Building Mathematical Excellence Through Time-Tested Principles
TRUTH CARRIERS EDUCATION SYSTEM
Practical Skills Series - All Ages
Purpose: Teach mathematics using classical methods that have proven successful for generations.
Philosophy:
| Tier | Ages | Focus |
|---|---|---|
| TIER 1 | 6-9 | Foundations: Numbers, Operations, Basic Geometry |
| TIER 2 | 10-13 | Intermediate: Fractions, Percentages, Pre-Algebra |
| TIER 3 | 14-18 | Advanced: Algebra, Geometry, Trigonometry, Calculus |
This workbook uses the 6 Rs Learning Method for deep understanding and long-term retention:
Understanding place value is the foundation of all mathematics.
In the number 456:
456 = 400 + 50 + 6
1. In 783, which digit is in the hundreds place?
○ A) 3
○ B) 8
○ C) 7
○ D) 0
2. What is 400 + 30 + 5?
○ A) 435
○ B) 345
○ C) 453
○ D) 534
Close this workbook. Write what hundreds, tens, and ones mean. Write an example number broken into place values.
Explain place value to a younger sibling using real objects (coins, blocks, etc.).
Person: Date:
1. 46 + 27 = ?
○ A) 63
○ B) 73
○ C) 83
○ D) 72
2. When ones add to 10+, you must:
○ A) Stop
○ B) Carry to tens place
○ C) Start over
○ D) Guess
Write the steps for addition with carrying from memory.
Multiplication facts should be automatic. Practice until instant recall!
5s: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
10s: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
9s Trick: 9×4=36 (3+6=9), 9×7=63 (6+3=9) - digits always add to 9!
| 3 × 4 = ____ | 5 × 6 = ____ | 2 × 9 = ____ | 4 × 7 = ____ |
| 6 × 8 = ____ | 7 × 7 = ____ | 8 × 9 = ____ | 9 × 6 = ____ |
| 12 × 5 = ____ | 11 × 8 = ____ | 7 × 8 = ____ | 9 × 9 = ____ |
1. 7 × 8 = ?
○ A) 54
○ B) 56
○ C) 63
○ D) 48
2. 9 × 6 = ?
○ A) 54
○ B) 45
○ C) 63
○ D) 56
Write out the 7 times table from memory (7×1 through 7×12).
Numerator (top) = parts you have
Denominator (bottom) = total parts in whole
Example: ¾ means 3 parts out of 4 total
1. ½ × ⅔ = ?
○ A) ⅓
○ B) ⅔
○ C) ⅙
○ D) 1
2. To divide fractions, you:
○ A) Multiply straight across
○ B) Keep-Change-Flip
○ C) Add them
○ D) Subtract them
Write the rules for multiplying and dividing fractions from memory.
Percent = "Per Hundred"
25% = 25/100 = 0.25
To find percent of a number: Convert to decimal, multiply
Example: 25% of 80 = 0.25 × 80 = 20
| Fraction | Decimal | Percent |
|---|---|---|
| ½ | 0.5 | 50% |
| ¼ | 0.25 | 25% |
| ⅓ | 0.333... | 33.3% |
| ¾ | 0.75 | 75% |
1. 20% of 60 = ?
○ A) 10
○ B) 12
○ C) 15
○ D) 20
2. A $100 item with 30% off costs:
○ A) $30
○ B) $70
○ C) $130
○ D) $80
Write how to calculate: discount, tip, and sales tax from memory.
Goal: Isolate the variable (get x alone)
Rule: What you do to one side, do to the other
1. If 2x + 3 = 11, then x = ?
○ A) 4
○ B) 5
○ C) 7
○ D) 8
2. To solve 5x = 45, you should:
○ A) Add 5
○ B) Subtract 5
○ C) Multiply by 5
○ D) Divide by 5
Write the steps to solve a two-step equation from memory.
a² + b² = c²
Where c = hypotenuse (longest side, opposite the right angle)
a and b = the two legs
1. In a right triangle with legs 6 and 8, the hypotenuse is:
○ A) 14
○ B) 10
○ C) 12
○ D) 100
2. The Pythagorean theorem only works for:
○ A) All triangles
○ B) Right triangles
○ C) Equilateral triangles
○ D) Squares
Write the Pythagorean theorem and 3 Pythagorean triples from memory.
Numbers in Scripture Reveal Divine Design
This section explores:
"The heavens declare the glory of Elohim; and the firmament shows His handiwork." — Psalm 19:1
Throughout the Bible, certain numbers carry consistent symbolic meaning. Understanding these patterns enriches our study of Scripture.
| Number | Meaning | Example |
|---|---|---|
| 1 | Unity, Oneness of Yahuah | "Yahuah is ONE" (Deut 6:4) |
| 3 | Divine completeness | Yahusha rose on the 3rd day |
| 4 | Earth/Creation | 4 corners, 4 seasons, 4 Gospels |
| 6 | Man (falling short) | Man created on day 6; 666 |
| 7 | Perfection/Completion | 7 days, 7 feasts, 7 churches |
| 10 | Testimony/Law | 10 Commandments, 10 plagues |
| 12 | Government/Authority | 12 tribes, 12 apostles |
| 40 | Testing/Trial | 40 days (Noah, Moses, Yahusha) |
| 70 | Restoration/Elders | 70 elders, 70 weeks (Daniel 9) |
1. The number 7 in Scripture represents:
○ A) Man's effort
○ B) Perfection and completion
○ C) Testing
○ D) Judgment
2. Why is 40 significant in the Bible?
○ A) It represents wealth
○ B) It represents testing/trial periods
○ C) It is a random number
○ D) It means victory
3. The number 12 appears with:
○ A) Tribes of Israel and Apostles
○ B) Days of creation
○ C) Years of famine
○ D) None of the above
1. The number 6 represents human effort falling short. ___
2. There were 10 plagues upon Egypt. ___
3. The number 3 represents testing. ___
Close the book and write the meanings of: 1, 3, 7, 12, 40.
Explain to someone why the number 7 appears so often in Scripture.
Person: Date:
In Hebrew, each letter also represents a number. This system is called gematria. The same word can be read as letters OR as a number!
| Letter | Name | Value | Letter | Name | Value |
|---|---|---|---|---|---|
| א | Aleph | 1 | ל | Lamed | 30 |
| ב | Bet | 2 | מ | Mem | 40 |
| ג | Gimel | 3 | נ | Nun | 50 |
| ד | Dalet | 4 | ס | Samech | 60 |
| ה | Hey | 5 | ע | Ayin | 70 |
| ו | Vav | 6 | פ | Pey | 80 |
| ז | Zayin | 7 | צ | Tsade | 90 |
| ח | Chet | 8 | ק | Qoph | 100 |
| ט | Tet | 9 | ר | Resh | 200 |
| י | Yod | 10 | ש | Shin | 300 |
| כ | Kaph | 20 | ת | Tav | 400 |
1. Gematria is:
○ A) A Hebrew prayer
○ B) A number system where letters = numbers
○ C) A type of Hebrew bread
○ D) Ancient astronomy
2. The Hebrew word חי (Chai = "life") equals:
○ A) 7
○ B) 12
○ C) 18
○ D) 40
3. Which letter has the highest value?
○ A) Aleph (1)
○ B) Yod (10)
○ C) Qoph (100)
○ D) Tav (400)
1. In Hebrew, the same symbol can be both a letter and a number. ___
2. The value of Yod is 100. ___
3. "Echad" (One) and "Ahavah" (Love) have the same gematria value. ___
Write the values of Aleph, Yod, and Tav from memory. Calculate חי.
Explain what gematria is to a family member and show them how חי = 18.
Person: Date:
The natural world reveals precise mathematical patterns that point to intelligent design rather than random chance.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
Each number = the sum of the two before it
1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13...
When you divide consecutive Fibonacci numbers, you approach 1.618:
13÷8 = 1.625, 21÷13 = 1.615, 34÷21 = 1.619...
This ratio appears throughout creation and is considered "divinely beautiful."
1. The Fibonacci sequence starts with:
○ A) 1, 2, 3, 4, 5
○ B) 0, 1, 1, 2, 3, 5
○ C) 2, 4, 6, 8, 10
○ D) 1, 3, 5, 7, 9
2. The Golden Ratio is approximately:
○ A) 3.14
○ B) 1.618
○ C) 2.718
○ D) 1.414
3. Which is NOT a Fibonacci number?
○ A) 5
○ B) 8
○ C) 9
○ D) 13
1. Sunflower seed spirals follow Fibonacci patterns. ___
2. The golden ratio appears in the structure of DNA. ___
3. The number 7 is in the Fibonacci sequence. ___
Write the first 10 Fibonacci numbers and explain how to calculate them.
Show a family member Fibonacci patterns in a flower, pinecone, or spiral shell.
Person: Date:
Instructions: After completing each lesson, return to review at these intervals.
| Lesson | Completed | Day 1 | Day 3 | Day 7 | Day 21 | Day 60 |
|---|---|---|---|---|---|---|
| 1. Place Value | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
| 2. Addition/Carrying | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
| 3. Multiplication Tables | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
| 4. Fractions | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
| 5. Percentages | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
| 6. Solving Equations | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
| 7. Pythagorean Theorem | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
| BIBLICAL MATHEMATICS | ||||||
| 8. Biblical Number Symbolism | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
| 9. Hebrew Gematria | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
| 10. Patterns in Creation | ___/___ | ☐ | ☐ | ☐ | ☐ | ☐ |
"Precept upon precept... line upon line..." — Isaiah 28:10
1) 3, 4, 7; 2) 582; 3) 2
MC: 1-C, 2-A
35+27=62, 58+34=92, 67+25=92, 89+47=136
Word: 1) 85, 2) 101
MC: 1-B, 2-B
12, 30, 18, 28, 48, 49, 72, 54, 60, 88, 56, 81
MC: 1-B, 2-A
1) ⅜, 2) 2⅔, 3) 7/3
MC: 1-A, 2-B
1) $30, 2) $5.25, $40.25, 3) $54
MC: 1-B, 2-B
1) 6, 2) 7, 3) 5, 4) 7
MC: 1-A, 2-D
1) 10, 2) 13, 3) 12
MC: 1-B, 2-B
1) 12, 2) 40, 3) 7, 4) 40, 5) 5
MC: 1-B (Perfection and completion), 2-B (Testing/trial periods), 3-A (Tribes and Apostles)
T/F: 1-TRUE, 2-TRUE, 3-FALSE (3 represents divine completeness)
1) 6, 2) 26 (YHVH), 3) 18, 4) 376 (Shalom)
MC: 1-B (Number system), 2-C (18), 3-D (Tav=400)
T/F: 1-TRUE, 2-FALSE (Yod=10), 3-TRUE (both=13)
1) 21, 2) 89, 3) 1.615 or 1.62, 4) 1.617 or 1.62, 5) 3
MC: 1-B (0,1,1,2,3,5), 2-B (1.618), 3-C (9 is not Fibonacci)
T/F: 1-TRUE, 2-TRUE, 3-FALSE (Fibonacci: 1,1,2,3,5,8,13... no 7)