This MCQ module is based on: Introducing Negative Numbers
TOPIC 37 OF 41
Introducing Negative Numbers
🎓 Class 6
Mathematics
CBSE
Theory
Ch 10 — The Other Side of Zero
⏱ ~30 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Introducing Negative Numbers
Targeting Class 6 level in Integers, with Basic difficulty.
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10.1 More and More Numbers!
We first met the counting numbers 1, 2, 3, 4, … . Later we met 0 — representing nothing, or an empty set. 0 was a major breakthrough: the Indian number system (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) is used worldwide today.
Then we met fractions — numbers like \(\tfrac{1}{2}\), \(\tfrac{3}{4}\), \(\tfrac{13}{5}\) — that fill in the spaces between whole numbers on a number line.
But are there numbers on the other side of zero — numbers less than 0? That is the question of this chapter.
The usual number line runs 0, 1, 2, 3, …. But what lies to the left of 0?
10.2 Everyday Uses of Numbers Below Zero
Negative numbers appear all around us:
Temperature
A thermometer in Shimla in winter might read −5°C — that is, 5 degrees below freezing (0°C). In Ladakh, winter temperatures can drop to −30°C.
Thermometer: positive temperatures above 0°C, negatives below.
Elevation (Sea Level)
Mount Everest stands at +8,848 m above sea level. The Dead Sea surface is at −430 m (430 m below sea level). Sea level itself is 0 m.
Money
If you have ₹500 in a bank account, that's +500. If you owe the bank ₹200 (overdraft), that's −200.
Building Floors
A shopping mall may label the entrance as Floor 0 (ground floor), the shop above as Floor 1, and the basement parking as Floor −1.
Definition
Negative numbers are numbers less than 0, written with a minus sign: −1, −2, −3, …. The number 0 is neither positive nor negative. Positive and negative whole numbers together with 0 are called integers?.10.3 The Token Model
A simple way to think about negative numbers is with tokens: yellow tokens are +1 each and red tokens are −1 each. One yellow and one red cancel out — together they equal 0. This is called a zero pair.
Yellow (+1) and red (−1) tokens cancel to make 0.
Example — Reading Token Piles
Pile A: 5 yellows + 2 reds → cancel 2 zero pairs → 3 yellows remain → value = +3.
Pile B: 2 yellows + 6 reds → cancel 2 zero pairs → 4 reds remain → value = −4.
Pile C: 3 yellows + 3 reds → 3 zero pairs → value = 0.
🔵 Try it: A pile has 7 yellow and 10 red tokens. What number does it represent? Cancel 7 pairs, 3 reds remain → −3.
Activity: Temperature Diary
L3 ApplyMaterials: Newspaper / weather app, notebook
Predict: In the week's data you will collect, will any city show a negative temperature?
- For 7 days, record the night-time minimum temperature of your own city and one Himalayan city (e.g. Shimla, Leh, Srinagar).
- Make a table with three columns: Date, Your city temp, Other city temp.
- Indicate each negative temperature with a minus sign.
- At the end of the week, find (a) the lowest temperature recorded, (b) the difference between the warmest and coldest days, (c) how many days were below 0°C.
In December–January, Leh and Srinagar often show −5°C to −20°C at night. The "difference between warmest and coldest" needs subtraction across zero — this prepares you for integer subtraction in the next part.
Figure it Out — Part A
Q1. Write these quantities using + and − signs:
(a) 200 m above sea level (b) loss of ₹150 (c) 7°C below freezing (d) deposit of ₹800 (e) 3 floors below ground.
(a) 200 m above sea level (b) loss of ₹150 (c) 7°C below freezing (d) deposit of ₹800 (e) 3 floors below ground.
(a) +200 m (b) −150 (c) −7°C (d) +800 (e) −3.
Q2. Express as a single integer:
(a) 6 yellows and 2 reds (b) 3 yellows and 3 reds (c) 1 yellow and 5 reds (d) 0 yellow and 4 reds.
(a) 6 yellows and 2 reds (b) 3 yellows and 3 reds (c) 1 yellow and 5 reds (d) 0 yellow and 4 reds.
(a) +4 (b) 0 (c) −4 (d) −4.
Q3. Suggest three more real-life situations where we use negative numbers.
Examples: golf scores below par (e.g. −4), change in stock price (−2%), depth of a submarine (−100 m), time before an event (T−10 seconds), weight loss, battery drain, elevator going down.
Historical Note
The first known systematic use of negative numbers was in the Chinese Nine Chapters on the Mathematical Art (~2nd century BCE), using black (negative) and red (positive) counting rods. In India, the great mathematician Brahmagupta (7th century CE) gave the first complete rules for arithmetic with negative numbers — what he called "debt" (rina) and "fortune" (dhana).Competency-Based Questions
Scenario: A city's weather record for one week shows the following minimum night temperatures (in °C): Mon +2, Tue −1, Wed −4, Thu −3, Fri 0, Sat +1, Sun −2.
Q1. On how many days was the temperature below 0°C?
L3 Apply4 days — Tue (−1), Wed (−4), Thu (−3), Sun (−2).
Q2. Order the week's temperatures from lowest to highest.
L4 Analyse−4 < −3 < −2 < −1 < 0 < +1 < +2. So: Wed, Thu, Sun, Tue, Fri, Sat, Mon.
Q3. A student claims, "Since −4 has a larger magnitude than +2, −4 is a bigger number than +2." Evaluate this claim.
L5 EvaluateThe claim is wrong. "Bigger" refers to position on the number line, not absolute value. On the number line, −4 lies to the left of +2, so −4 is smaller, not bigger. Colder night Wed (−4°C) is colder — not warmer — than Mon (+2°C).
Q4. Design a simple pictorial scheme using coloured tokens or arrows to record a week's daily temperatures so that both magnitude and sign are shown clearly.
L6 CreateOne design: A horizontal bar chart centred on 0. Bars going up coloured red (warm, positive); bars going down coloured blue (cold, negative). Length of bar = magnitude. Label each day. Alternatively, use red-hot and blue-cold tokens — one token per °C — above or below a central 0 line.
Assertion–Reason Questions
Assertion (A): 0 is neither a positive nor a negative number.
Reason (R): A positive number is greater than 0 and a negative number is less than 0.
Reason (R): A positive number is greater than 0 and a negative number is less than 0.
(a) 0 is not greater than 0 nor less than 0; by the definitions in R, it is neither positive nor negative.
Assertion (A): A pile of 5 yellow and 5 red tokens has value 0.
Reason (R): Yellow tokens and red tokens cancel each other in zero pairs.
Reason (R): Yellow tokens and red tokens cancel each other in zero pairs.
(a) 5 zero pairs = 0. The cancellation rule exactly explains the value.
Frequently Asked Questions
Why do we need negative numbers?
We need negative numbers to represent temperatures below zero, debts, losses, depths below sea level and directions opposite to a chosen positive direction.
What is the difference between 3 and -3?
3 and -3 are at equal distance from 0 on the number line but in opposite directions. They are called additive inverses or opposites of each other.
Is zero positive or negative?
Zero is neither positive nor negative. It is the boundary point that separates positive numbers from negative numbers on the number line.
What is an integer?
Integers include all whole numbers (0, 1, 2, 3, ...) and their negatives (-1, -2, -3, ...). Integers do NOT include fractions or decimals.
How are negative numbers written?
Negative numbers are written with a minus sign before the digit, such as -5, -12 or -100. The minus sign is part of the number, not a subtraction operation.
Where do we see negative numbers in daily life?
In winter weather forecasts (-2 C), lift buttons (B1, B2 for basements), bank statements (withdrawals), mountain altitudes and game scores.
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Mathematics Class 6 — Ganita Prakash
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