Exponents

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Grade 6 Exponents Lesson

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Exponents

  1. 1. Exponents Chapter 2 Lesson 2.8
  2. 2. How does a secret spread so fast? <ul><li>The person with a secret tells a friend. </li></ul><ul><li>The friend promises never to tell anyone. </li></ul><ul><li>That same friend breaks the promise and tells two more friends. </li></ul><ul><li>The two new friends tell two new friends. </li></ul><ul><li>The two new friends decide to tell two more friends. </li></ul><ul><li>This pattern occurs over and over until many people have been told. </li></ul><ul><li>By the end of the day it is no longer a secret! </li></ul>
  3. 3. Here is how a secret can spread. (Real Fast!) <ul><li>Round 1 Round 2 </li></ul>I have a secret and I tell 3 of my best friends. My 3 friends each tell 3 more people. Look how many people now know the secret! 3 x 3 = 9 9 people know!
  4. 4. In an exponential expression, the base is the factor, and the exponent tells the amount of times to multiple that number by itself. (That is a mouthful!) <ul><li>3 </li></ul>4 Your BASE = 3 Your EXPONENT = 4 A base is a number that can be expressed using an exponent. An exponent is the small number and is referred to as a “power.” 3 4 means 3 x 3 x 3 x 3 OR 3 to the forth power.
  5. 5. There are 3 ways to write an exponent. <ul><li>2 </li></ul>4 Factored Form is one way. In factored form you spread the equation apart – piece by piece to show what it means. 2 4 Means 2 x 2 x 2 x 2 This is factored form!
  6. 6. Here is another way! <ul><li>Write a set of numbers as an exponent </li></ul><ul><li>x 2 x 2 x 2 = </li></ul><ul><li>List the base first = 2 </li></ul><ul><li>Then count up the number of two’s you see. There are 4 number 2’s. </li></ul><ul><li>Therefore 2 x 2 x 2 x 2 = </li></ul>2 4
  7. 7. Here is the last way! (The Most Important Way) <ul><li>Standard Form is the easiest to write. </li></ul><ul><li>To write an exponent in standard form – JUST MULTIPLY! </li></ul>2 4 = 2 x 2 x 2 x 2 Now solve! 2 x 2 = 4 x 2 = 8 x 2 = 16
  8. 8. Try This! <ul><li>3 5 – Write in factored form. </li></ul><ul><li>4 x 4 x 4 </li></ul><ul><li>Write as an exponent. </li></ul><ul><li>2 6 – Write in standard form. </li></ul><ul><li>3 x 3 x 3 x 3 x 3 </li></ul><ul><li>4 3 </li></ul><ul><li>2 x 2 x 2 x 2 x 2 x 2 = 64 </li></ul>
  9. 9. Exponents in Shape Form <ul><li>Write the factored shape in exponent form. </li></ul>X X =
  10. 10. <ul><li>Answer: </li></ul>3
  11. 11. Try this! X X X X = The yellow block = y Write this factored equation as an exponent. Answer: y 5
  12. 12. Task Rotation Exercise <ul><li>I will give each student an index card with one problem. </li></ul><ul><li>The problem will ask for you to solve the problem in standard form, factored form, and exponent form. </li></ul><ul><li>After you complete the problem do not move until I blow the whistle. </li></ul><ul><li>The person who has the card that says “Water” is to complete the problem first then may leave the room to get a drink of water. </li></ul><ul><li>When the person who gets the drink returns, I will blow the whistle and you will rotate to the next desk. </li></ul>
  13. 13. Task Rotation Answers <ul><li>Question </li></ul><ul><li>Write as an exponent </li></ul><ul><li>4x4x4x4x4 </li></ul><ul><li>Write as an exponent </li></ul><ul><li>12x12 </li></ul><ul><li>Write as an exponent </li></ul><ul><li>7x7x7x7x7x7 </li></ul><ul><li>Answers </li></ul><ul><li>4 5 </li></ul><ul><li>12 2 </li></ul><ul><li>7 6 </li></ul>
  14. 14. Write in Factored Form <ul><li>Question </li></ul><ul><li>6 3 </li></ul><ul><li>43 2 </li></ul><ul><li>0.3 5 </li></ul><ul><li>10 5 </li></ul><ul><li>15 4 </li></ul><ul><li>100 6 </li></ul><ul><li>Answer </li></ul><ul><li>6x6x6 </li></ul><ul><li>43x43 </li></ul><ul><li>0.3 x 0.3 x 0.3 x 0.3 x 0.3 </li></ul><ul><li>10 x 10 x 10 x 10 x 10 </li></ul><ul><li>15 x 15 x 15 x 15 </li></ul><ul><li>100 x 100 x 100 x 100 x </li></ul><ul><li>100 x 100 </li></ul>
  15. 15. Write in Standard Form <ul><li>Questions </li></ul><ul><li>10 4 = </li></ul><ul><li>5 4 = </li></ul><ul><li>6 3 = </li></ul><ul><li>6 4 = </li></ul><ul><li>6 5 = </li></ul><ul><li>Answers </li></ul><ul><li>10,000 </li></ul><ul><li>625 </li></ul><ul><li>216 </li></ul><ul><li>1296 </li></ul><ul><li>7776 </li></ul>
  16. 16. Write as an exponent <ul><li>Question </li></ul><ul><li>15. 6x6x6x6x6 </li></ul><ul><li>16. 74 x 74 x 74 </li></ul><ul><li>17. 0.4 x 0.4 x 0.4 x 0.4 </li></ul><ul><li>Answers </li></ul><ul><li>6 5 </li></ul><ul><li>74 3 </li></ul><ul><li>0.4 4 </li></ul>
  17. 17. Write in Standard Form <ul><li>Question </li></ul><ul><li>2 6 = </li></ul><ul><li>7 4 = </li></ul><ul><li>4 5 = </li></ul><ul><li>Answer </li></ul><ul><li>64 </li></ul><ul><li>2401 </li></ul><ul><li>1024 </li></ul>
  18. 18. Let’s Review! <ul><li>5 2 </li></ul>Which number is the “exponent?” Which number is the “base?” Write the exponent in factored form? Write the exponent in standard form? 2 5 5 x 5 25
  19. 19. What to expect next…… <ul><li>Solve </li></ul><ul><li>2 3 + 3 3 = </li></ul><ul><li>Answer: 2x2x2=8 / 3x3x3=27 </li></ul><ul><li>8 + 27 = 35 </li></ul>
  20. 20. Homework <ul><li>Complete “Reteaching 2.8” </li></ul>

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