2. DO NOW: Use long division to change 3/4 to a decimal. What is the decimal representation of pi? What is the square root of 2? What is the decimal representation of 1/9, 2/9, 3/9? Explain in complete sentences the pattern you see.

3. CORRECT ANSWERS: 0.75 3.14 1.4142135623730950488016887242097 0.111…,0.222…,0.333…

4. My Goal for Class Today: I can tell the difference between rational and irrational numbers. I understand that any number that can be written as a fraction is a rational number and I can convert a repeating decimal into a fraction. By the end of class I should be able to answer: What is the difference between a rational and irrational number?

5. TODAY’S AGENDA I Do: The Real Number System Venn Diagram We Do: Skittles Challenge You Do: Intendent Practice and Teach the Class Exit Ticket

6. Whole Numbers Counting Numbers Integers Rational Numbers Irrational Numbers The Real Number System

7. SKITTLES CHALLENGE I will call out a number On your white board write down if the number is a counting number, whole number, integer, rational number or irrational number If you’re correct you win a skittle! If every member of the team is correct the team gets a point The Team with the most points at the end wins!

8. IS 0.4444….RATIONAL OR IRRATIONAL?

9. IT IS RATIONAL! BUT WHY?

10. YOU DO: CONVERT THESE TO FRACTIONS WITH YOUR TABLE PARTNER 0.7777… 2.050505… 12.141414…

11. EXIT TICKET 1.Convert the following into a fraction: 3.070707…. 2.Is the answer from number one rational or irrational? 3.Write down one “ah-ha” moment from today or one question you still have about rational and irrational numbers.

12. DO NOW:

13. My Goal for Class Today: Is to be able to use rational approximations to define and compare irrational numbers. By the end of class I should be able to: locate and graph irrational numbers on the number line and estimate the value of those numbers.

14. TODAY’S AGENDA I Do: Estimate irrational numbers We Do: Compare rational and irrational numbers You Do: Laundry Line Activity- Locate irrational numbers on a number line Independent Practice Exit Ticket

15. I DO: HOW WE ESTIMATE IRRATIONAL NUMBERS Rational approximation: using a sequence of rational numbers to get closer and closer to a given number to estimate the value of a number.

16. WE DO: LAUNDRY LINE We will be creating “special laundry” to hang on the clothesline. Rational numbers will be placed on tee shirts and irrational numbers on pants. You will each chooses a number from the bag and then cut out a pair of pants or a shirt from the construction paper provided Once you are finished, it is time to hang the laundry. Come up and pin your laundry items on the clothesline. As more clothing is added you may need to move laundry to accurately place yours on the number clothing line.

17. INDEPENDENT PRACTICE Determine what is the interval of numbers √28 will lie between, Why? Classify the following numbers as rational or irrational. Be prepared to explain your reasoning. √10 0.123123123 … √64 5 11

18. HOME LEARNING Watch the following Khan Academy Videos and complete the practice problems with notes: https://www.khanacademy.org/math/cc-eighth-grade- math/cc-8th-numbers-operations/cc-8th- roots/v/introduction-to-square-roots https://www.khanacademy.org/math/cc-eighth-grade- math/cc-8th-numbers-operations/cc-8th- roots/v/introduction-to-square-roots Or Complete the Provided Worksheet

19. EXIT TICKET Summarize 3 main points from today’s lesson

20. DO NOW:

21. My Goal for Class Today: Is to understand squares and square roots, to realize that imperfect squares are irrational, and to be able to plot imperfect squares on the number line using rational approximation. By the end of class I should be able to answer: What does a square root represent?

22. AGENDA I Do: Perfect Squares Notes You Do: Khan Academy Square Roots Video We Do: Discovering Squares and Square Roots Activity You Do: Powers and Roots Worksheet Exit Ticket

23. HOME LEARNING Complete your Powers and Roots Worksheet

24. EXIT TICKET Place the following numbers on a number line: √16, √9, √11, 3.5 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0

25. DO NOW: Evaluate the following equations: 1 x 1 x1= 2 x 2 x2= 3 x 3 x 3 =

26. My Goal for Class Today: I can evaluate cube exponents, and I can identify cube roots. By the end of class I should be able to answer: What is the relationship between cubes and cube roots?

27. AGENDA I Do: Perfect Squares Notes You Do: Perfect Squares Video We Do: Discovering Cubes Activity You Do: Cubes and Cube Roots Independent Practice Exit Ticket

28. I Do: What does cube root mean? The cube root of a number is… …the value when multiplied by itself three times gives the original number.

29. CUBE ROOT VOCABULARY index radicand radical sign

30. If a number is a perfect cube, then you can find its exact cube root. A perfect cube is a number that can be written as the cube (raised to third power) of another number. Perfect Cubes

31. WHAT ARE PERFECT CUBES? 1 3 = 1 x 1 x 1 = 1 2 3 = 2 x 2 x 2 = 8 3 3 = 3 x 3 x 3 = 27 4 3 = 4 x 4 x 4 = 64 5 3 = 5 x 5 x 5 = 125 and so on and on and on…..

32. Examples: because

33. Not all numbers or expressions have an exact cube root as in the previous examples. If a number is NOT a perfect cube, then you might be able to SIMPLIFY it. Simplify Cube Roots

34. 2 Extract the cube root of the factor that is a perfect cube. 1 Write the radicand as a product of two factors, where one of the factors is a perfect cube. To simplify a cube root... 3 The factors that are not perfect cubes will remain as the radicand.

35. perfect cube Examples: 1)2) 3)

36. Not all cube roots can be simplified! 30 is not a perfect cube. 30 does not have a perfect cube factor. Example: cannot be simplified!

37. AGENDA I Do: Perfect Squares Notes-DONE You Do: Perfect Squares Video We Do: Discovering Cubes Activity You Do: Cubes and Cube Roots Independent Practice Exit Ticket

38. USING YOUR CUBES FIND THE ANSWERS FOR THE FOLLOWING CHART REMEMBER THE VOLUME OF A CUBE IS LENGTH X WIDTH X HEIGHT Side LengthVolume of CubeTherefore…That Means the Cube Root is … 2 27 64 125 9 1000

39. HOME LEARNING

40. EXIT TICKET

41. DO NOW: Pulse Check: How has your first two weeks of school gone? How do you feel? What fun plans do you have this weekend?

42. My goal for you today is that you will all become masters at square and cube roots by the end of class, and that you will enjoy your weekend and come in next week with a positive attitude, ready to start fresh and learn.

43. AGENDA We Do: Cube and Square Roots Jeopardy Competition- Winning team gets homework passes! You Do: Cube Roots Coloring Project Enjoy your weekend!

44. JEOPARDY Square & Cube Roots Rational/ Irrational Simplifying Radicals Estimating Roots Misc. 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500

45. $100 SQUARE AND CUBE ROOTS

46. $100 ANSWER SQUARE AND CUBE ROOTS 169

47. RETURN

48. $200 SQUARE AND CUBE ROOTS 5³

49. $200 ANSWER SQUARE AND CUBE ROOTS 125

50. RETURN

51. $300 SQUARE AND CUBE ROOTS

52. $300 ANSWER SQUARE AND CUBE ROOTS 14

53. RETURN

54. $400 SQUARE AND CUBE ROOTS

55. $400 ANSWER SQUARE AND CUBE ROOTS 256

56. RETURN

57. $500 SQUARE AND CUBE ROOTS

58. $500 ANSWER SQUARE AND CUBE ROOTS 17

59. RETURN

60. $100 RATIONAL OR IRRATIONAL 1.25

61. $100 ANSWER RATIONAL OR IRRATIONAL Rational

62. RETURN

63. DAILY DOUBLE

64. DAILY DOUBLE RATIONAL OR IRRATIONAL -0.6666…

65. DAILY DOUBLE ANSWER RATIONAL OR IRRATIONAL Rational

66. RETURN

67. $300 RATIONAL OR IRRATIONAL

68. $300 ANSWER RATIONAL OR IRRATIONAL Irrational

69. RETURN

70. $400 RATIONAL OR IRRATIONAL -0.1113…

71. $400 ANSWER RATIONAL OR IRRATIONAL Irrational

72. RETURN

73. $500 RATIONAL OR IRRATIONAL

74. $500 ANSWER RATIONAL OR IRRATIONAL Rational

75. RETURN

76. $100 SIMPLIFYING RADICALS

77. $100 ANSWER SIMPLIFYING RADICALS

78. RETURN

79. $200 SIMPLIFYING RADICALS

80. $200 ANSWER TOPIC 3 6

81. RETURN

82. $300 SIMPLIFYING RADICALS

83. $300 ANSWER SIMPLIFYING RADICALS

84. RETURN

85. $400 SIMPLIFYING RADICALS

86. $400 ANSWER SIMPLIFYING RADICALS

87. RETURN

88. $500 SIMPLIFYING RADICALS

89. $500 ANSWER SIMPLIFYING RADICALS

90. RETURN

91. $100 ESTIMATING ROOTS

92. $100 ANSWER ESTIMATING ROOTS

93. RETURN

94. $200 ESTIMATING ROOTS

95. $200 ANSWER ESTIMATING ROOTS

96. RETURN

97. $300 ESTIMATING ROOTS

98. $300 ANSWER ESTIMATING ROOTS 3.3

99. RETURN

100. $400 ESTIMATING ROOTS

101. $400 ANSWER ESTIMATING ROOTS

102. RETURN

103. $500 ESTIMATING ROOTS

104. $500 ANSWER ESTIMATING ROOTS 2.6

105. RETURN

106. $100 MISC. What are the square roots of 81?

107. $100 ANSWER MISC.

108. RETURN

109. $200 MISC. What kind of decimals are rational?

110. $200 ANSWER MISC. Repeating and Terminating

111. RETURN

112. $300 MISC.

113. $300 ANSWER MISC. 16

114. RETURN

115. $400 MISC.

116. $400 ANSWER MISC.

117. RETURN

118. $500 MISC. Area = 100 ft squared What are the side lengths?

119. $500 ANSWER MISC. 10 ft.

120. RETURN

121. THANK YOU FOR PLAYING