MATHEMATICS: TRADITIONAL METHODS

Youth Edition (Ages 12-17) • Truth Carriers 6Rs

Proverbs 22:29
"Do you see a person skilled in their work? They will stand before kings."

Why Traditional Methods?

Clear, efficient algorithms that work every time
Mastery first — automatic facts free brain space for higher math
Real-world practice (money, measurements, science, trades)
Biblical stewardship: excellence, honesty, and diligence

How to Use (6Rs Method)

1. RECEIVE
Read the teaching and examples.

2. REFLECT
Work the practice problems.

3. RECALL
Close the book; write steps from memory.

4. RECITE
Teach a friend or sibling.

5. REVIEW
Use the spaced-review table.

6. RESPOND
Apply math in real-life tasks.

Lesson 1: Strong Foundations (Place Value & Facts)

Solid place value and automatic facts make every other topic faster and clearer.

Place Value: Each digit’s value depends on its position (ones, tens, hundreds, thousands).

Number	Expanded Form	Say It
4,506	4,000 + 500 + 6	"Four thousand five hundred six"
72,019	70,000 + 2,000 + 19	"Seventy-two thousand nineteen"

Quick Drills

1) 3,407 = ______ thousands + ______ tens + ______ ones

2) What digit is in the ten-thousands place of 56,912? ______

3) 8 hundreds + 7 tens + 5 ones = ______

Multiple Choice

1. In 29,681 the digit 9 means:

○ A) 9 ones ○ B) 9 tens ○ C) 9 thousands

2. 7,050 said correctly is:

○ A) Seven thousand fifty ○ B) Seven zero five zero ○ C) Seven hundred fifty

True / False

○ T ○ F — 40,012 has a 4 in the ten-thousands place.

○ T ○ F — Memorizing facts frees your brain for tougher problems.

Scripture Memory: Colossians 3:23

"Whatever you do, work at it with all your heart, as working for Yahuah."

Day 1 Day 3 Day 7

Recall (Close your book)

Write the place values from ones to hundred-thousands and give one example.

Teach-Back

Teach someone how to say and expand 17,304 correctly.

Person: Date:

Apply

Read a grocery receipt; identify place value of three prices.
Practice a 2-minute math-fact drill (× and ÷ up to 12s).

Lesson 2: Standard Algorithms (Add, Subtract, Multiply, Divide)

Traditional algorithms are reliable, fast, and easy to check.

Steps to Add/Subtract Multi-Digit

Line up place values.
Start in ones; carry or borrow as needed.
Check with inverse (add back or subtract back).

Long Multiplication (example 347 × 26)

347 × 6 (ones row)
347 × 2 (tens row) → write one zero first
Add the two partial products

Long Division (example 864 ÷ 7)

Divide → Multiply → Subtract → Bring down (repeat)
Write remainders clearly or express as fraction

Practice

1) 4,785 + 2,968 = ______

2) 6,003 − 2,458 = ______

3) 243 × 18 = ______

4) 952 ÷ 7 = ______ remainder ______

Multiple Choice

1. When multiplying by a tens digit you should:

○ A) Ignore the zero ○ B) Add a zero placeholder ○ C) Start from left

2. The inverse to check subtraction is:

○ A) Multiply ○ B) Add ○ C) Divide

True / False

○ T ○ F — In long division you bring down one digit at a time.

○ T ○ F — Estimating first helps you catch place-value mistakes.

Recall

Write the four steps of long division without looking.

Teach-Back

Show a friend how to multiply a 3-digit by a 2-digit number with placeholders.

Person: Date:

Apply

Add the prices of 3 items and subtract a coupon.
Split a cost among friends using long division.

Lesson 3: Fractions, Decimals, Percents

These are three ways to write the same quantity. Converting quickly is key.

Basics: Fraction → divide top by bottom to get decimal; move decimal ×100 to get percent.

Fraction	Decimal	Percent
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%

Operations

Add/Subtract: Common denominator, add numerators, simplify.
Multiply: Multiply tops, multiply bottoms, simplify.
Divide: Keep-Change-Flip (invert the second fraction, then multiply).

Practice

1) 3/8 + 1/4 = ______

2) 2/3 × 3/5 = ______

3) 5/6 ÷ 2/3 = ______

4) 18% of 50 = ______

5) Convert 0.35 to fraction (simplest): ______

Multiple Choice

1. To divide fractions you should:

○ A) Common denominator first ○ B) Keep-Change-Flip ○ C) Cross-add

2. 30% as a decimal is:

○ A) 0.03 ○ B) 0.30 ○ C) 3.0

True / False

○ T ○ F — Simplifying at the end is okay, but checking mid-step can help.

○ T ○ F — Percent means “per hundred.”

Scripture Memory: Proverbs 11:1

"A false balance is abomination to Yahuah, but a just weight is His delight."

Recall

Write the three conversions (fraction ↔ decimal ↔ percent) and one example of each.

Teach-Back

Explain to someone how to do Keep-Change-Flip with 5/8 ÷ 1/4.

Person: Date:

Apply

Calculate sale price of a $40 item at 25% off.
Double or halve a recipe using fractions.

Lesson 4: Algebra Basics (Solve for x)

Solving equations is about isolating the variable with inverse operations.

Steps

Simplify both sides (combine like terms).
Undo addition/subtraction first.
Undo multiplication/division second.
Keep balance: what you do to one side, do to the other.

Examples

x + 7 = 19 → x = 12

3x − 5 = 16 → 3x = 21 → x = 7

4(x + 2) = 28 → x + 2 = 7 → x = 5

Practice

1) x + 9 = 21 → x = ______

2) 5x = 45 → x = ______

3) 2x + 6 = 22 → x = ______

4) (x − 3)/4 = 5 → x = ______

Multiple Choice

1. First step to solve 2x + 5 = 19:

○ A) Multiply by 2 ○ B) Subtract 5 ○ C) Add 5

2. Inverse of multiplying by 4 is:

○ A) Add 4 ○ B) Divide by 4 ○ C) Subtract 4

True / False

○ T ○ F — Distributing 3 over (x + 2) gives 3x + 6.

○ T ○ F — You can check by plugging your answer back in.

Recall

Write the “undo” order for two-step equations.

Teach-Back

Show someone how to solve 3(x − 2) = 18.

Person: Date:

Apply

Write a real-life equation: 3 friends split $48 → amount each?
Check an answer by substitution.

Lesson 5: Geometry & Pythagorean Theorem

Right triangles unlock distances and design.

Pythagorean Theorem: a² + b² = c² (c is the hypotenuse).

Triangle	a	b	c
3-4-5	3	4	5
5-12-13	5	12	13

Practice

1) Legs 6 and 8 → c = ______

2) Leg 9, hypotenuse 15 → other leg = ______

3) How long is a ladder reaching 12 ft up with base 5 ft out? ______

Multiple Choice

1. Pythagorean theorem works for:

○ A) All triangles ○ B) Right triangles only ○ C) Squares

2. The hypotenuse is the side:

○ A) Opposite the right angle ○ B) Shortest side ○ C) With a right angle

True / False

○ T ○ F — 7, 24, 25 is a Pythagorean triple.

○ T ○ F — To solve for a leg: subtract squares, then square root.

Recall

Write the formula and one real-life use (carpentry, measuring a diagonal, etc.).

Teach-Back

Explain how to test if a corner is square using 3-4-5.

Person: Date:

Apply

Find the diagonal of your TV (measure width/height; use a²+b²=c²).
Draw a right triangle and label a, b, c.

Lesson 6: Patterns, Stewardship, and Faith

Math reveals order in creation and helps us steward resources with integrity.

Patterns: Fibonacci (0,1,1,2,3,5,8,13...) appears in flowers, shells, galaxies. Golden ratio ≈ 1.618 shows design.

Psalm 19:1
"The heavens declare the glory of Elohim; the skies proclaim the work of His hands."

Financial Stewardship Basics

Track: Income − Giving − Saving − Spending = 0 (zero-based plan)
Percentage sense: 10% giving, 10% saving, planned spending
Honesty: accurate totals, no “fuzzy math” (Proverbs 11:1)

Practice

1) Next Fibonacci number after 13 is ______

2) If you earn $80, 10% giving + 10% saving = ______ each

3) Golden ratio rounded to two decimals = ______

Multiple Choice

1. Which is NOT a Fibonacci number?

○ A) 8 ○ B) 21 ○ C) 14

2. A “false balance” in Proverbs 11:1 warns against:

○ A) Checking math twice ○ B) Cheating weights/measurements ○ C) Using calculators

True / False

○ T ○ F — Math patterns in nature point to design.

○ T ○ F — Stewardship includes truthful numbers and planned giving.

Recall

List the first 7 Fibonacci numbers from memory.

Teach-Back

Show someone how to compute a 10% tithe from any amount.

Person: Date:

Apply

Make a simple budget for $100 (giving, saving, spending).
Find a Fibonacci pattern in nature (petals, pinecone, shell).

SPACED REVIEW

Check when you review each lesson.

Lesson	Day 1	Day 3	Day 7	Day 21	Day 60
1. Foundations
2. Algorithms
3. Fractions/Percent
4. Algebra
5. Geometry
6. Patterns & Stewardship

Answer Key (Quick Check)

Lesson 1

3,407 = 3 thousands, 0 tens, 7 ones; digit = 6 in ten-thousands of 56,912; 875. MC: 1-C, 2-A. TF: T, T.

Lesson 2

1) 7,753 2) 3,545 3) 4,374 4) 136 r 0 (if 952÷7 = 136) — MC: 1-B, 2-B. TF: T, T.

Lesson 3

1) 5/8 2) 2/5 3) 1 1/4 4) 9 5) 7/20. MC: 1-B, 2-B. TF: T, T.

Lesson 4

1) 12 2) 9 3) 8 4) 23. MC: 1-B, 2-B. TF: T, T.

Lesson 5

1) 10 2) 12 3) 13. MC: 1-B, 2-A. TF: T, T.

Lesson 6

Next Fibonacci: 21; 10% of $80 = $8; Golden ratio ≈ 1.62. MC: 1-C, 2-B. TF: T, T.

TRUTH CARRIERS EDUCATION SYSTEM

“Test all things; hold fast what is good.” — 1 Thessalonians 5:21