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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 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. Essential Question: Why are and both real numbers? VOCABULARY Perfect Cube: The volume of a cube when the sides are whole numbers. _________________________________ Cube Root: The opposite of cubing a number. That means finding the length of a cube’s side from it’s volume. _________________________________ Essential Question: Why are and 3 2 1 13 = 1 both real numbers? 23 = 8 33 = 27 The cube of an integer is a perfect cube. The opposite of cubing a number is taking the cube root. Essential Question: Why are and both real numbers? For example 3 125 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. 5 Essential Question: Why are and both real numbers? Simplify each square root on your iPad 3 8 2 ______ 3 27 3 ______ Essential Question: Why are and both real numbers? But watch this… 3 -8 -2 ______ Possible: Because any negative number multiplied by itself three times in a row still equals a negative answer. 3 - 8 -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?” Essential Question: Why are and both real numbers? Do you see that cubes and cube roots are inverses (opposites) of each other? Essential Question: Why are and both real numbers? Draw Number Line from board. Essential Question: Why are and both real numbers? Commercial Break Quote of the Day: “You always pass failure on the way to success.” 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 3 11 ? 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. . . 3 8 and 3 27 Look at them on the number line on the board: Essential Question: Why are and both real numbers? Estimating cubre roots 3 We can see that 11 is between 2 and 3 but is closer to 2. We would say that 3 11 is a little more than 2, or approximately 2.1. 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. 3 147 3 3 3 3 125 216 3 15 411 3 3 8 27 3 343 512 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. 3 79 4 And 5 3 303 6 And 7 3 275 6 And 7 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.