesson. • What did you learn today? • How do you multiply exponential expressions with the same bases? • How do you divide exponential expressions with the same bases?

  37. Exit Ticket: Complete and turn in for your classwork grade! • Homework: Complete for homework • Pick expressions from # 3 • Complete # 5

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