📚 GRADE 9 · ACADEMIC YEAR 2025–2026
Freshman
Math Explorer
Your colorful, friendly guide to mastering 9th Grade Mathematics
Meet Max the Math Wizard — he'll guide you through every unit!
🔢 Unit 1: Numbers & Ops 🔡 Unit 2: Algebra
📈 Unit 3: Linear Functions 📐 Unit 4: Geometry
📊 Unit 5: Statistics 🔭 Unit 6: Functions II
"Mathematics is not about numbers, equations, or algorithms: it is about
understanding."
— William Paul Thurston
🌟 🔥 🏆 🧠
EXPLORER STREAK CHAMPION GENIUS
🚀
ROCKET
Earn badges by completing chapters & quizzes!
, UNIT 1
🔢 Numbers & Operations
From integers to scientific notation — master the building blocks of
all mathematics.
Real Numbers Fractions & Decimals Exponents
Radicals Scientific Notation
📊 Unit Progress Tracker
REAL NUMBERS FRACTIONS EXPONENTS RADICALS
SCI NOTATION
,🔢 1.1 — The Real Number System
Every number you'll ever use belongs to the Real Number System.
Think of it like a family tree of numbers:
ℝ Real Numbers
ℚ Rational Numbers Irrational Numbers
ℤ Integers π ≈ 3.14159…
√2 ≈ 1.41421…
𝕎 Whole Nos.
e ≈ 2.71828…
ℕ Natural: 1, 2, 3… √3, √5, √7…
🎯 Key Idea
Natural numbers: 1, 2, 3, 4… (counting numbers)
Whole numbers: 0, 1, 2, 3… (naturals + zero)
Integers: …−3, −2, −1, 0, 1, 2, 3… (whole + negatives)
Rational: any number expressible as p/q (e.g. ½, 0.75, −3)
Irrational: decimals that never end or repeat (e.g. π, √2)
💡 Did You Know? The number π has been calculated to over
100 trillion decimal places and it never repeats! Ancient
Egyptians used 3.16 as their approximation of π.
, ⚡ 1.2 — Exponents & Their Laws
DEFINITION
aⁿ = a × a × a × … × a (n times)
Law Rule Example
Product aᵐ · aⁿ = aᵐ⁺ⁿ 2³ · 2⁴ = 2⁷ = 128
Quotient aᵐ ÷ aⁿ = aᵐ⁻ⁿ 5⁶ ÷ 5² = 5⁴ = 625
Power of Power (aᵐ)ⁿ = aᵐⁿ (3²)⁴ = 3⁸ = 6561
Zero Exponent a⁰ = 1 (a ≠ 0) 99⁰ = 1
Negative Exponent a⁻ⁿ = 1/aⁿ 2⁻³ = 1/8
⚠️ Mistake Alert!
❌ (2 + 3)² ≠ 2² + 3² → ✅ (2+3)² = 5² = 25
❌ 2³ ≠ 2×3=6 → ✅ 2³ = 2×2×2 = 8
🎮 Interactive: Explore Powers
Base (a): 2 2
Exponent (n): 3 3
2³ = 8
Freshman
Math Explorer
Your colorful, friendly guide to mastering 9th Grade Mathematics
Meet Max the Math Wizard — he'll guide you through every unit!
🔢 Unit 1: Numbers & Ops 🔡 Unit 2: Algebra
📈 Unit 3: Linear Functions 📐 Unit 4: Geometry
📊 Unit 5: Statistics 🔭 Unit 6: Functions II
"Mathematics is not about numbers, equations, or algorithms: it is about
understanding."
— William Paul Thurston
🌟 🔥 🏆 🧠
EXPLORER STREAK CHAMPION GENIUS
🚀
ROCKET
Earn badges by completing chapters & quizzes!
, UNIT 1
🔢 Numbers & Operations
From integers to scientific notation — master the building blocks of
all mathematics.
Real Numbers Fractions & Decimals Exponents
Radicals Scientific Notation
📊 Unit Progress Tracker
REAL NUMBERS FRACTIONS EXPONENTS RADICALS
SCI NOTATION
,🔢 1.1 — The Real Number System
Every number you'll ever use belongs to the Real Number System.
Think of it like a family tree of numbers:
ℝ Real Numbers
ℚ Rational Numbers Irrational Numbers
ℤ Integers π ≈ 3.14159…
√2 ≈ 1.41421…
𝕎 Whole Nos.
e ≈ 2.71828…
ℕ Natural: 1, 2, 3… √3, √5, √7…
🎯 Key Idea
Natural numbers: 1, 2, 3, 4… (counting numbers)
Whole numbers: 0, 1, 2, 3… (naturals + zero)
Integers: …−3, −2, −1, 0, 1, 2, 3… (whole + negatives)
Rational: any number expressible as p/q (e.g. ½, 0.75, −3)
Irrational: decimals that never end or repeat (e.g. π, √2)
💡 Did You Know? The number π has been calculated to over
100 trillion decimal places and it never repeats! Ancient
Egyptians used 3.16 as their approximation of π.
, ⚡ 1.2 — Exponents & Their Laws
DEFINITION
aⁿ = a × a × a × … × a (n times)
Law Rule Example
Product aᵐ · aⁿ = aᵐ⁺ⁿ 2³ · 2⁴ = 2⁷ = 128
Quotient aᵐ ÷ aⁿ = aᵐ⁻ⁿ 5⁶ ÷ 5² = 5⁴ = 625
Power of Power (aᵐ)ⁿ = aᵐⁿ (3²)⁴ = 3⁸ = 6561
Zero Exponent a⁰ = 1 (a ≠ 0) 99⁰ = 1
Negative Exponent a⁻ⁿ = 1/aⁿ 2⁻³ = 1/8
⚠️ Mistake Alert!
❌ (2 + 3)² ≠ 2² + 3² → ✅ (2+3)² = 5² = 25
❌ 2³ ≠ 2×3=6 → ✅ 2³ = 2×2×2 = 8
🎮 Interactive: Explore Powers
Base (a): 2 2
Exponent (n): 3 3
2³ = 8
