HavenHub Math • Edition 9 • Student Workbook

Unit 5: The Master Plan

"Order out of Chaos: Solving Multi-Step Mysteries"

The Scribe's Meditation: The Sequence of the King

When God created the world, He didn't just speak everything into existence at once. He followed a Plan. He created the light, then the sky, then the land, then the life. Each step built upon the one before it.

In Algebra, complex problems can look like chaos. But a Scribe knows that chaos is just a truth waiting for a Plan. In this unit, you will learn to dismantle complexity by following the Order of Honor. You will open gates, tidy your room, and peel away layers until the identity of the Unknown is revealed.

"Let all things be done decently and in order." — 1 Corinthians 14:40

Lesson 5.1: The Shoe and the Sock (Two-Step Logic)

The Peeling Rule: When you dress, you put on your socks first, then your shoes. But when you get ready for bed, you must take the SHOE off first!

In Algebra, we undo the addition/subtraction (the shoe) BEFORE we undo the multiplication/division (the sock).
1. The Standard Path: Solve for the identity of the Unknown.
A. $2x + 10 = 30$
$x = $
B. $3n - 5 = 16$
$n = $
C. $5y + 12 = 47$
$y = $
D. $10x - 20 = 80$
$x = $
2. The Narrow Path: Watch the signs in the deep waters!
A. $-2x + 4 = 12$
$x = $
B. $4n + (-10) = 14$
$n = $
3. The Divider's Path: Fractions are just divisions in disguise.
A. $\frac{x}{2} + 5 = 10$
$x = $
B. $\frac{n}{3} - 4 = 2$
$n = $

Echad Extension: Priority and Order

In life, some things must happen before others. You cannot harvest until you plant. You cannot lead until you serve. In math, you cannot "divide the sock" until you "move the shoe."

Reflection: Why is it important to follow the correct order? What happens if you try to divide the whole side by 2 before subtracting the 10? Try it on $2x + 10 = 30$ and see if it makes the mystery easier or harder.

Lesson 5.2: Tiding the Sanctuary (Combining Like Terms)

The Rule of Harmony: Before you move anything across the Wall of Integrity (the equals sign), you must tidy your own room. You can only combine terms that look like each other.

$2x + 3x$ becomes $5x$. But $2x + 3$ stays exactly as it is!
1. Sorting the Offerings: Circle the Like Terms that can be combined.
$3x \quad 5 \quad -2x \quad 10n \quad 4 \quad x$
2. Cleaning the Left Side: Simplify before you solve.
A. $4x + 2x + 5 = 23$
$\implies$ $+ 5 = 23$
B. $10n - 3n - 4 = 17$
$\implies$ $- 4 = 17$
3. Full Tidy and Solve: Show the two-step solve after you simplify.
A. $5x + x + 10 = 40$
$x = $
B. $12n - 2n - 8 = 22$
$n = $

🛠️ The Scribe's Repair Bench

A student sees $3x + 5 = 20$ and writes $8x = 20$.

What is the Rupture? Can you add an "$x$" to a number that has no variable? Why or why not?

Lesson 5.3: Opening the Gates (Distributive Property)

The Gift for All: The number outside the parentheses is a gift for EVERYONE inside. To open the gate, you must multiply the outside number by every term inside.

Draw your Rainbow Arrows to make sure no one is forgotten!
1. The Distributive Rainbow: Draw arrows and multiply.
A. $3(x + 5)$
Result:
B. $5(n - 4)$
Result:
C. $10(y + 2)$
Result:
D. $2(3x + 4)$
Result:
2. The Deep Water Gate: Distributing with Negatives.
A. $-2(x + 3)$
Result:
B. $-3(n - 5)$
Result:
3. Opening and Solving: Distribute first, then use your 5.1 skills.
A. $2(x + 4) = 20$
$x = $
B. $5(n - 2) = 15$
$n = $

Lesson 5.4: The Synthesis (The Master Plan)

The Master Plan Checklist:
  1. Distribute: Open any gates (parentheses).
  2. Combine: Tidy each side of the room.
  3. Move the Shoe: Add or subtract the loose number.
  4. Remove the Sock: Multiply or divide to isolate the Unknown.
  5. Verify: Plug your answer back in to ensure it is Truth.
1. Executing the Plan: Solve these multi-step mysteries.
A. $2(x + 5) + 4 = 24$
$x = $
B. $3(n - 2) - n = 10$
$n = $

The Scribe's Precision Grid: 60 Challenges

Solve these rapid-fire to build your endurance. Check your results with your Mentor.

1. $2x+1=5 \implies$
2. $3x-2=7 \implies$
3. $5n+5=30 \implies$
4. $x/2+4=10 \implies$
5. $x/4-1=4 \implies$
6. $2(x+1)=10 \implies$
7. $3(n-4)=0 \implies$
8. $x+x+5=15 \implies$
9. $10-x=5 \implies$
10. $20-2n=10 \implies$
11. $2x+3x=25 \implies$
12. $5y-y=16 \implies$
13. $4(x+2)=20 \implies$
14. $2(n-5)=10 \implies$
15. $x/3+1=2 \implies$
16. $100x+1=101 \implies$
17. $x+10=2x \implies$
18. $3n=n+10 \implies$
19. $2(x+2)+1=9 \implies$
20. $5(n-1)-5=0 \implies$
21. $-2x=10 \implies$
22. $x/(-2)=5 \implies$
23. $x-10=-5 \implies$
24. $2(x-4)=-8 \implies$
25. $x+x+x+x=4 \implies$
26. $10/x = 2 \implies$
27. $0.5x = 10 \implies$
28. $x+0.5=1 \implies$
29. $2(x+0.5)=3 \implies$
30. $x/10-10=0 \implies$
31. $x+5=12 \implies$
32. $x-7=3 \implies$
33. $4x=20 \implies$
34. $x/5=2 \implies$
35. $2x+4=12 \implies$
36. $3n-1=20 \implies$
37. $x/2+5=15 \implies$
38. $10y-20=30 \implies$
39. $5(x+1)=25 \implies$
40. $2(n-10)=0 \implies$
41. $x+x=20 \implies$
42. $3x+2x=50 \implies$
43. $10n-5n=25 \implies$
44. $x/(-1)=10 \implies$
45. $-x=5 \implies$
46. $2(x+3)+x=15 \implies$
47. $3(n-2)+2=14 \implies$
48. $x/2-1=0 \implies$
49. $100/x=10 \implies$
50. $2x-x=5 \implies$
51. $x+1=1 \implies$
52. $x-1=-1 \implies$
53. $0x=0 \implies$
54. $1x=7 \implies$
55. $2(x+x)=8 \implies$
56. $x/4+x/4=1 \implies$
57. $10(x-1)=90 \implies$
58. $5(y+2)=10 \implies$
59. $2x+2x+2x=18 \implies$
60. $x-x+5=5 \implies$

Edition 9 Capstone: The Full Reveal

The Journey Review: You have traveled from the Mystery Box to the Master Plan. Use all your tools to solve these final challenges.
1. The Unit 1 Legacy (The Mystery Box): If $x + 10 = 25$, what is $x$?
$x = $
2. The Unit 2 Legacy (The Balance Scale): Draw the scale for $3x = 12$.
$x = $
3. The Unit 3 Legacy (Deep Waters): Solve $-5 + x = -12$.
$x = $
4. The Unit 4 Legacy (The Watchman): Is $x = 5$ a solution for $2x + 1 > 10$? Show your check.
Result:

The Scribe's Journal: Reflections on Edition 9

Meditation: The Architecture of Identity

Throughout this edition, you have searched for the "Unknown." You have learned that even when something is hidden, it still has a value. It still has an identity. You just need to follow the path of truth to reveal it.

Reflect: How has solving for $x$ changed the way you look at problems in your life? Do you feel more confident that order can be found in a messy situation? Write your thoughts below.

The Scribe's Dictionary: Edition 9 Vocabulary

Variable:
A symbol (like $x$ or $n$) that stands for a hidden truth or unknown value.
Equation:
A mathematical sentence that declares two things are exactly equal, separated by the Wall of Integrity ($=$).
Inverse Operation:
The "opposite" action that undoes a previous move (e.g., Subtraction undoes Addition).
Isolate:
The act of moving everything away from the variable so it stands alone, revealing its identity.
Coefficient:
The number "hugging" the variable (e.g., the 5 in $5x$). It tells you how many of the unknown you have.
Constant:
A number that stands alone and does not change (e.g., the 10 in $2x + 10$).
Distributive Property:
The law that allows a multiplier to visit every member of a group inside parentheses.
Like Terms:
Terms that share the same variable part and can be combined into a single, unified group.
Linear:
A path that is straight and direct, where the variable is never squared or hidden in complex powers.
Shalom:
The state of perfect balance and peace found when an equation is solved and verified.

The Prophet's Vision: Real-World Multi-Step Logic

1. The Stewardship of Seeds: A farmer has 2 bags of seeds. Each bag has the same number of seeds ($x$). He finds 5 more seeds on the ground. He now has 25 seeds in total. How many seeds were in each bag?
Equation: Answer:
2. The Builder's Measurement: A builder needs to cut 3 boards of the same length ($L$). Each board needs to have 2 inches trimmed off. The total length of the 3 trimmed boards is 30 inches. What was the original length of each board?
Equation: Answer:
3. The Tithing Challenge: A man wants to give away 10% of his coins. He has 3 identical pouches of coins, and he finds 50 extra coins. If he gives away 20 coins, and that equals his 10% tithe of a total 200 coins... wait, let's simplify! A man has 3 identical pouches ($p$) and 5 extra coins. The total number of coins is 50. How many coins are in each pouch?
Equation: Answer:
4. The Sanctuary Flooring: You are tiling a floor that is 100 square feet. You have 4 boxes of tiles, but each box has 5 tiles that are broken. If the total number of good tiles you have is 80, how many tiles were originally in each box?
Equation: Answer:
5. The Shepherd's Gathering: A shepherd has 5 flocks of sheep. Each flock has the same number ($s$). He buys 10 more sheep. Later, half of his total sheep are moved to another field. If 30 sheep are moved, how many sheep were in each original flock? (Hint: This is a triple-step mystery!)
Equation: Answer:

C.A.M.E. Verification Node: The Scribe's Audit

A student is solving the mystery: $4(x + 3) = 20$.

They write:
Step 1: $4x + 3 = 20$
Step 2: $4x = 17$
Step 3: $x = 17/4$

Is this the Truth? Look closely at the "Gate" in Step 1. What did the student forget to distribute? Show the correct path below.

Verdict of the Scribe:

The Covenant

"I, a Master Architect of Edition 9, solemnly promise to follow the Master Plan in all my works. I will distribute my gifts fairly, tidy my heart of clutter, and always maintain the balance of truth. I have learned that complexity is no match for a sequence of honor. I will use the tools of Algebra to reveal the hidden shalom in every challenge."

Signed:

Date:

EDITION 9 MASTERED!

You have walked the path from the Unknown to the Revealed.

HALLELUYAH!

🕊️