2. Lesson 2 Pawn = x Lesson 3 Legal moves pawns Lesson 4 Legal moves #s Lesson 5 Set-up subtraction Lesson 6 parentheses Lesson 7 Symbols only Lesson 1 Trial & Error

3. Equal and Balanced

4. 100 pounds = ? pounds

5. Materials for Book 1 Eight blue pawns Two red cubes, numbered 0-5 Two red cubes, numbered 5- 10 A laminated balance scale Put the other items back in the bag.

6. 5 X = Check: Lesson 1 What is the value for the blue pawn to balance the scale? 55 555 =

7. 8 X = Check: Lesson 1 Use trial and error to solve. 4+ 4 8 8 4 88 =

8. 8 X = Check: Lesson 1 2 Use trial and error method to solve. 1, 2, 3, etc. 6 14 = The blue pawn has a special name, “x”.

9. 10 X = Check: Lesson 1 Please place number cubes facing upward so I can see the numbers when I pass by. Black triangles are symbols for blue pawns

10. 9 X = Check: Lesson 1 2 99 = 7 7 + 2 99

11. 7 X = Check: Lesson 1 3 77 = 2 2+2 + 3 77

12. X = Check: Lesson 1 8 12 = 4 4 + 8 12 4+4+4

13. X = Check: Lesson 1 24 44 = 1 1 + 1 + 2 44

14. X = Check: Lesson 1 8410 14 = 6 6 + 8 14 10 +4

15. X = Check: Lesson 1 4 88 = 4 4+ 4 88 4 + 4

16. X = Check: Lesson 1 727 14 = 4 4+4+4 + 2 14 7 + 7

17. X = Check: Lesson 1 410 16 = 6 6+6 + 4 16 6 + 10

18. X = Check: Lesson 1 210 18 = 6 6+6 +6 18 6+10+ 2

19. Lesson 2 Pawn = x Lesson 3 Legal moves pawns Lesson 4 Legal moves #s Lesson 5 Set-up subtraction Lesson 6 parentheses Lesson 7 Symbols only Lesson 1 Trial & Error

20. X = Check: Lesson 2 2 The pawn has a special name, “x.” Therefore, the problem 4 12 = 2x + x = x + 8 8

21. X = Check: Lesson 2 3 10 = 3x + 1 = x + 7 17

22. X = Check: Lesson 2 = 1. 2x = x + 3 3 3 66

23. X = Check: Lesson 2 = 2. 3x = x + 4 4 2 66

24. X = Check: Lesson 2 = 3. x + 4 = 2x + 3 34 1 55

25. X = Check: Lesson 2 = 4. 4x = 2x + 6 6 3 12

28. Lesson 2 Pawn = x Lesson 3 Legal moves pawns Lesson 4 Legal moves #s Lesson 5 Set-up subtraction Lesson 6 parentheses Lesson 7 Symbols only Lesson 1 Trial & Error

29. Lesson 3 Try this one. 4x + 2 = 3x + 9 “Would you like to learn an easier way of getting the answer than by using trial and error?”

31. Lesson 3 4x + 2 = 3x + 9 29 Legal Moves X =7

32. Check: Lesson 3 7 30 = 4x + 2 = 3x + 9 29 Reset the original equation to check.

33. Lesson 3 1. 3x + 7 = 4x Set up X =

34. Lesson 3 1. 3x + 7 = 4x 7 Legal Moves X =7

35. Lesson 3 1. 3x + 7 = 4x 7 X =7 Check: 28 =

36. Lesson 3 2. x + 2 +2x = x + 10 Set up X =

37. Lesson 3 2. x + 2 +2x = x + 10 210 Legal Moves X =4

38. Lesson 3 2. x + 2 +2x = x + 10 210 X =4 Check: 14 =

39. Lesson 3 3. x + 3x = x + x + 10 Set up X =

40. Lesson 3 3. x + 3x = x + x + 10 10 Legal Moves X =5

41. Lesson 3 3. x + 3x = x + x + 10 10 X =5 Check: 20 =

42. Lesson 3 4. 2x + 3 + 3x = x + 11 Set up X =

43. Lesson 3 4. 2x + 3 + 3x = x + 11 10 Legal Moves X =2 13

44. Lesson 3 4. 2x + 3 + 3x = x + 11 10 X =2 13 Check: 13 =

46. Lesson 2 Pawn = x Lesson 3 Legal moves pawns Lesson 4 Legal moves #s Lesson 5 Set-up subtraction Lesson 6 parentheses Lesson 7 Symbols only Lesson 1 Trial & Error

51. Lesson 4 1. x + 2x +5 = x + 19 Set up X =

52. Lesson 4 1. x + 2x +5 = x + 19 Legal Moves X =7 510459

53. Lesson 4 1. x + 2x +5 = x + 19 X =7 510459 Check: 26 =

54. Lesson 4 2. x + 2x + 14 = 5x + 2 Set up X =

55. Lesson 4 2. x + 2x + 14 = 5x + 2 Legal Moves X =6 102224

56. Lesson 4 2. x + 2x + 14 = 5x + 2 X =6 102224 Check: 32 =

57. Lesson 4 3. x + 4 + 2x = x + 20 Set up X =

58. Lesson 4 3. x + 4 + 2x = x + 20 Legal Moves X =8 46410

59. Lesson 4 3. x + 4 + 2x = x + 20 X =8 46410 Check: 28 =

60. Lesson 4 4. x + 2 + 2x = x + 12 Set up X =5

61. Lesson 4 4. x + 2 + 2x = x + 12 Legal Moves X =5 2210

62. Lesson 4 4. x + 2 + 2x = x + 12 X =5 2210 Check: 17 =

64. Lesson 2 Pawn = x Lesson 3 Legal moves pawns Lesson 4 Legal moves #s Lesson 5 Set-up subtraction Lesson 6 parentheses Lesson 7 Symbols only Lesson 1 Trial & Error

66. Lesson 5 1. 4x – 2x + 4 = x + 10 Set up X = 104

67. Lesson 5 1. 4x – 2x + 4 = x + 10 Legal Moves X =6 64410

68. Lesson 5 1. 4x – 2x + 4 = x + 10 X =6 64410 Check: 16 =

69. Lesson 5 2. x + 3x - x = 30 10 55 X =10 Check: 30 =

70. Lesson 5 3. 8 + 2x + 3 - x = 2x + 1 Set up X = 183

71. Lesson 5 3. 8 + 2x + 3 - x = 2x + 1 Legal Moves X = 18213 10

72. Lesson 5 3. 8 + 2x + 3 - x = 2x + 1 X = 18213 10 Check: 21 =

73. Lesson 5 4. x + 2x - x + 7 = 4x – x + 2 Set up X = 27

74. Lesson 5 4. x + 2x - x + 7 = 4x – x + 2 Legal Moves X = 2527 5

75. Lesson 5 4. x + 2x - x + 7 = 4x – x + 2 2527 X = 5 Check: 1715 =

77. Lesson 2 Pawn = x Lesson 3 Legal moves pawns Lesson 4 Legal moves #s Lesson 5 Set-up subtraction Lesson 6 parentheses Lesson 7 Symbols only Lesson 1 Trial & Error

79. Lesson 6 1. 2(x +3) = 10 Set up X = 103 3

80. Lesson 6 1. 2(x +3) = 10 Legal Moves X = 43 3 610 2

81. Lesson 6 1. 2(x +3) = 10 43 3 610 X = 2 Check: 10 =

82. Lesson 6 2. 2(x +3) = 9 + x Set up 93 3

83. Lesson 6 2. 2(x +3) = 9 + x Legal Moves 33 3 69 X = 3

84. Lesson 6 2. 2(x +3) = 9 + x 33 3 69 X = 3 Check: 12 =

85. Lesson 6 3. 2(2x +1) = 3x + 8 Set up X = 81 1

86. Lesson 6 3. 2(2x +1) = 3x + 8 Legal Moves X = 61 1 28 6

87. Lesson 6 3. 2(2x +1) = 3x + 8 X = 6 61 6 6 1 6 6 6 6 28 6 Check: 26 =

88. Lesson 6 4. 2(2x + 3) = x + 9 Set up X = 93 3

89. Lesson 6 4. 2(2x + 3) = x + 9 Legal Moves X = 33 3 69 1

90. Lesson 6 4. 2(2x + 3) = x + 9 X = 33 3 69 1 Check: 10 =

92. Lesson 2 Pawn = x Lesson 3 Legal moves pawns Lesson 4 Legal moves #s Lesson 5 Set-up subtraction Lesson 6 parentheses Lesson 7 Symbols only Lesson 1 Trial & Error

95. Lesson 2 Pawn = x Lesson 3 Legal moves pawns Lesson 4 Legal moves #s Lesson 5 Set-up subtraction Lesson 6 parentheses Lesson 7 Symbols only Lesson 1 Trial & Error