MATHEMATICS: TRADITIONAL METHODS

Building Mathematical Excellence Through Time-Tested Principles

TRUTH CARRIERS EDUCATION SYSTEM
Practical Skills Series - All Ages

WORKBOOK OVERVIEW

Purpose: Teach mathematics using classical methods that have proven successful for generations.

Philosophy:

THREE TIERS BY AGE

TierAgesFocus
TIER 16-9Foundations: Numbers, Operations, Basic Geometry
TIER 210-13Intermediate: Fractions, Percentages, Pre-Algebra
TIER 314-18Advanced: Algebra, Geometry, Trigonometry, Calculus

HOW TO USE THIS WORKBOOK

The Truth Carriers Learning Method — 6 Rs

This workbook uses the 6 Rs Learning Method for deep understanding and long-term retention:

1. RECEIVE
Read the teaching content. Study the examples. Take notes.
2. REFLECT
Complete practice problems, multiple choice, and true/false questions.
3. RECALL
Close the book and write formulas/methods from memory.
4. RECITE
Teach a concept to someone else. Explaining deepens understanding.
5. REVIEW
Use the spaced review tracker. Review at Day 1, 3, 7, 21, 60.
6. RESPOND
Apply math in real life: measuring, budgeting, building.

TIER 1 - LESSON 1: PLACE VALUE (Ages 6-9)

Core Teaching

Understanding place value is the foundation of all mathematics.

Place Value Chart

In the number 456:

456 = 400 + 50 + 6

Practice Problems

1. 347 = ____ hundreds + ____ tens + ____ ones
2. 5 hundreds + 8 tens + 2 ones = ____
3. What digit is in the tens place of 629? ____

Multiple Choice

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

RECALL EXERCISE

Close this workbook. Write what hundreds, tens, and ones mean. Write an example number broken into place values.

TEACH-BACK CHALLENGE

Explain place value to a younger sibling using real objects (coins, blocks, etc.).

Person: Date:

APPLICATION STEP

TIER 1 - LESSON 2: ADDITION WITH CARRYING (Ages 7-8)

Core Teaching: The Traditional Algorithm

47 + 28 ------ Step 1: Add ones: 7 + 8 = 15 Write 5, carry 1 to tens Step 2: Add tens: 1 + 4 + 2 = 7 ¹ 47 + 28 ------ 75

Practice Problems

35 58 67 89 + 27 + 34 + 25 + 47 ----- ----- ----- -----

Word Problems

1. A farmer has 48 chickens. He buys 37 more. Total: ____
2. 56 students in one class, 45 in another. Total: ____

Multiple Choice

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

RECALL EXERCISE

Write the steps for addition with carrying from memory.

APPLICATION

TIER 1 - LESSON 3: MULTIPLICATION TABLES (Ages 7-9)

The Times Tables to MEMORIZE

Multiplication facts should be automatic. Practice until instant recall!

Key Tables

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!

Timed Drill - Solve in 2 minutes

3 × 4 = ____5 × 6 = ____2 × 9 = ____4 × 7 = ____
6 × 8 = ____7 × 7 = ____8 × 9 = ____9 × 6 = ____
12 × 5 = ____11 × 8 = ____7 × 8 = ____9 × 9 = ____

Multiple Choice

1. 7 × 8 = ?

○ A) 54
○ B) 56
○ C) 63
○ D) 48

2. 9 × 6 = ?

○ A) 54
○ B) 45
○ C) 63
○ D) 56

RECALL

Write out the 7 times table from memory (7×1 through 7×12).

APPLICATION

TIER 2 - LESSON 4: FRACTIONS (Ages 10-11)

Core Teaching

Fraction Parts

Numerator (top) = parts you have

Denominator (bottom) = total parts in whole

Example: ¾ means 3 parts out of 4 total

Multiplying Fractions

2 3 2×3 6 1 - × - = ----- = -- = - 3 4 3×4 12 2 Multiply numerators, multiply denominators, simplify.

Dividing Fractions (Keep-Change-Flip)

2 1 2 2 4 - ÷ - = - × - = - 3 2 3 1 3 Keep first, Change ÷ to ×, Flip second.

Practice

1. ½ × ¾ = ____
2. ⅔ ÷ ¼ = ____
3. Convert 2⅓ to improper fraction: ____

Multiple Choice

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

RECALL

Write the rules for multiplying and dividing fractions from memory.

APPLICATION

TIER 2 - LESSON 5: PERCENTAGES (Ages 11-12)

Core Teaching

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

Common Conversions

FractionDecimalPercent
½0.550%
¼0.2525%
0.333...33.3%
¾0.7575%

Practice - Real World Problems

1. A shirt is $40, on sale for 25% off. Sale price: ____
2. Meal costs $35. 15% tip: ____ Total: ____
3. Sales tax is 8%. Item costs $50. Total with tax: ____

Multiple Choice

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

RECALL

Write how to calculate: discount, tip, and sales tax from memory.

APPLICATION

TIER 3 - LESSON 6: SOLVING EQUATIONS (Ages 14-15)

Core Teaching

Solving One-Step Equations

Goal: Isolate the variable (get x alone)

Rule: What you do to one side, do to the other

x + 5 = 12 3x = 24 x + 5 - 5 = 12 - 5 3x ÷ 3 = 24 ÷ 3 x = 7 x = 8

Two-Step Equations

2x + 5 = 17 Step 1: Subtract 5: 2x = 12 Step 2: Divide by 2: x = 6 Check: 2(6) + 5 = 17 ✓

Practice

1. x + 9 = 15 → x = ____
2. 5x = 35 → x = ____
3. 3x + 7 = 22 → x = ____
4. 4x - 8 = 20 → x = ____

Multiple Choice

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

RECALL

Write the steps to solve a two-step equation from memory.

APPLICATION

TIER 3 - LESSON 7: PYTHAGOREAN THEOREM (Ages 14-16)

Core Teaching

The Pythagorean Theorem

a² + b² = c²

Where c = hypotenuse (longest side, opposite the right angle)

a and b = the two legs

Find hypotenuse: legs = 3 and 4 a² + b² = c² 3² + 4² = c² 9 + 16 = c² 25 = c² c = 5

Common Pythagorean Triples (memorize these!)

Practice

1. Legs = 6 and 8. Hypotenuse = ____
2. Legs = 5 and 12. Hypotenuse = ____
3. Leg = 9, Hypotenuse = 15. Other leg = ____

Multiple Choice

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

RECALL

Write the Pythagorean theorem and 3 Pythagorean triples from memory.

APPLICATION

BIBLICAL MATHEMATICS

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

LESSON 8: BIBLICAL NUMBER SYMBOLISM (All Ages)

Core Teaching: Numbers Have Meaning in Scripture

Throughout the Bible, certain numbers carry consistent symbolic meaning. Understanding these patterns enriches our study of Scripture.

Key Biblical Numbers

NumberMeaningExample
1Unity, Oneness of Yahuah"Yahuah is ONE" (Deut 6:4)
3Divine completenessYahusha rose on the 3rd day
4Earth/Creation4 corners, 4 seasons, 4 Gospels
6Man (falling short)Man created on day 6; 666
7Perfection/Completion7 days, 7 feasts, 7 churches
10Testimony/Law10 Commandments, 10 plagues
12Government/Authority12 tribes, 12 apostles
40Testing/Trial40 days (Noah, Moses, Yahusha)
70Restoration/Elders70 elders, 70 weeks (Daniel 9)

Practice: Finding Number Patterns

1. Yahusha chose ____ disciples (represents authority/government)
2. Israel wandered ____ years in the wilderness (testing)
3. The week has ____ days, with the 7th being Sabbath (completion)
4. Yahusha fasted ____ days in the wilderness (testing)
5. There are ____ books of Moses (Torah = grace/teaching)

Multiple Choice

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

True or False

1. The number 6 represents human effort falling short. ___

2. There were 10 plagues upon Egypt. ___

3. The number 3 represents testing. ___

RECALL EXERCISE

Close the book and write the meanings of: 1, 3, 7, 12, 40.

TEACH-BACK CHALLENGE

Explain to someone why the number 7 appears so often in Scripture.

Person: Date:

APPLICATION STEP

LESSON 9: INTRODUCTION TO HEBREW GEMATRIA (Ages 12+)

Core Teaching: Hebrew Letters Have Number Values

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!

The Hebrew Alphabet Values

LetterNameValueLetterNameValue
אAleph1לLamed30
בBet2מMem40
גGimel3נNun50
דDalet4סSamech60
הHey5עAyin70
וVav6פPey80
זZayin7צTsade90
חChet8קQoph100
טTet9רResh200
יYod10שShin300
כKaph20תTav400

Example Calculations

The Hebrew word for "life" is חי (Chai) ח (Chet) = 8 י (Yod) = 10 ----------- חי = 18 This is why 18 is considered a "lucky" number! Gifts are often given in multiples of 18.
The Hebrew word אחד (Echad = "One") א (Aleph) = 1 ח (Chet) = 8 ד (Dalet) = 4 ----------- אחד = 13 The word אהבה (Ahavah = "Love") also = 13! This shows One Elohim = Love

Practice: Gematria Calculations

1. Aleph (1) + Bet (2) + Gimel (3) = ____
2. Yod (10) + Hey (5) + Vav (6) + Hey (5) = ____ (this spells YHVH!)
3. What is the value of חי (8 + 10)? ____
4. Shin (300) + Lamed (30) + Vav (6) + Mem (40) = ____ (Shalom = Peace)

Multiple Choice

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)

True or False

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. ___

RECALL EXERCISE

Write the values of Aleph, Yod, and Tav from memory. Calculate חי.

TEACH-BACK CHALLENGE

Explain what gematria is to a family member and show them how חי = 18.

Person: Date:

APPLICATION STEP

LESSON 10: MATHEMATICAL PATTERNS IN CREATION (Ages 12+)

Core Teaching: Yahuah's Creation Displays Mathematical Order

The natural world reveals precise mathematical patterns that point to intelligent design rather than random chance.

The Fibonacci Sequence

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...

Fibonacci in Creation

The Golden Ratio (Phi = φ ≈ 1.618)

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."

The Golden Ratio in Creation

Practice: Fibonacci Calculations

1. What is the next number: 1, 1, 2, 3, 5, 8, 13, ____?
2. What is 34 + 55 = ____? (Next Fibonacci number)
3. 21 ÷ 13 = ____ (approximately)
4. 55 ÷ 34 = ____ (approximately)
5. A lily has ____ petals, which is a Fibonacci number.

Multiple Choice

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

True or False

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. ___

RECALL EXERCISE

Write the first 10 Fibonacci numbers and explain how to calculate them.

TEACH-BACK CHALLENGE

Show a family member Fibonacci patterns in a flower, pinecone, or spiral shell.

Person: Date:

APPLICATION STEP

📅 SPACED REVIEW TRACKER

Instructions: After completing each lesson, return to review at these intervals.

LessonCompletedDay 1Day 3Day 7Day 21Day 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

ANSWER KEY

Lesson 1: Place Value

1) 3, 4, 7; 2) 582; 3) 2

MC: 1-C, 2-A

Lesson 2: Addition

35+27=62, 58+34=92, 67+25=92, 89+47=136

Word: 1) 85, 2) 101

MC: 1-B, 2-B

Lesson 3: Multiplication

12, 30, 18, 28, 48, 49, 72, 54, 60, 88, 56, 81

MC: 1-B, 2-A

Lesson 4: Fractions

1) ⅜, 2) 2⅔, 3) 7/3

MC: 1-A, 2-B

Lesson 5: Percentages

1) $30, 2) $5.25, $40.25, 3) $54

MC: 1-B, 2-B

Lesson 6: Equations

1) 6, 2) 7, 3) 5, 4) 7

MC: 1-A, 2-D

Lesson 7: Pythagorean

1) 10, 2) 13, 3) 12

MC: 1-B, 2-B

BIBLICAL MATHEMATICS

Lesson 8: Biblical Number Symbolism

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)

Lesson 9: Hebrew Gematria

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)

Lesson 10: Patterns in Creation

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)