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Negative numbers are the first numbers most children meet that they cannot count on their fingers. A question like 4 − (−6) looks strange, and many students simply guess the sign. This post explains how NCERT's new Class 6 chapter on integers builds the idea, works through additions and subtractions with numbers, lists the sign slips to watch for and ends with a practice routine.
What does the Class 6 integers chapter cover?
Chapter 10 of Ganita Prakash, NCERT's Class 6 mathematics book (first edition August 2024, Reprint 2026-27), is called "The Other Side of Zero". It has five sections: Bela's Building of Fun, the token model, integers in other places, explorations with integers, and a pinch of history.
The chapter summary gives the key definitions:
The integers are …, −3, −2, −1, 0, 1, 2, 3, …
1, 2, 3, … are positive integers; −1, −2, −3, … are negative integers.
Zero is neither positive nor negative.
Every number has an additive inverse that adds to it to make zero. The inverse of 7 is −7.
The chapter teaches addition, subtraction and comparison of integers. Multiplication and division of integers come later; the Class 7 book has a chapter called "Operations with Integers" in Ganita Prakash Part 2.
How does the lift in Bela's building explain integers?
Bela's building has floors above ground (+1, +2, …) and below ground (−1, −2, …), with the ground floor as 0. Pressing "+" moves you up one floor and "−" moves you down one.
The book gives two ways to read addition:
Starting position + movement = target position. Start at −2 and go up 5: −2 + 5 = +3.
Movement 1 + movement 2 = total movement. Up 4 then down 6 is a total movement of −2.
Subtraction asks for the movement: target − start = movement. To go from floor −3 to floor +4 you move +4 − (−3) = +7 floors, which you can check by counting.
How does the token model work?
In the chapter's token model, a green token is +1 and a red token is −1. One of each makes a zero pair, worth 0.
Worked example 1 (from the book). The lift attendant's pocket has 5 positive and 3 negative tokens. Remove 3 zero pairs and 2 positive tokens are left, so (+5) + (−3) = +2.
Worked example 2 (from the book). (+5) + (−8): remove 5 zero pairs, and 3 negative tokens are left. So (+5) + (−8) = −3.
Worked example 3 (from the book). (+5) − (+6): put down 5 positives. You cannot take away 6 positives, so add one zero pair. That does not change the value. Now take away 6 positives, leaving 1 negative. So (+5) − (+6) = −1.
Worked example 4 (from the book). +4 − (−6): start with 4 positives. There are no negatives to take away, so add 6 zero pairs. Take away the 6 negatives, and 4 + 6 = 10 positives remain. So +4 − (−6) = +10.
Notice that taking away −6 gave the same answer as adding +6. The book states this as a rule: subtracting an integer is the same as adding its additive inverse.
Where else do integers appear?
The chapter uses credits and debits, heights above and below ground level, and temperatures above and below the freezing point of water.
Worked example 5 (temperature). At 6 a.m. it is −3°C in a hill town. By noon it has risen 8 degrees: −3 + 8 = +5°C. By midnight it falls 10 degrees from noon: 5 − 10 = −5°C.
Worked example 6 (money). A shop's account book shows a credit of ₹200 and a debit of ₹350. The balance is 200 − 350 = −150, which means the shop owes ₹150.
To compare integers, use the number line: smaller numbers sit to the left. So −7 < −2, even though 7 is bigger than 2.
Where do the rules come from?
The MacTutor History of Mathematics archive at the University of St Andrews records that Brahmagupta wrote the Brahmasphutasiddhanta in 628 and gave rules in terms of fortunes (positive numbers) and debts (negative numbers), such as "A debt subtracted from zero is a fortune." The NCERT chapter calls this the first general treatment of positive numbers, negative numbers and zero as equally valid numbers. It also notes that China's Nine Chapters on the Mathematical Art used red and black rods for positive and negative numbers, much like the tokens.
Why are negative numbers hard at first?
In a study of 61 first graders, Laura Bofferding (2014) found that children at first over-relied on whole-number principles when thinking about negative integers, though many developed correct mental models after instruction. Older students show the same habit when they decide −7 is bigger than −2. The cure is to keep checking with the number line or tokens until the rules feel natural.
Which mistakes cost the most marks?
Ordering by size of digits. −7 is less than −2.
Dropping a sign in subtraction. −3 − 5 is −8, not −2.
Wrong sign in mixed additions. For −5 + 3, subtract 3 from 5 and keep the sign of the larger: −2.
Calling zero positive. It is neither.
Skipping brackets. Write 4 − (−6), not 4 − −6, so you see the double sign.
How should you practise this week?
Day 1: Draw a number line from −10 to 10 and place ten temperatures on it.
Day 2: Use tokens (coins or paper squares in two colours) for eight additions.
Day 3: Do eight subtractions with tokens, including two like −2 − (−7).
Day 4: Rewrite every subtraction from Day 3 as adding the inverse and check the answers match.
Day 5: Write three real situations, such as floors or bank balances, and the integer sum for each.
If you want to see the rule behind a wrong answer, the Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer. The token model comes back in Class 7, when the book uses it to explain terms in arithmetic expressions.
Check today's weather for a cold city abroad, and work out how many degrees warmer your town is.
