Lesson 1: Whole Numbers and Basic Operations

1⃣ What Are Integers?

An integer is any whole number, including negative numbers and zero.

Examples:

✅ Integers: -3, -1, 0, 5, 100

❌ Not Integers: 0.5, 2.75, ⅓ (because they are fractions or decimals)

2⃣ What Is a Negative Number?

A negative number is any number less than zero.

• Negative integers include: -1, -33, -500

• Zero (0) is also an integer, but it is neither positive nor negative.

📌 Key Concept: Numbers become more negative as they move farther from zero.

For example: -1 is greater than -5 because -1 is closer to zero.

3⃣ Understanding Addition and Subtraction

Addition

✔ Combining two or more numbers to make a larger number.

Example: 3 + 2 = 5

Subtraction

✔ Taking away one number from another.

Example: 5 - 2 = 3

4⃣ Using a Number Line for Addition and Subtraction

A number line is a tool that helps visualize adding and subtracting numbers.

📍 How to Use a Number Line for Addition:

1. Find the first number on the number line.

2. Move to the right for addition.

3. The number you land on is the answer.

Example: 1 + 4 = 5

(Start at 1, move 4 spaces to the right, land on 5.)

📍 How to Use a Number Line for Subtraction:

1. Find the first number on the number line.

2. Move to the left for subtraction.

3. The number you land on is the answer.

Example: 1 - 4 = -3

(Start at 1, move 4 spaces to the left, land on -3.)

5⃣ Adding and Subtracting Negative Numbers

🔹 Adding a Negative Number = Subtracting

Example: 5 + (-3) = 5 - 3 = 2

🔹 Subtracting a Negative Number = Adding

Example: 5 - (-3) = 5 + 3 = 8

📌 Key Rule:

When two negative signs are next to each other (like -(-3)), they turn into a plus (+) sign!

6⃣ Word Problem: Solving Without a Calculator

🔹 Example Question:

Roland has $150 for the week.

• He spends $15 on a shirt.

• He gives $25 each to his two daughters for school lunches.

• He spends $100 on groceries.

• His wife gives him $40.

How much money does he have left?

✔ Step 1: Add all the money he has:

$150 (Roland’s money) + $40 (from his wife) = $190

✔ Step 2: Add all the expenses:

$100 (groceries) + $15 (shirt) + $25 + $25 (lunch) = $165

✔ Step 3: Subtract expenses from total money:

$190 - $165 = $25

✅ Answer: Roland has $25 left.

📌 Test Tip:

For word problems, always:

1. Identify what the question is asking.

2. Choose the correct operation (add or subtract).

3. Write down numbers and calculate step by step.

📌 Lesson Recap

✔ An integer is a whole number.

✔ Negative numbers are numbers less than zero.

✔ Addition combines numbers into a larger value.

✔ Subtraction takes one number away from another.

✔ A number line helps with adding and subtracting.

✔ Adding a negative number is the same as subtracting.

✔ Subtracting a negative number is the same as adding.