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.
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Whole Numbers Lesson
Whole Numbers Quiz
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
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Roman Numerals Lesson
Roman Numeral Quiz (10 Questions)
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
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Integers Lesson
Integer Quiz (10 Questions)
Rational Numbers
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Rational Numbers Lesson
Rational Numbers Quiz (10 Questions)
Real Numbers
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Real Numbers Lesson
Real Numbers Quiz (10 Questions)
Pythagorean Theorem
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Pythagorean Theorem Lesson
Pythagorean Theorem Quiz (5 Questions)
Absolute Value
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Absolute Value Lesson
Absolute Value Quiz (5 Questions)
Factors
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Factors Lesson
Factor Quiz
Multiples
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Multiples Lesson
Multiples Quiz
Prime and Composite Numbers
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Prime and Composite Numbers Lesson
Prime and Composite Numbers Quiz
Prime Factorization
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Prime Factorization Lesson
Prime Factorization Quiz
Algebraic Expressions
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Algebraic Expressions Lesson
Algebraic Expressions Quiz
Solving Linear Systems by Substitution
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Solving Linear Systems by Substitution Lesson
Solving Linear Systems by Substitution Quiz
Solving System of Equations
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Solving System of Equations Lesson
Solving Systems of Equations Quiz
Solutions of a Linear Equation
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Solutions of a linear Equation Lesson
Solutions of Linear Equations Quiz
Variable Expressions
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Variable Expression Lesson
Variable Expressions Quiz
Linear Equations
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Linear Equations Lesson
Linear Equations Quiz
Ratios and Proportions
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Ratios and Proportions Lesson
Ratios and Proportions Quiz
Fractions
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Fractions Lesson
Fractions Quiz
Exponents
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Exponents Lesson
Exponents Quiz
Order of Operations
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Order of Operations Lesson
Order of Operations Quiz
Square roots
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Square roots
Square Roots Quiz
Mean, Median, Mode
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Mean, Median, Mode Lesson
Mean, Median, Mode Quiz
Probability
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Probability Lesson
Probability Quiz
Pre-Algebra

The order of operations is a set of rules that tells us the correct order to perform mathematical operations in an expression. Following these rules makes sure everyone gets the same answer.

To remember the order, we often use PEMDAS.

PEMDAS Explained

PEMDAS stands for:

  1. P – Parentheses
    Solve everything inside parentheses first.

  2. E – Exponents
    Solve exponents (powers) next.

  3. MD – Multiplication and Division
    Do multiplication and division from left to right.

  4. AS – Addition and Subtraction
    Do addition and subtraction from left to right.

⚠️ Important:
Multiplication and division are equal in priority, as are addition and subtraction. Always work left to right.

Example 1

8 + 2 × 5

❌ Wrong way (addition first):

(8 + 2) × 5 = 50

✅ Correct way (multiplication first):

8 + (2 × 5) = 8 + 10 = 18

Example 2

(6+4)^2 ÷ 5

Step-by-step:

  1. Parentheses: 6 + 4 = 10

  2. Exponents: 10^2 = 100

  3. Division: 100 ÷ 5 = 20

✅ Final answer: 20

Why Is the Order of Operations Important?

  • It prevents confusion

  • It makes math consistent

  • It ensures correct answers in algebra, science, and real life

Common Mistakes

  • Adding before multiplying

  • Forgetting to work left to right

  • Ignoring parentheses

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