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Essential Question : Why are and both real numbers?

Essential Question : Why are and both real numbers?. Estimating Irrational numbers… Prt 2 Cube Roots and Non-perfect cubes. Essential Question : Why are and both real numbers?. Vocabulary – Shoot For The Stars 30 seconds.

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Essential Question : Why are and both real numbers?

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  1. Essential Question: Why are and both real numbers? • Estimating Irrational numbers… Prt 2 • Cube Roots and Non-perfect cubes

  2. Essential Question: Why are and both real numbers? Vocabulary –Shoot For The Stars 30 seconds • I got this! I know this word AND I could even teach it to somebody else. • I think I know this word, but I need more practice. • I am clueless! I have no idea what this word means.

  3. Essential Question: Why are and both real numbers? VOCABULARY Perfect Cube: _________________________________ Cube Root: _________________________________ The volume of a cube when the sides are whole numbers. The opposite of cubing a number. That means finding the length of a cube’s side from it’s volume.

  4. Essential Question: Why are and both real numbers? 3 2 1 The cube of an integer is a perfect cube. The opposite of cubing a number is taking the cube root.

  5. Essential Question: Why are and both real numbers? • For example Means… if a cube has a volume of 125, then how big is one of it’s sides? In other words, what number multiplied by itself three times in a row is equal to 125? That number is 5. 125 5

  6. Essential Question: Why are and both real numbers? Simplify each square root on your iPad ______ ______ 2 3

  7. Essential Question: Why are and both real numbers? But watch this… ______ ______ -2 Possible: Because any negative number multiplied by itself three times in a row still equals a negative answer. -2 Possible: Since the negative sign is on the OUTSIDE of the cube root sign, it just means “what number is the opposite of the cube root of 8?”

  8. Essential Question: Why are and both real numbers? • Do you see that cubes and cube roots are inverses (opposites) of each other?

  9. Essential Question: Why are and both real numbers? Draw Number Line from board.

  10. Essential Question: Why are and both real numbers? Commercial Break • Quote of the Day: “You always pass failure on the way to success.”

  11. Essential Question: Why are and both real numbers? Estimating cube roots • Once we have memorized the perfect cubes from 1 to 10 and their roots, we can estimate irrational cube roots that are not perfect cubes. • For example, what about ?

  12. Essential Question: Why are and both real numbers? Estimating cube roots • We already know the two perfect cubes that are before and after the cube root of 11. . . • and • Look at them on the number line on the board:

  13. Essential Question: Why are and both real numbers? Estimating cubre roots • We can see that is between 2 and 3 but is closer to 2. We would say that is a little more than 2, or approximately 2.1.

  14. Essential Question: Why are and both real numbers? TRY THIS:What two perfect cube roots come before and after the non-perfect cube roots below? Use your iPad.

  15. Essential Question: Why are and both real numbers? TRY THIS:What two whole numbers on the number line come before and after the non-perfect cube roots below? Use your iPad. 4 And 5 6 And 7 6 And 7

  16. Essential Question: Why are and both real numbers? THINK / PAIR / SHARE • Step 1 – Spend 20 seconds thinking silently about the Essential Question. • Step 2 – Spend 30 seconds pairing up with your learning partner. • Step 3 – Volunteer to share your answer with the class… Volunteers will receive a Goodybuck.

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