HavenHub Math • Edition 9
Unit 2 Workbook: The Balance Scale
The Scribe's Log of Algebraic Justice and Restoration
Lesson 2.1: Expressions vs. Equations
1.Is $x + 5$ an equation?
[ ] Yes
[ ] No
2.Is $x + 5 = 10$ an equation?
[ ] Yes
[ ] No
3.What symbol makes a sentence?
4.True or False: An equation is like a balanced scale.
5.Circle the Equation:
$3n$ $3n - 1$ $3n = 12$
6.Circle the Expression:
$x+1=2$ $x+1$ $1=1$
7.True or False: An expression has no solution.
8.True or False: An equation can be false.
Draw a balance scale. Put "x + 2" on the left and "10" on the right. Draw the Equals sign in the middle.
Lesson 2.2: The Trial of the Solution
1.Equation: $x + 5 = 10$. Is $x=2$ the solution?
2.Equation: $x - 2 = 8$. Is $x=10$ the solution?
3.Equation: $2x = 12$. Is $x=6$ the solution?
4.Equation: $n/3 = 4$. Is $n=7$ the solution?
5.Equation: $10 - y = 3$. Is $y=7$ the solution?
6.Equation: $5x = 50$. Is $x=10$ the solution?
7.Equation: $x + x = 20$. Is $x=5$ the solution?
8.Equation: $x + 0 = 9$. Is $x=9$ the solution?
Lesson 2.3: Restoring Shalom (+ / -)
1.$x + 5 = 15$
Solution:
2.$n - 10 = 20$
Solution:
3.$y + 12 = 30$
Solution:
4.$x - 50 = 50$
Solution:
5.$z + 100 = 100$
Solution:
6.$a - 1 = 99$
Solution:
7.$x + 1.5 = 2.5$
Solution:
8.$n - 0.5 = 0.5$
Solution:
Lesson 2.4: Breaking the Hug (x / ÷)
1.$2x = 10$
Solution:
2.$5n = 25$
Solution:
3.$x / 2 = 10$
Solution:
4.$n / 4 = 5$
Solution:
5.$10y = 100$
Solution:
6.$z / 10 = 7$
Solution:
7.$3x = 21$
Solution:
8.$x / 3 = 12$
Solution:
Lesson 2.5: The Faithful Witness (The Check)
Case: $x + 10 = 25$. We think: $x = 15$.
Check: + 10 = . Is it level?
Case: $4n = 20$. We think: $n = 5$.
Check: 4 ( ) = . Is it level?
Appendix A: The 100-Problem Density Block
Complete all 100 to earn the Master's Seal of Justice.
1. $x + 1 = 5 \to 4$
2. $x + 2 = 10 \to 8$
3. $x + 3 = 12 \to 9$
4. $x + 4 = 20 \to 16$
5. $x + 5 = 25 \to 20$
6. $x - 1 = 10 \to 11$
7. $x - 2 = 20 \to 22$
8. $x - 5 = 5 \to 10$
9. $x - 10 = 90 \to 100$
10. $x - 50 = 50 \to 100$
11. $2x = 10 \to 5$
12. $2x = 20 \to 10$
13. $2x = 100 \to 50$
14. $3x = 30 \to 10$
15. $5x = 50 \to 10$
16. $x / 2 = 5 \to 10$
17. $x / 2 = 10 \to 20$
18. $x / 5 = 5 \to 25$
19. $x / 10 = 10 \to 100$
20. $x / 1 = 7 \to 7$
21. Inverse of $+$ is $-$
22. Inverse of $-$ is $+$
23. Inverse of $\times$ is $/$
24. Inverse of $/$ is $\times$
25. Fulcrum = Equals Sign
26. Equation = Sentence
27. Expression = Phrase
28. Solution = Truth
29. Variable = Mystery
30. Constant = Rock
31. $x + 0 = 5 \to 5$
32. $x - 0 = 10 \to 10$
33. $x \times 1 = 12 \to 12$
34. $x / 1 = 15 \to 15$
35. $x \times 0 = 0$ (Any!)
36. $x + 10 = 11 \to 1$
37. $x - 10 = 0 \to 10$
38. $10x = 10 \to 1$
39. $x / 10 = 1 \to 10$
40. $x + 9 = 10 \to 1$
41. 2-sided add
42. 2-sided sub
43. 2-sided mul
44. 2-sided div
45. Isolation act
46. Verification act
47. Restoration act
48. Alignment act
49. Equilibrium act
50. Integrity act
51. $x + 7 = 14 \to 7$
52. $x - 7 = 7 \to 14$
53. $7x = 49 \to 7$
54. $x / 7 = 7 \to 49$
55. $x + 7 = 7 \to 0$
56. $x + 15 = 20 \to 5$
57. $x - 15 = 5 \to 20$
58. $4x = 40 \to 10$
59. $x / 4 = 10 \to 40$
60. $x + 100 = 200 \to 100$
61. If $x=1, x+1=2$
62. If $x=5, 2x=10$
63. If $x=10, x/2=5$
64. If $x=0, x+10=10$
65. If $x=100, x-1=99$
66. Balance $x+1=2$
67. Balance $x-1=0$
68. Balance $2x=2$
69. Balance $x/2=1$
70. Balance $x=x$
71. Check $1+1=2$
72. Check $5-2=3$
73. Check $3 \times 3=9$
74. Check $10/2=5$
75. Check $0+0=0$
76. Solve for the bag
77. Solve for the jar
78. Solve for the coin
79. Solve for the land
80. Solve for the soul
81. 1 is the Identity
82. 0 is the Identity
83. $x$ is the Justice
84. $=$ is the Peace
85. Inverse is the Key
86. Measure the Balance
87. Label the Wall
88. Protect the Equal
89. Reveal the Truth
90. Simplify the Life
91. $x$ + Mercy = Truth
92. $n$ - Error = Clean
93. $y \times$ Growth = Fruit
94. $z /$ Sharing = Peace
95. The Scale is Level
96. The Decree is Firm
97. The Scribe is Honest
98. The King is Pleased
99. The Matter is Established
100. 1.00 Shalom
Instructions for the Scribe: Continue this pattern until you reach 100. Practice solving equations by performing the inverse operation on both sides of the wall. Accuracy is your Honor.
Appendix D: The Scribe's Balance Project
Use this page to practice the art of restoring Shalom to the sentence.
Step 1: The Covenant. Write an equation for this story: "A mystery bag of gold ($x$) has 5 coins added to it. The total weight is 50 coins."
Equation:
Step 2: The Restoration. Solve the equation. Show the "Wall of Integrity" and perform the inverse on both sides.
Step 3: The Witness. Check your answer by substituting the value back into the original box.
Step 4: The Multi-Step Mystery. Solve: $2x + 10 = 20$.
Hint: Peel the outer layer first!
$x =
Appendix B: The Master's Final Audit
Check the boxes only when you have mastered the skill.
- [ ] I know that $=$ means "is perfectly balanced with."
- [ ] I can identify the inverse of any basic operation.
- [ ] I always draw "The Wall" down through the equal sign.
- [ ] I perform the same action on both sides of the equation.
- [ ] I can solve one-step addition equations (e.g., $x + 5 = 12$).
- [ ] I can solve one-step subtraction equations (e.g., $x - 3 = 7$).
- [ ] I can solve one-step multiplication equations (e.g., $4x = 20$).
- [ ] I can solve one-step division equations (e.g., $x \div 2 = 6$).
- [ ] I use the Check Step to verify my answer is true.
- [ ] I am a faithful Steward of the Balance.
Appendix C: The Litany of the Scale
Recite this to close the unit.
Mentor: Scribe, what is an equation?
Student: A covenant of balance. A sentence of truth.
Mentor: Why do we act on both sides?
Student: To maintain the shalom and protect the equality.
Mentor: What do we seek in the check step?
Student: The witness of the result. The establishment of the matter.
Mentor: Go now, and walk the level path of the King.
Student: Amen. To the left, To the right, To the glory of God.
Unit 2 Complete!
You are ready for the Deep Waters.
HALLELUYAH!