Pre-Algebra

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About Course

Pre-Algebra is the bridge between arithmetic and real algebraic thinking. This course prepares students to move from working with numbers to working with variables, expressions, and multi-step reasoning.

You’ll build the foundation needed for Algebra I and beyond.

What You’ll Learn

  • Number Theory

    • Whole Numbers
    • Roman Numerals
    • Integers
    • Rational Numbers
    • Real Numbers
    • Pythagorean Theorem
    • Absolute Value

    Factors and Multiples

    • Factors
    • Multiples
    • Prime numbers and Composite numbers
    • Prime factorization

    Linear Equations

    • Algebraic Expressions
    • Solving Linear Systems by Substitution
    • System of Equations Solver
    • Solutions of a Linear Equation
    • Variable expressions
    • Linear Equations

    Ratio and Proportion

    • Ratio
    • Proportion

    Exponents and Square Root

    • Fractions
    • Exponents
    • Order of Operations
    • Square root

    Statistics

    • Mean, Median, Mode
    • Probability

Target Audience

  • 6th–8th grade students

  • Students preparing for Algebra I

  • Anyone who struggles with fractions or negative numbers

  • Homeschool students building a strong math foundation

  • Adults returning to math

For more practice and access to exclusive practice tests, join our Patreon here:

Tethyra | Patreon

To succeed in this course, we recommend:

(Using these links helps support Tethyra at no extra cost to you.)

 

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What Will You Learn?

  • By completing this course, students will:
  • Understand whole numbers, place value, and number operations
  • Perform addition, subtraction, multiplication, and division with confidence
  • Master factors, multiples, GCF, and LCM
  • Work with fractions and decimals: simplify, compare, and convert
  • Grasp ratios, proportions, and basic percent concepts
  • Explore foundational geometry concepts like area, perimeter, and angles
  • Build critical thinking skills with real-world math problems
  • Lay a strong foundation for Algebra and beyond

Course Content

Whole Numbers
1. Place Value Learn how digits represent different values depending on their place in a number. Understand the ones, tens, hundreds, and beyond. 2. Comparing Numbers Master how to determine which numbers are greater or smaller using inequality symbols and number lines. 3. Rounding Numbers Practice rounding numbers to the nearest ten, hundred, or thousand to estimate values more easily.

Roman Numerals
Roman numerals are a number system from Ancient Rome that uses letters to represent numbers instead of digits. Basic Roman Numerals I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000 Quick Rules ✅ If a smaller numeral comes after a bigger one → add Example: VI = 5 + 1 = 6 ✅ If a smaller numeral comes before a bigger one → subtract Example: IV = 5 − 1 = 4

Integers
Integers are whole numbers that can be positive, negative, or zero. Integers do NOT include: ❌ decimals (like 2.5, -0.7) ❌ fractions (like ½, -3/4) 🔢 Types of Integers 1) Positive Integers These are numbers greater than 0: 1, 2, 3, 4, 5, … Example: +8 means you have 8 dollars. 2) Negative Integers These are numbers less than 0: -1, -2, -3, -4, -5, … Example: -8 means you owe 8 dollars or you are 8 below zero. 3) Zero 0 is an integer too! It is the number in the middle of positive and negative numbers. 📍 Integers on a Number Line Integers can be shown on a number line: Numbers to the right of 0 are positive Numbers to the left of 0 are negative Example: … -3, -2, -1, 0, 1, 2, 3 … ➕➖ Integer Operations (How They Work) Adding Integers ✅ Same signs → add, keep the sign 5 + 3 = 8 (-5) + (-3) = -8 ✅ Different signs → subtract, keep the sign of the bigger number 7 + (-2) = 5 (-9) + 4 = -5 Subtracting Integers Subtracting is the same as adding the opposite: Example: 6 − 2 = 4 6 − (-2) = 6 + 2 = 8 (-6) − 2 = -8 (-6) − (-2) = -6 + 2 = -4 Multiplying & Dividing Integers ✅ Same signs → positive (-4)(-3) = 12 4 ÷ 2 = 2 ✅ Different signs → negative (-4)(3) = -12 12 ÷ (-3) = -4 🌎 Real-Life Examples of Integers Integers are used all the time: 📌 Temperature 10°C (positive) -5°C (negative) 📌 Money $20 = you have money -$20 = you owe money 📌 Elevation 200 feet above sea level -50 feet below sea level 📌 Sports +3 points gained -3 points lost

Rational Numbers

Real Numbers

Pythagorean Theorem

Absolute Value

Factors

Multiples

Prime and Composite Numbers

Prime Factorization

Algebraic Expressions

Solving Linear Systems by Substitution

Solving System of Equations

Solutions of a Linear Equation

Variable Expressions

Linear Equations

Ratios and Proportions

Fractions

Exponents

Order of Operations

Square roots

Mean, Median, Mode

Probability