Chapter focus: Integers extend whole numbers to include numbers on both sides of zero. Students use the number line to understand direction, order, comparison and operations with positive and negative numbers.

🎯 Learning Goals

• Understand positive and negative integers.
• Locate integers on a number line.
• Compare and order integers.
• Understand opposite numbers.
• Add and subtract integers using number-line reasoning.
• Apply integers to temperature, height, money and other real situations.

0️⃣ 1. What Are Integers?

Integers include negative whole numbers, zero and positive whole numbers: …, −3, −2, −1, 0, 1, 2, 3, …

Positive integers lie to the right of zero on a number line. Negative integers lie to the left.

📍 2. The Number Line

On a horizontal number line, values increase as we move right and decrease as we move left.

↔️ 3. Opposite Integers

Opposite integers are equally far from zero but on opposite sides. Examples: 5 and −5; 8 and −8.

Zero is its own opposite.

⚖️ 4. Comparing Integers

Use the number line. The integer farther to the right is greater.

Examples: 4 > −2, −1 > −6, and −7 < 0.

➕ 5. Adding Integers

Adding a positive integer moves right on the number line. Adding a negative integer moves left.

Examples: 3 + 4 = 7; 3 + (−5) = −2.

➖ 6. Subtracting Integers

Subtracting a positive integer moves left. Subtracting a negative integer means moving right by the corresponding amount.

Examples: 5 − 3 = 2; 5 − (−3) = 8.

🌡️ 7. Integers in Real Life

• Temperatures below zero can be represented by negative integers.
• Floors below ground level can be represented with negative numbers.
• Gains and losses can be represented with positive and negative values.
• Distances above and below a reference level can use signed numbers.

📋 Worked Examples

Example 1 – Compare

Which is greater, −3 or −8?

On the number line, −3 is to the right of −8. Therefore −3 > −8.

Example 2 – Addition

−4 + 7 = 3. Starting at −4 and moving 7 steps right reaches 3.

Example 3 – Subtraction

2 − 6 = −4. Starting at 2 and moving 6 steps left reaches −4.

Example 4 – Temperature

If the morning temperature is −2°C and it rises by 5°C, the new temperature is 3°C.

🧠 Integer Reasoning

1. Why is −2 greater than −7?
2. Why is zero neither positive nor negative?
3. Why are 6 and −6 called opposites?
4. How does a number line make integer addition easier to understand?
5. Can the sum of two negative integers be positive? Explain.

📝 Important Practice Questions

1. Write five positive and five negative integers.
2. Locate −4, 0 and 5 on a number line.
3. Write the opposite of 7, −9 and 0.
4. Compare −3 and −8.
5. Arrange −2, 5, −7, 0 and 3 in ascending order.
6. Find 4 + (−6).
7. Find −3 + 8.
8. Find 7 − 10.
9. Find 5 − (−4).
10. Give three real-life situations involving negative integers.

🔥 Competency / HOTS Questions

1. A temperature changes from −5°C to 4°C. By how many degrees did it rise?
2. A lift moves from floor −2 to floor 5. How many floors does it move upward?
3. A student says −10 is greater than −2 because 10 is greater than 2. Explain the mistake.
4. If a number and its opposite are added, what is the result? Explain.
5. Invent a real-life problem that can be represented by 3 − (−4), and solve it.

🧩 MCQ Practice

1. Which is an integer? A. 1/2 B. −4 C. 2.5 D. √2
2. Which is greater? A. −7 B. −3 C. −9 D. −12
3. The opposite of −8 is — A. −8 B. 0 C. 8 D. 16
4. Zero is — A. positive only B. negative only C. both positive and negative D. neither positive nor negative
5. −3 + 7 = — A. −10 B. −4 C. 4 D. 10
6. 5 − 8 = — A. −3 B. 3 C. 13 D. −13
7. 4 − (−2) = — A. 2 B. −2 C. 6 D. −6
8. On a number line, numbers increase when moving — A. left B. right C. randomly D. nowhere

Answer Key: 1-B, 2-B, 3-C, 4-D, 5-C, 6-A, 7-C, 8-B

📄 Printable Worksheet

1. Write all integers from −5 to 5.
2. Mark −6, −2, 0, 3 and 7 on a number line.
3. Write the opposites of 12, −4, 0 and 9.
4. Compare −5 and −1.
5. Arrange 4, −3, 0, −8 and 2 in ascending order.
6. Calculate −6 + 9.
7. Calculate 3 + (−8).
8. Calculate 4 − 9.
9. Calculate 6 − (−3).
10. Create a temperature problem involving negative integers and solve it.

🔁 Quick Revision Table

✅ Chapter Mastery Checklist

• ☐ I can identify integers.
• ☐ I can locate integers on a number line.
• ☐ I can identify opposites.
• ☐ I can compare and order integers.
• ☐ I can add and subtract integers.
• ☐ I can apply integers to real-life situations.
• ☐ I can explain my reasoning using a number line.

🔗 Complete Class 6 Mathematics

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