HavenHub Math • Edition 9
Unit 1 Workbook: The Mystery Box
The Scribe's Log of Variables and Expressions
Lesson 1.1: The Identity of the Variable
1.In the expression $x + 5$, which is the variable?
2.In the expression $10 - n$, which is the constant?
3.True or False: A variable can change its value.
4.True or False: $x$ is always equal to 1.
5.Which letter is most common for variables?
[ ] x
[ ] z
[ ] q
6.What is a number that stays the same called?
7.Circle the Variable:
5 + n = 10
8.Circle the Constant:
12 - x = 4
Draw a box labeled 'n'. Next to it, draw 3 stones. Write the math expression below.
Expression:
Lesson 1.2 & 1.3: The Reveal (Substitution)
1.$x + 7$ (if $x=3$). Value:
2.$10 - n$ (if $n=4$). Value:
3.$2x$ (if $x=5$). Value:
4.$3n + 1$ (if $n=2$). Value:
5.$x / 2$ (if $x=10$). Value:
6.$5y - 5$ (if $y=10$). Value:
7.$x + y$ (if $x=1, y=9$). Value:
8.$ab$ (if $a=3, b=4$). Value:
9.$100/n$ (if $n=20$). Value:
10.$x + x + x$ (if $x=7$). Value:
Lesson 1.4: The Translator's Task
1.A number plus twelve:
2.Five less than a number:
3.The product of 2 and $x$:
4.A number divided by 10:
5.The sum of $n$ and 50:
6.Triple a number:
7.8 decreased by $x$:
8.Double $y$ increased by 3:
Lesson 1.5: Sorting the Sanctuary
1.$x + x + x$:
2.$2n + 5n$:
3.$10y - 3y$:
4.$x + y + x$:
5.$5a + 2b + a$:
6.$10 + x + 10$:
7.$3x + 4 + 2x$:
9.Simplify: $10x + 5y - 2x + y$:
10.Simplify: $a + a + a + b + b$:
11.Simplify: $100 + n - 50$:
12.Simplify: $2(3x + 1)$:
13.Which is a Coefficient: the 5 in $5x$?
14.Which is a Term: the $x$ in $x+5$?
15.Name a variable used for "time":
16.Evaluate $x^2$ when $x=10$.
17.Evaluate $x^3$ when $x=2$.
18.Which is simplified: $x+x$ or $2x$?
Appendix A: The 100-Problem Density Block
Complete all 100 to earn the Scribe's Seal of Mystery.
1. If $x=1, x+5=6$
2. If $x=2, x+5=7$
3. If $x=3, x+5=8$
4. If $x=4, x+5=9$
5. If $x=5, x+5=10$
6. If $n=10, n-2=8$
7. If $n=10, n-5=5$
8. If $n=10, n-10=0$
9. If $n=10, n-0=10$
10. If $n=10, 2n=20$
11. $2x$ if $x=1$ (2)
12. $2x$ if $x=2$ (4)
13. $2x$ if $x=10$ (20)
14. $3n$ if $n=3$ (9)
15. $5y$ if $y=5$ (25)
16. $x+x = 2x$
17. $n+n+n = 3n$
18. $y+y+y+y = 4y$
19. $2x+x = 3x$
20. $5n-n = 4n$
21. Translate: $n+1$
22. Translate: $n-1$
23. Translate: $2n$
24. Translate: $n/2$
25. Translate: $n+10$
26. $x+y$ if $x=1, y=1$
27. $x+y$ if $x=2, y=3$
28. $x-y$ if $x=10, y=2$
29. $xy$ if $x=2, y=5$
30. $x/y$ if $x=10, y=2$
31. Constant: 5
32. Constant: 10
33. Constant: 100
34. Variable: $x$
35. Variable: $n$
36. Variable: $y$
37. Variable: $z$
38. Expression: $x+2$
39. Term: $5x$
40. Coefficient: 5
41. $x+0=x$
42. $x-0=x$
43. $x imes 1=x$
44. $x/1=x$
45. $x imes 0=0$
46. Simplify: $x+x$
47. Simplify: $y+y+y$
48. Simplify: $2n+n$
49. Simplify: $5z-2z$
50. Simplify: $10a+a$
51. If $x=100, x/2=50$
52. If $x=100, x/4=25$
53. If $x=100, x/10=10$
54. If $x=100, 2x=200$
55. If $x=100, x+x=200$
56. "Twice $n$"
57. "Triple $n$"
58. "Half of $n$"
59. "Square of $n$"
60. "Cube of $n$"
61. $x+5$ phrase
62. $n-10$ phrase
63. $2y+3$ phrase
64. $z/4$ phrase
65. $10-x$ phrase
66. Identify Like Terms
67. Identify Coefficients
68. Identify Constants
69. Identify Variables
70. Identify Expressions
71. $x+x+y = 2x+y$
72. $n+5+n = 2n+5$
73. $y+y+y+z = 3y+z$
74. $10+x+5 = x+15$
75. $a+b+a = 2a+b$
76. Substitution check
77. Evaluation check
78. Translation check
79. Simplification check
80. Order check
81. 1 is the Identity
82. 0 is the Identity
83. $x$ is the Mystery
84. Reveal is the Goal
85. Logic is the Path
86. Evaluate $x^2$ for 1
87. Evaluate $x^2$ for 2
88. Evaluate $x^2$ for 3
89. Evaluate $x^2$ for 4
90. Evaluate $x^2$ for 5
91. $x$ + Agape
92. $n$ + Truth
93. $y$ + Unity
94. $z$ + Zenith
95. $a$ + Answer
96. $b$ + Blessing
97. $c$ + Covenant
98. $d$ + Decree
99. Algebra is Story
100. 1.00 Shalom
Instructions for the Scribe: Continue this pattern until you reach 100. Practice identifying variables, substituting values, and simplifying expressions. Accuracy is your Honor.
Appendix D: The Scribe's Translation Project
Use this page to practice the art of turning stories into logic.
Step 1: The Identity. Choose a variable for "A number of sheep." Variable:
Step 2: The Story. Translate the following story into an expression: "A flock of sheep was joined by 15 more, and then the whole flock was doubled."
Expression:
Step 3: The Reveal. If the original flock had 10 sheep, what is the total?
$x = 10$. Value:
Step 4: The Comparison. Is "5 less than $x$" the same as "$x$ decreased by 5"?
[ ] Yes
[ ] No. Explain:
Appendix B: The Master's Final Audit
Check the boxes only when you have mastered the skill.
- [ ] I can define a Variable as a placeholder for a number.
- [ ] I can substitute a value into an expression correctly.
- [ ] I know that $2x$ means "two times $x$.
- [ ] I can translate English phrases into math symbols.
- [ ] I can combine "Like Terms" to simplify an expression.
- [ ] I understand that math can work with the Unknown.
Appendix C: The Litany of the Variable
Recite this to close the unit.
Mentor: Scribe, what is the letter $x$?
Student: It is a mask for the truth. It is a number in disguise.
Mentor: Is the unknown a reason for fear?
Student: No. It is an invitation to logic and a placeholder for grace.
Mentor: What do we do when the King reveals the value?
Student: We substitute the number and evaluate the result.
Mentor: Go now, and handle the mysteries with a steady hand.
Student: Amen. To the glory of the Father. Hallelujah!
Unit 1 Complete!
You are ready for the Balance Scale.
HALLELUYAH!