Day 1: Integers (Positive and Negative Numbers) | Middle Stage | Crash Course

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Day 1: Integers (Positive and Negative Numbers) | Middle Stage | Crash Course

Day 1: The World Below Zero 🌡️

Middle Stage (Grades 6, 7 & 8) | Apex Institute of Maths and Sciences

🎯 1. Concept: Introduction to Integers

Welcome to the Middle Stage! Up until now, you’ve mostly dealt with whole numbers (0, 1, 2, 3…). But what happens when you subtract 5 from 3? You enter the world below zero!

Integers are a collection of numbers that include positive numbers, negative numbers, and zero. We represent them on a Number Line. Numbers to the right of zero are positive (+), and numbers to the left of zero are negative (-).

💡 2. Positive vs. Negative

Think of positive and negative numbers as exact opposites:

  • Moving: Walking 5 steps forward is +5. Walking 5 steps backward is -5.
  • Money: Earning ₹100 is +100. Spending or losing ₹100 is -100.
  • Temperature: Water boils at +100°C. Water freezes at 0°C. Ice cream is kept at -18°C.

Note: Zero (0) is neither positive nor negative. It is the center point!

🌍 3. Math in Our Daily Life

Integers aren’t just for math class; adults use them constantly!

Scenario 1 (Banking): When your parents deposit ₹5000 into the bank, the passbook shows it as a credit (+5000). When they withdraw ₹2000 from an ATM, it is recorded as a debit (-2000).

Scenario 2 (Geography): Mount Everest is 8,848 meters above sea level (+8848). The Mariana Trench is roughly 11,000 meters below sea level (-11000). Sea level itself represents exactly 0.

📝 4. Application Tasks

Grab your math journal and complete these tasks to solidify your understanding:

  • Task A: Draw a horizontal number line from -10 to +10. Mark the current temperature of your city on it.
  • Task B: The Elevator Challenge: If you start on the Ground Floor (0), go up 4 floors (+4), then go down 6 floors (-6), what floor are you on now? Write it as an integer.
  • Task C: Ask your parents to show you a bank statement (they can hide the total balance!). Identify three positive numbers (deposits) and three negative numbers (withdrawals).

✅ 5. Day 1 Practice Test

Test your knowledge of integers! Select the correct answers below and click submit to check your score and view the step-by-step solutions.

1. How would you write “A withdrawal of ₹500” as an integer?
Solution: Withdrawing means taking money out (decreasing your balance), which is represented by a negative sign (-500).
2. On a number line, where are negative integers located compared to zero?
Solution: As values decrease, they move to the Left on a standard horizontal number line.
3. Which of the following is true about the number zero (0)?
Solution: Zero is the origin point. It has no sign and is completely neutral.
4. Which integer is GREATER?
Solution: -2 is greater. Think of debt: owing someone ₹2 (-2) is better (greater financial position) than owing them ₹7 (-7).
5. What is the opposite of -15?
Solution: The opposite of a negative number is its positive counterpart. The opposite of -15 is +15.
6. A submarine is diving 100 meters below sea level. How is this depth written as an integer?
Solution: Sea level is 0. Going “below” means descending into negative numbers, so it is -100.
7. Arrange these integers in Ascending (smallest to largest) order: 4, -1, 0, -5
Solution: Look at the number line from left to right. -5 is the furthest left (smallest), then -1, then 0, and 4 is the largest.
8. If you are at -3 on the number line and move 4 spaces to the RIGHT, where do you land?
Solution: Moving right means adding. -3 + 4 = 1. (Count: -2, -1, 0, 1).
9. Which of these temperatures is the COLDEST?
Solution: The coldest temperature is the lowest value on the number line. -12 is further down than -5.
10. An airplane flies at 30,000 feet. What integer represents this?
Solution: The airplane is high “above” sea level, which represents a positive quantity (+30,000).
⚠️ Please answer all 10 questions before submitting!

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