HavenHub Math • Edition 9
Unit 3 Workbook: The Deep Waters
The Scribe's Log of Magnitude and Depth
Lesson 3.1: The Identity of Depth
1.Is -5 greater than or less than 0?
2.Which is colder: -10 or -20?
3.Which is deeper: -50 ft or -5 ft?
4.A debt of 100 silver is written as .
5.The opposite of 15 is .
6.The opposite of -9 is .
7.True or False: Zero is a positive number.
8.True or False: -1 is larger than -100.
Mark the points -5, 0, and 3 on the number line below.
Lesson 3.2: Distance from the Heart (Absolute Value)
1.$| -5 | =
2.$| 10 | =
3.$| -100 | =
4.$| 0 | =
5.True or False: Absolute Value is always positive.
6.Which has a larger magnitude: -10 or 5?
7.Which is closer to zero: -2 or 3?
9.Look at a thermometer. If the mercury is 10 steps below zero, what is it?
10.Which is larger: -1 or -1,000?
11.Evaluate $| -12 | + | -8 |$:
12.Which has more distance: -50 or 40?
13.Name a place on earth that is a negative elevation:
14.If you have -10 coins, do you have any money?
15.How many steps from -1 to 1?
16.Is 0 an integer?
17.Is $|x|$ always positive?
18.Which is further left: -5 or -10?
Lesson 3.3 & 3.4: The Battle of the Signs (Addition)
1.$-5 + (-3) =
2.$-10 + (-10) =
3.$-8 + 5 =
4.$10 + (-2) =
5.$-50 + 50 =
6.$-1 + 100 =
7.$-20 + (-5) =
8.$15 + (-20) =
9.$-7 + 7 =
10.$-100 + (-1) =
Lesson 3.5: Redeeming the Debt (Subtraction)
1.$5 - (-2) =
2.$10 - (-10) =
3.$-5 - (-5) =
4.$-10 - 2 =
5.$0 - (-7) =
6.$15 - 20 =
7.$-100 - (-50) =
8.$-1 - (-1) =
Appendix A: The 100-Problem Density Block
Complete all 100 to earn the Diver's Seal of Depth.
1. -5 + -5 = -10
2. -10 + 5 = -5
3. 10 + -10 = 0
4. 5 - (-5) = 10
5. -5 - (-5) = 0
6. | -10 | = 10
7. | 7 | = 7
8. Opposite of 1
9. Opposite of -1
10. Zero is neutral
11. -1 - 1 = -2
12. -1 - (-1) = 0
13. -10 + -20 = -30
14. 20 + -10 = 10
15. -50 + 100 = 50
16. 100 - 200 = -100
17. -5 x 2 = -10
18. -5 x -2 = 10
19. 10 / -2 = -5
20. -10 / -2 = 5
21. $| -50 |$
22. $| 50 |$
23. $| 0 |$
24. $| -1 |$
25. $| 1 |$
26. $-2 + -3 = -5$
27. $-2 + 3 = 1$
28. $2 + -3 = -1$
29. $2 + 3 = 5$
30. $-2 - 3 = -5$
31. Dive -10
32. Rise +10
33. Surface = 0
34. Depth = Negative
35. Height = Positive
36. Debt = -
37. Gift = +
38. Cold = -
39. Heat = +
40. Zero = Balance
41. $x + 5 = 0 o -5$
42. $x - 5 = 0 o 5$
43. $2x = -10 o -5$
44. $x / -2 = 5 o -10$
45. $x + (-1) = 9 o 10$
46. Compare: -5, -2
47. Compare: -10, 0
48. Compare: -1, 1
49. Compare: |-5|, 5
50. Compare: |-10|, 2
51. -10 + -10 + -10 = -30
52. 5 + -5 + 5 = 5
53. -8 + 10 - 2 = 0
54. 100 - 150 = -50
55. -1 x -1 x -1 = -1
56. Keep Change Change
57. Add the Opposite
58. The Battle Rule
59. The Mirror World
60. The Deep Waters
61. If $x=-1, 2x=-2$
62. If $x=-5, x+5=0$
63. If $x=10, -x=-10$
64. If $x=-10, |x|=10$
65. If $x=0, |x|=0$
66. Balance $x-5=-10$
67. Balance $x+5=-2$
68. Balance $2x=-8$
69. Balance $x/-3=3$
70. Balance $x=x$
71. Check -1+-1 = -2
72. Check 5-10 = -5
73. Check -3 x 3 = -9
74. Check -10 / 2 = -5
75. Check -(-5) = 5
76. Solve for the dive
77. Solve for the debt
78. Solve for the chill
79. Solve for the fall
80. Solve for the soul
81. -1 is less than 0
82. 0 is less than 1
83. -100 is far from sun
84. +100 is close to sun
85. Magnitude is weight
86. Measure the Depth
87. Label the Line
88. Protect the Zero
89. Reveal the Opposite
90. Simplify the Sign
91. $x$ + Depth = Level
92. $n$ - Debt = Free
93. $y imes$ Inverse = Identity
94. $z /$ Unity = Portion
95. The Line is Long
96. The Water is Clear
97. The Scribe is True
98. The King is Mercy
99. The Matter is Firm
100. 1.00 Shalom
Instructions for the Scribe: Continue this pattern until you reach 100. Practice addition, subtraction, and absolute value with integers. Accuracy is your Honor.
Appendix D: The Scribe's Altimeter Project
Use this page to practice the art of measuring the heights and the depths.
Step 1: The Mountain. Draw a vertical number line. Mark sea level as 0. Draw a mountain peak at +50 units. Label it "The Height of Praise".
Step 2: The Valley. On the same line, mark a point at -30 units. Label it "The Valley of Need".
Step 3: The Total Walk. If a traveler walks from the valley (-30) all the way to the peak (+50), how far did they walk?
Magnitude: units.
Step 4: The Anchor. Draw a ship at 0. Draw its anchor at -15. If the captain "takes away" the anchor, what is the new depth of the anchor relative to the ship? (It's gone!). Show the math: $0 - (-15) = $.
Appendix B: The Master's Final Audit
Check the boxes only when you have mastered the skill.
- [ ] I can place negative numbers correctly on a number line.
- [ ] I know that Absolute Value is distance from Zero.
- [ ] I can add integers with different signs (The Battle).
- [ ] I can subtract a negative using Keep-Change-Change.
- [ ] I understand that -10 is smaller than -2.
- [ ] I am a faithful Steward of the Deep Waters.
Appendix C: The Litany of the Depth
Recite this to close the unit.
Mentor: Scribe, where does the light of math end?
Student: It never ends. It reaches above the zero and below the zero.
Mentor: What is the weight of a debt?
Student: It is a negative substance, waiting for the restoration of grace.
Mentor: What do we find in the deepest waters?
Student: The symmetry of God's truth and the magnitude of His love.
Mentor: Go now, and do not fear the valley.
Student: Amen. His logic is the floor of the sea.
Unit 3 Complete!
You are ready for the Comparison.
HALLELUYAH!